This composite shape is a rectangle with a semicircle attached on one end. The diameter of the semicircle is 6 feet. A rectangle with length 10 feet and width 6 feet. A semicircle with diameter 6 feet is on one side of the rectangle. What is the approximate area of this composite figure? Use 3. 14 for Pi and round to the nearest whole number. 46 feet squared

74 feet squared

88 feet squared

117 feet squared

Answers

Answer 1

The approximate area of the composite figure is 117 square feet.

To find the area of the composite figure, we need to calculate the sum of the areas of the rectangle and the semicircle.

1. The rectangle has a length of 10 feet and a width of 6 feet. The area of a rectangle is calculated by multiplying the length and width: Area of rectangle = length * width = 10 * 6 = 60 square feet.

2. The semicircle has a diameter of 6 feet. The radius of the semicircle is half of the diameter, which is 3 feet. The area of a semicircle is half the area of a full circle, so we need to calculate the area of a full circle and then divide it by 2: Area of semicircle = (π * radius^2) / 2 = (3.14 * 3^2) / 2 ≈ 14.13 square feet.

3. To find the approximate area of the composite figure, we add the area of the rectangle and the area of the semicircle: Approximate area = Area of rectangle + Area of semicircle = 60 + 14.13 ≈ 74.13 square feet.

4. Finally, we round the approximate area to the nearest whole number: Rounded area ≈ 74 square feet.

Therefore, the approximate area of the composite figure is 74 square feet.

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Related Questions

​$7000 principal earning ​7% compounded​ annually, 8 years

Answers

With a principal of $7000 earning a 7% annual interest rate compounded annually over 8 years, the total amount accumulated at the end of the period would be $11,595.76.

To calculate the total amount accumulated, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the principal (P) is $7000, the interest rate (r) is 7%, the interest is compounded annually (n = 1), and the number of years (t) is 8.

Using the formula, we have A = 7000(1 + 0.07/1)^(1*8) = 7000(1.07)^8 ≈ $11,595.76.

Therefore, at the end of 8 years, the total amount accumulated would be approximately $11,595.76.

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Shutterfly charges $20 to make a photo book with 15


pages. Each extra page costs $1. 65. The cost to ship the completed photo


book is $5. Write an expression to determine the total cost in dollars to


make and ship a photo book with x extra pages

Answers

The expression to determine the total cost in dollars to make and ship a photo book with x extra pages is: 25 + 1.65x.

To calculate the total cost of making and shipping a photo book with x extra pages, we need to consider the base cost, the cost of extra pages, and the shipping cost.

The base cost of making a photo book with 15 pages is $20.

Each additional page beyond the initial 15 pages incurs a cost of $1.65 per page.

Therefore, the cost of x extra pages would be 1.65x.

The shipping cost to ship the completed photo book is a fixed $5.

To calculate the total cost, we add the base cost, the cost of extra pages, and the shipping cost together:

Total Cost = Base Cost + Cost of Extra Pages + Shipping Cost

Total Cost = $20 + $1.65x + $5

Total Cost = $25 + $1.65x

Thus, the expression to determine the total cost in dollars to make and ship a photo book with x extra pages is 25 + 1.65x.

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3 of the students in Cole's grade have been on a radio show. 3 students have been in a choir, and 0 students have been both on a radio show and in a choir. How many students have been in a choir but not on a radio show?

Answers

3 students have been in a choir but not on a radio show.

In order to determine how many students have been in a choir but not on a radio show, we can use the Principle of Inclusion-Exclusion (PIE) to solve the problem.

The PIE formula is: n(A or B) = n(A) + n(B) - n(A and B)

Here, A represents the set of students who have been on a radio show, B represents the set of students who have been in a choir, and A and B represents the intersection of the two sets.

Using the information provided, we know that:

n(A) = 3 (3 students have been on a radio show)n(B) = 3 (3 students have been in a choir)n(A and B) = 0 (0 students have been both on a radio show and in a choir)

Therefore, using the PIE formula:

n(A or B) = n(A) + n(B) - n(A and B)n(A or B) = 3 + 3 - 0n(A or B) = 6

So, 6 students have either been on a radio show or in a choir. However, we want to find the number of students who have been in a choir but not on a radio show. To do this, we can subtract the number of students who have been in both from the total number of students who have been in a choir:

n(B but not A)

= n(B) - n(A and B)n(B but not A)

= 3 - 0n(B but not A)

= 3

Therefore, 3 students have been in a choir but not on a radio show.

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There are three paths through a triangular park. Each path connects the midpoint of one side to the opposite corner. The paths meet at point P, which is the centroid



Find PS and PC when SC = 24000 feet

Answers

PS and PC are both equal to 16000 feet when SC is 24000 feet. These lengths are determined based on the relationship between the centroid and the midpoints of the sides in a triangle.

In a triangular park, with point P as the centroid, if SC (one of the sides) is equal to 24000 feet, the lengths of PS and PC can be determined.

To find the lengths of PS and PC, we need to consider the properties of a centroid in a triangle. The centroid divides each median into two segments, with the ratio of 2:1.

In other words, the distance from the centroid to the midpoint of a side is two-thirds of the length of the entire median.

In this case, since SC is equal to 24000 feet, PS and PC can be calculated as follows:

PS = (2/3) * SC = (2/3) * 24000 = 16000 feet.

PC = (2/3) * SC = (2/3) * 24000 = 16000 feet.

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A school for learning foreign languages has 72 students who learn German, and 54 of those students also learn Russian. There are 12 students who do not learn German but learn Russian, and 10 students do not learn either German or Russian. Which table best shows the conditional relative frequency of rows for the data? Learn German Do not learn German Total Learn Russian 0. 82 0. 18 1 Do not learn Russian 0. 64 0. 36 1 Total 0. 77 0. 23 1 Learn German Do not learn German Total Learn Russian 0. 57 0. 13 1 Do not learn Russian 0. 19 0. 11 1 Total 0. 77 0. 23 1 Learn German Do not learn German Total Learn Russian 0. 75 0. 55 1 Do not learn Russian 0. 25 0. 45 1 Total 0. 77 0. 23 1 Learn German Do not learn German Total Learn Russian 0. 54 0. 12 1 Do not learn Russian 0. 18 0. 10 1 Total 0. 72 0. 22 1.

Answers

The table that best shows the conditional relative-frequency of rows for the data is the fourth option for A school for learning foreign languages has 72 students who learn German, and 54 of those students also learn Russian. There are 12 students who do not learn German but learn Russian, and 10 students do not learn either German or Russian using data-handling.

Given data, 72 students learn German

54 students learn Russian and German

12 students learn Russian but not German

10 students learn neither Russian nor German.

Therefore, The total number of students in the school is 72 + 10 = 82.

Let's fill the table:Learn German Do not learn German Total Learn Russian 54     12      66

Do not learn Russian 18    10     28

Total 72    22     82

Now, we can find the conditional relative frequency of rows as follows:

For students who learn Russian:0.82 = 66/81.00 = 1For students who do not learn Russian:0.64 = 18/28 0.36 = 10/28 1For students who learn German:0.54 = 54/1.00 = 1For students who do not learn German:0.12 = 12/28 0.88 = 22/28 1Thus, the fourth option shows the conditional relative frequency of rows for the given data.

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Laura opened a deposit account. In the first month, she made an initial deposit of $2500, and plans to contribute an additional $225 every month. The account does not pay any interest. After how many months will she have a total of $6,775?

Answers

It will take Laura 19 months to have a total of $6,775 in her deposit account.

To find the number of months it will take for Laura to have a total of $6,775 in her deposit account, we can set up an equation based on the given information.

Let's break down the steps:

1. Laura made an initial deposit of $2500.

2. She plans to contribute an additional $225 every month.

3. The account does not pay any interest.

4. We need to find the number of months it will take for her total balance to reach $6,775.

Let's denote the number of months as "n." In the first month, Laura's total balance is the initial deposit of $2500. For the following months, her total balance will increase by $225 each month.

We can set up the equation:

Total balance = Initial deposit + Monthly contributions

$6,775 = $2500 + ($225 * n)

Now, we can solve for "n" by rearranging the equation:

$6,775 - $2500 = $225n

$4,275 = $225n

Dividing both sides of the equation by $225:

n = $4,275 / $225

n = 19

Therefore, it will take Laura 19 months to have a total of $6,775 in her deposit account.

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How do you find the hight of the equation v=pi*r^2*h/3

Answers

The formula of height h = (3v) / (π * r^2)To find the height (h) of a cone given the volume (v) and the radius of the base (r), we can rearrange the equation v = (π * r^2 * h) / 3.

By multiplying both sides by 3 and dividing by π * r^2, we isolate the variable h and obtain the formula h = (3v) / (π * r^2). Substituting the appropriate values for volume and radius into this equation allows us to calculate the height of the cone.

To solve for the height (h) in the equation v = (π * r^2 * h) / 3, we first multiply both sides by 3 to eliminate the fraction. This results in the equation 3v = π * r^2 * h. Next, we isolate the variable h by dividing both sides of the equation by π * r^2, giving us the formula h = (3v) / (π * r^2). By substituting the known values for volume (v) and radius (r) into this equation, we can calculate the height (h) of the cone. It is important to ensure that the units for volume and radius are consistent and compatible to obtain the correct result.

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A number line going from negative 5 to positive 5. Which of the following statements is true when comparing numbers using a number line? The number closest to zero is always the least. The number farthest from zero is always the greatest. The number farthest right is always the least. The number left is always the least.

Answers

1: The number closest to zero is not always the least.

2: The number farthest from zero is not always the greatest.

3: The number farthest right is not always the least.

4: The number left is always the least.

The first statement, "The number closest to zero is always the least," is not necessarily true.

It depends on whether the numbers being compared are positive or negative.

For example, -2 is closer to zero than -4, but it is actually greater than -4.

The second statement, "The number farthest from zero is always the greatest," is also not necessarily true.

Just like the first statement, it depends on whether the numbers being compared are positive or negative.

For example, -5 is farther from zero than -3, but -3 is actually greater than -5.

The third statement, "The number farthest right is always the least," is definitely not true.

The direction of the number line (left or right) has nothing to do with whether a number is greater or lesser than another number.

That leaves us with the fourth statement, "The number left is always the least."

This statement is true! On a number line going from negative to positive numbers, the numbers to the left of zero (the negative numbers) are always less than the numbers to the right of zero (the positive numbers).

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A force of 80. Newtons pushes a 50. -kilogram object across a level floor for 8. 0 meters. The work done is

Answers

The work done is 400.0 Joules A force of 80 Newtons pushes a 50-kilogram object across a level floor for 8.0 meters.

To find the work done, we can use the formula:work = force x distance x cos(theta)where force is 80 N, distance is 8.0 m, and theta is the angle between the force and the displacement. Since the force is applied in the direction of motion, theta is 0° and cos(0°) is 1.

we can simplify the formula as:work = force x distance x cos(theta)work = 80 N x 8.0 m x cos(0°)work = 640.0 JHowever, we need to check the units of our answer to make sure they are in Joules (J). The units of force are Newtons (N), the units of distance are meters (m), and the units of cos(theta) are dimensionless. Therefore, our answer is in Joules (J).So, the work done is 640.0 Joules.

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A florist company makes regular and mini bouquets for sale.The florist has 100 bouquets and 60 peonies to use. Each regular bouquet has 6 roses and 2 peonies and each mini bouquet has 2 roses and 2 peonies. How many of each type of bouquet does the florist make?

Answers

Let x be the number of regular bouquets and y be the number of mini bouquets the florist makes.so the florist makes 5 regular bouquets and 15 mini bouquets

Then we can write the following system of equations based on the given information:

6x + 2y = 60

(since each regular bouquet has 6 roses and 2 peonies)

2x + 2y = 40

(since each mini bouquet has 2 roses and 2 peonies)We can use any method to solve this system of equations, but we will use the substitution method. We will solve the first equation for y in terms of x:y = 30 - 3xSubstitute this expression for y into the second equation and solve for

x:2x + 2(30 - 3x) = 402x + 60 - 6x = 40-4x = -20x = 5Substitute x = 5 into the expression we found for y:y = 30 - 3(5) = 15

Therefore, the florist makes 5 regular bouquets and 15 mini bouquets. Another method to solve the system of equations is by graphing: Graph the two equations on the same set of axes and find the intersection point. The x-coordinate of the intersection point will give us the number of regular bouquets, and the y-coordinate will give us the number of mini bouquets. We can see that the intersection point is (5, 15), which agrees with the solution we found using the substitution method.

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2 dot plots. The highlands have a mean rainfall of 15. 27 millimeters, and the Lowlands have a mean rainfall of 12. 05 millimeters. The dot plots show rainfall totals for several spring storms in highland areas and lowland areas. What is the mean rainfall for the highland storms? What is the mean rainfall for the lowland storms?.

Answers

The mean rainfall for the highland storms is 15.27 millimeters, and the mean rainfall for the lowland storms is 12.05 millimeters.

In the dot plots, each dot represents the rainfall total for a spring storm in either the highland or lowland areas. To find the mean rainfall, we calculate the average of all the rainfall values in each plot.

For the highland storms, the mean is 15.27 millimeters, which indicates that, on average, the rainfall for the spring storms in the highland areas is 15.27 millimeters.

For the lowland storms, the mean is 12.05 millimeters, suggesting that the average rainfall for the spring storms in the lowland areas is 12.05 millimeters.

These values provide a measure of the central tendency or average rainfall for the respective areas and can help in comparing the rainfall patterns between the highlands and lowlands.

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What is not equivalent to 5yA. Y+Y+Y+Y+YB. YxYxYxYxYC. Y(5)D. Y(1+1+1+1+1)

Answers

The expressions "5yA," "Y+Y+Y+Y+YB," "YxYxYxYxYC," and "Y(5)D" are not equivalent to "Y(1+1+1+1+1)." The latter expression represents the multiplication of "Y" by the sum of five "1"s, while the former expressions involve different operations or arrangements of "Y" and other characters.

The expression "5yA" does not have a clear meaning without additional context. It could be a combination of the number 5, the variable "y," and the letter "A," but it lacks an operation or defined relationship between these elements.

The expression "Y+Y+Y+Y+YB" represents the addition of five instances of "Y" and the letter "B." It does not involve multiplication or a sum of "1"s, making it different from "Y(1+1+1+1+1)."  

The expression "YxYxYxYxYC" suggests repeated multiplication of "Y" and "C." It does not involve the sum of "1"s, nor does it match the arrangement of elements in "Y(1+1+1+1+1)."

Lastly, "Y(5)D" represents the product of "Y" and "D" multiplied by 5. This expression does not include the sum of "1"s and has a different structure compared to "Y(1+1+1+1+1)."

In summary, the expressions "5yA," "Y+Y+Y+Y+YB," "YxYxYxYxYC," and "Y(5)D" are not equivalent to "Y(1+1+1+1+1)" as they involve different operations, arrangements, or elements altogether.

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B.



zoom in



Find the value of the variables for



which ABCD must be a parallelogram.



~ 3x



X



3



3y



3y



D



21



Required



X =



?/1



I



22



Required



y =



?/1

.



D

Answers

Given a quadrilateral ABCD, with the sides AB and DC parallel and equal in length. Let us denote angle BAD as ∠α and angle ADC as ∠β. Now, we have to find the values of the variables x and y such that ABCD is a parallelogram.

Parallelogram has a pair of parallel sides. So, we have AB ∥ CD. It is given that ∠α = ∠β and AB = CD. So, by angle-angle-side rule, the two triangles ABD and DCA are congruent.

In triangle ABD, we have:∠DAB = 180° - ∠α = 180° - ∠β (as ∠α = ∠β)⇒ ∠DAB + ∠CDA = 180° (linear pair of angles)⇒ ∠CDA = ∠β.In triangle DCA, we have:∠CDA = ∠β (as obtained above)⇒ ∠CAD = ∠α (as ∠α = ∠β)⇒ ∠BDC = 180° - ∠α = 180° - ∠β (linear pair of angles)⇒ ∠BDC = ∠DAB.In quadrilateral ABCD, the adjacent angles are supplementary. So, we have:∠BDC + ∠BCD = 180° (adjacent angles are supplementary)⇒ ∠DAB + ∠BCD = 180° (as ∠BDC = ∠DAB)⇒ ∠BCD = 180° - ∠DAB.In triangle ACD, we have:∠C = ∠C (common)⇒ ∠CAD + ∠BCD = 180° (angles of a triangle add up to 180°)⇒ ∠α + (180° - ∠DAB) = 180°⇒ ∠α + ∠β = 180°.

Now, we can solve for x and y.In triangle ABD, we have:AB = BD⇒ 3x = 21 - x⇒ 4x = 21⇒ x = 21/4.In triangle DCA, we have:CD = DA⇒ 3y = 22 - y⇒ 4y = 22⇒ y = 11/2. Therefore, the value of x is 21/4 and the value of y is 11/2.

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1: name a plane parallel to plane WXT
2: name 2 segments parallel to VU
3: name 2 segments parallel to SW
4: name 2 segements skew to XY
5: name 2 segments skew to VZ​

Answers

1. One of the planes parallel to plane WXT is the plane WXY.2. Two segments parallel to VU are AB and CD.3. Two segments parallel to SW are PQ and RS.4. Two segments skew to XY are QR and PS.5.

Two segments skew to VZ are RT and PU.A plane parallel to plane WXT:Consider the following figure below: Here, WX is parallel to YZ. Now, any plane which passes through any of the point, say X and Y, which lie on the line WX and YZ respectively, will be parallel to plane WXT. One of such plane is plane WXY.

Two segments parallel to VU:Segments AB and CD are parallel to VU in the following figure below:Two segments parallel to SW:Segments PQ and RS are parallel to SW in the following figure below:Two segments skew to XY:Segments QR and PS are skew to XY in the following figure below:Two segments skew to VZ:Segments RT and PU are skew to VZ in the following figure below:

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Jen traveled from Boston to Cape Cod at 60mph. On her way back, there was a lot of traffic, so her return trip took 3 times as long. What was Jen's average speed?

Please answer

Answers

Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

To determine Jen's average speed for the entire round trip, we need to calculate the total distance traveled and the total time taken.

Let's assume the distance between Boston and Cape Cod is "d" miles.

For the outbound trip from Boston to Cape Cod, Jen traveled at a speed of 60 mph. The time taken for this leg of the trip is given by:

Time = Distance / Speed

Time = d / 60

For the return trip, it took Jen 3 times longer due to heavy traffic. Therefore, the time taken for the return trip is 3 times the time taken for the outbound trip:

Time for return trip = 3 * (d / 60) = (3d) / 60

The total time for the round trip is the sum of the outbound and return trip times:

Total Time = d / 60 + (3d) / 60 = (d + 3d) / 60 = 4d / 60 = d / 15

The total distance for the round trip is twice the distance from Boston to Cape Cod:

Total Distance = 2d

Now, we can calculate Jen's average speed by dividing the total distance by the total time:

Average Speed = Total Distance / Total Time

Average Speed = 2d / (d / 15)

Average Speed = 2 * 15

Average Speed = 30 mph

Therefore, Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

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What number should be added to (-5)/8 so as to get 5/9

Answers

Therefore, the value that needs to be added to (-5)/8 in order to get 5/9 is -5/72.

To get 5/9, what number should be added to (-5)/8?

We can begin the solution by adding "x" to (-5)/8. Then, we will have:((-5)/8) + x = 5/9

The next step is to isolate the variable x, which is accomplished by subtracting (-5)/8 from both sides. The equation becomes:(-5/8) + (5/9) = x

We'll need to find a common denominator for this expression:

((-45)/72) + (40/72) = xSimplifying, we get:

((-45) + 40)/72 = x(-5)/72 = x

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Please fill in the blank(5x)2 = _ x2the twos are cubes

Answers

The expression (5x)² is equal to ___ x², where the twos are cubes.

To simplify the expression (5x)², we need to apply the exponent rules. Since the twos are cubes, we need to cube both the base and the exponent.

(5x)² can be rewritten as (5x)³³. Applying the exponent rule for a power of a product, we raise each factor inside the parentheses to the third power:

(5x)³³ = (5)³(x)³ = 125x³.

Therefore, the expression (5x)² is equal to 125x³, where the twos are cubes.

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My earn 7 per hour mowing that her neighbors lawns she also earned $14 for hauling away bags of recyclable for neighbors

Answers

my friend earned a total of $21 by mowing neighbors' lawns and hauling away bags of recyclables.

To calculate the total amount earned by my friend, we need to find the sum of the earnings from mowing lawns and hauling away recyclables.

Given:

Earnings per hour for mowing lawns: $7

Earnings for hauling away recyclables: $14

To calculate the total earnings, we can add the two amounts together:

Total earnings = Earnings from mowing lawns + Earnings from hauling recyclables

Total earnings = $7 + $14

Total earnings = $21

Therefore, my friend earned a total of $21 by mowing neighbors' lawns and hauling away bags of recyclables.

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Question: When mowing her neighbors' lawns, Sarah earns $7 per hour. Additionally, she earned $14 for hauling away bags of recyclables for her neighbors. Please provide the missing information to complete this question.

Answer choices:

a) Number of hours Sarah spent mowing

b) Total amount earned by Sarah for mowing

c) Number of bags of recyclables hauled by Sarah

d) Total amount earned by Sarah for both mowing and hauling recyclables

The pair of points (7,4) and (3,y) lie on the same line with a slope of 1/4 , what is the value of y?


- CAN SOMEONE PLEASE HELP I NEED THE ANSWER NOW.

Answers

The value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

The value of y can be determined by using the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, we have the points (7, 4) and (3, y), with a slope of 1/4. Plugging in the values, we get (y - 4) / (3 - 7) = 1/4. Simplifying this equation, we have (y - 4) / (-4) = 1/4. Cross-multiplying, we get -4(y - 4) = 1(-4), which simplifies to -4y + 16 = -4. Solving for y, we subtract 16 from both sides, giving us -4y = -20. Dividing by -4, we find y = 5.

To summarize, the value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

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Analyze the function algebraically

f(x) = -4xsquared plus 32x minus 48

Answers

The function f(x) = -4x^2 + 32x - 48 is a quadratic function.

To analyze the function algebraically, we can look at its key characteristics:

Quadratic term: The term -4x^2 indicates that the function is a quadratic function.

Coefficients: The coefficient of the quadratic term is -4, the coefficient of the linear term is 32, and the constant term is -48.

Vertex: The vertex of the quadratic function can be found using the formula x = -b/(2a). In this case, the vertex is located at x = -32/(2*(-4)) = 4. Substitute this value back into the function to find the y-coordinate of the vertex: f(4) = -4(4)^2 + 32(4) - 48 = 0. Hence, the vertex is (4, 0).

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Consider the field above. It has 5 sides. The total perimeter is LaTeX: 16x^2+21x+1616 x 2 + 21 x + 16. The lengths of the four shortest sides are LaTeX: 3x+8,\:2x^2+4x,\:2x^2+2x,\:and\:5x^2+3x+23 x + 8 , 2 x 2 + 4 x , 2 x 2 + 2 x , a n d 5 x 2 + 3 x + 2. Find the length of the longest side.

Answers

The answer is "The length of the longest side is 6x² - 12x + 16. Here, the total perimeter is given as LaTeX: 16x² + 21x + 16.

As there are five sides, we can express the total perimeter as the sum of all the five sides. Let the length of the longest side be 'l'.

So, the total perimeter is equal to the sum of all five sides, which can be expressed as:  

3x + 8 + 2x² + 4x + 2x² + 2x + 5x² + 3x + 2 + l16x + 21x + 16

= 10x + 9x + l.                                                                                        

Now, we can find the length of the longest side by simplifying the above equation and solving for 'l'.

16x² + 21x + 16 = 10x² + 9x + l

l = 6x² - 12x + 16

Therefore, the length of the longest side is 6x² - 12x + 16.

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The expression (y to the power of 20)(y to the power of −5)2i s equivalent to yn. What is the value of n?20010-20030

Answers

the value of n remains indeterminate in this case.To find the value of n in the expression (y^20)(y^-5)^2i equivalent to yn, we can simplify the expression first.

Starting with (y^20)(y^-5)^2i, we can simplify the exponent by multiplying the exponents of y:
(y^20)(y^-5)^2i = y^(20 + (-5 * 2))i = y^(20 + (-10))i = y^10i.

Now, we can equate this simplified expression to yn:
y^10i = yn.

To find the value of n, we can compare the exponents:
10i = n.

Since the imaginary unit i represents the square root of -1, and the exponent in this case is not purely real, we cannot find a specific value for n. Therefore, the value of n remains indeterminate in this case.

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An algebra tile configuration. There are 3 large tiles, 5 tiles each half the size of a large tile, and 8 tiles each one-quarter the size of a large tile. Two of the large tiles are labeled plus x squared and 1 is labeled negative x square. Two smaller tiles are labeled plus x and 3 are labeled negative x. Six of the smallest tiles are labeled + and 2 are labeled minus.

Which polynomial is represented by the algebra tiles?

Answers

The polynomial represented by the algebra tiles is: x - 4

Given algebra tile configuration:

3 large tiles, 5 tiles each half the size of a large tile, and 8 tiles each one-quarter the size of a large tile.

Two of the large tiles are labeled plus x squared and 1 is labeled negative x square. Two smaller tiles are labeled plus x and 3 are labeled negative x. Six of the smallest tiles are labeled + and 2 are labeled minus.

In order to find the polynomial represented by the algebra tiles, let us consider the number of positive and negative tiles.

Polynomials represented by the algebra tiles:

There are 2 large tiles labeled as x² and a single large tile labeled as -x²

Hence, the net contribution from these 3 large tiles is equal to

+ x² + (-x²) = 0

Now, let's look at the smaller tiles, there are two tiles labeled +x and three tiles labeled -x.

Therefore, the net contribution from these tiles is equal to

2x + (-3x) = -x

Similarly, six smallest tiles are labeled as positive and two are labeled as negative, thus the net contribution from the smallest tiles is equal to 6 - 2 = 4

Hence, the polynomial represented by the algebra tiles is:

x - 4

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At Lyft drivers charge $2.7 per mile driven and a booking fee of $2.5 when a customer rides with them. At Uber drivers charge $2.5 per mile and a $3.7 booking fee. After how many miles do the two services cost the same?

Answers

After 6 miles, the cost of using Lyft and Uber becomes the same. To find the number of miles at which the cost of using Lyft and Uber becomes the same, we can set up an equation based on the given information.

This is a problem based on solving equation with one variable. Let's denote the number of miles as "x". The cost of using Lyft can be expressed as:

Cost of Lyft = 2.7x + 2.5

The cost of using Uber can be expressed as:

Cost of Uber = 2.5x + 3.7

To find the number of miles at which the costs are equal, we can set the two equations equal to each other and solve for x:

2.7x + 2.5 = 2.5x + 3.7

Simplifying the equation:

0.2x = 1.2

x = 1.2 / 0.2

x = 6

Therefore, after 6 miles, the cost of using Lyft and Uber becomes the same.

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If it takes 3\2 of an hour to paint 2\5 of a room how long would it take to paint one room

Answers

It would take 15/4 or 3.75 hours to paint one full room.

If it takes 3/2 of an hour to paint 2/5 of a room, we can use proportions to find how long it would take to paint one full room. Let's represent the time it takes to paint one full room as x.

Then we have the following proportion:

2/5 room : 3/2 hour = 1 room : x

To solve for x, we can cross-multiply: (2/5) * x = (3/2) * 1

Simplifying the right side gives:(2/5) * x = 3/2

Multiplying both sides by the reciprocal of 2/5 gives us:x = (3/2) / (2/5)

Multiplying by the reciprocal is the same as dividing, so we have:x = (3/2) * (5/2)

Simplifying gives:x = 15/4

Therefore, it would take 15/4 or 3.75 hours to paint one full room.

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A television offer advertised a set of knives for $20 down and $5 a month for 6 months. What is the total cost of the knives?

Answers

Therefore, the total cost of the knives is $50.

Arithmetic is the fundamental of mathematics that includes the operations of numbers. These operations are addition, subtraction, multiplication and division. Arithmetic is one of the important branches of mathematics, that lays the foundation of the subject 'Maths', for students.

The total cost of the knives is $50.

What is being offered in the television ad?

A set of knives is being offered in the television ad. The knives are being sold for $20 down and $5 a month for six months.How to determine the total cost of the knives?To calculate the total cost of the knives, we will use the formula:

Total cost = Down payment + Monthly payment × Number of monthsTotal cost

= $20 + $5 × 6 = $20 + $30

= $50

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The area of a rectangle is 384 square inches and length is 8 inches greater than width. What are the dimensions

Answers

The dimensions of the rectangle are 16 inches in width and 24 inches in length.

Let's assume the width of the rectangle is x inches. According to the problem, the length is 8 inches greater than the width, so the length can be represented as (x + 8) inches.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 384 square inches. So, we can set up the equation:

Length * Width = Area

(x + 8) * x = 384

Expanding the equation:

x^2 + 8x = 384

Rearranging the equation to solve for x:

x^2 + 8x - 384 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring it, we find:

(x - 16)(x + 24) = 0

So, x = 16 or x = -24.

Since dimensions cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 16 inches.

Substituting this value back into the equation for the length:

Length = x + 8 = 16 + 8 = 24 inches

Hence, the dimensions of the rectangle are 16 inches in width and 24 inches in length, which gives an area of 384 square inches.

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Two number cubes, each with faces labeled 1 through 12, are rolled at the same time.
Enter the probability that both number cubes land with the number 11 facing up in one roll.

Answers

Based on the information, the probability is 1/144, or approximately 0.0069.

How to calculate the probability

Each number cube has 12 possible outcomes, as there are 12 faces labeled from 1 to 12.

The probability of rolling an 11 on one number cube is 1 out of 12, as there is only one face labeled 11 out of the 12 possible outcomes.

Since the two number cubes are rolled simultaneously, the total number of possible outcomes is the product of the possible outcomes for each cube, which is 12 * 12 = 144.

The number of favorable outcomes, in this case, is 1, as both number cubes need to show 11.

Therefore, the probability that both number cubes land with the number 11 facing up in one roll is:

Number of favorable outcomes / Total number of possible outcomes

= 1 / 144

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A cash withdrawal of R5 000. 00 was made at Signet Blue on the
20/05/2019. Calculate what percentage the withdrawal fee is of the
transaction amount. Calculate the percentage of R5000. 00​

Answers

The withdrawal fee of R100.00 is 2% of the transaction amount of R5,000.00.

To calculate the percentage that the withdrawal fee is of the transaction amount, we need to determine the fee amount and then express it as a percentage of the transaction amount.

Let's assume that the withdrawal fee is 2% of the transaction amount. To calculate the fee amount, we multiply the transaction amount by the fee percentage:

Fee Amount = 2% of R5,000.00

= 0.02 * R5,000.00

= R100.00

Therefore, the withdrawal fee is R100.00.

To calculate the percentage of R5000.00, we can divide the fee amount by the transaction amount and then multiply by 100 to express it as a percentage:

Percentage = (Fee Amount / Transaction Amount) * 100

= (R100.00 / R5000.00) * 100

= 2%

Hence, the withdrawal fee of R100.00 is 2% of the transaction amount of R5,000.00.

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What is the coefficient for m in the equation, d = 9m + 12

Answers

the coefficient is 9

The coefficient is:

⇨ 9

Work/explanation:

To find the coefficient of m, we will take a look at the number that comes in front of m.

That number is 9. Hence, that's the coefficient.

Extra info

The variables are d and mThe constant is 12

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