the distance from City A to City C is approximately 346 km.
To find the distance from City A to City C, we can use the Law of Cosines, which states that[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex], where c is the side opposite to angle C, and a and b are the lengths of the other two sides.
Given that City A is 300 km due east of City B, and City C is 200 km on a bearing of 123 degrees from City B, we have two sides and the included angle. The side opposite to angle C is the distance we want to find.
Using the Law of Cosines, we have:[tex]c^2 = 300^2 + 200^2 - 2 * 300 * 200 cos(123).[/tex]
Evaluating the expression, we get: c^2 ≈ 120,200.
Taking the square root of both sides, we find: c ≈ √120,200 ≈ 346 km.
Therefore, the distance from City A to City C is approximately 346 km.
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John flipped a coin 9 times and recorded 5 heads. What is the ratio of heads to tails John recorded?
John recorded 5 heads and flipped a coin 9 times. The ratio of heads to tails recorded by John is 5:4.
John flipped a coin 9 times and recorded 5 heads. To determine the ratio of heads to tails, we need to compare the number of heads to the number of tails. Since John recorded 5 heads, the remaining flips would be tails.
Therefore, the number of tails recorded would be 9 - 5 = 4. The ratio of heads to tails recorded by John is thus 5:4, which means for every 5 heads, there were 4 tails. This ratio represents the relative frequency of heads and tails in John's coin flips.
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a blueprint of a house is drawn using a scale of 1/4 in = 3ft. If the bedroom of the actual house is 16 by 12 in, what are the dimensions of the bedroom of the blueprint
The dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.
To find the dimensions of the bedroom in the blueprint, we can use the given scale of 1/4 in = 3 ft.
First, let's convert the dimensions of the actual bedroom into feet:
Length of the actual bedroom = 16 in * (1 ft / 12 in) = 16/12 ft = 4/3 ft
Width of the actual bedroom = 12 in * (1 ft / 12 in) = 12/12 ft = 1 ft
Now, let's use the scale to find the dimensions of the bedroom in the blueprint:
Length of the bedroom in the blueprint = Length of the actual bedroom * Scale
Length of the bedroom in the blueprint = (4/3 ft) * (1/4 in / 3 ft)
Length of the bedroom in the blueprint = 4/3 * 1/12
Length of the bedroom in the blueprint = 4/36
Length of the bedroom in the blueprint = 1/9 ft
Width of the bedroom in the blueprint = Width of the actual bedroom * Scale
Width of the bedroom in the blueprint = (1 ft) * (1/4 in / 3 ft)
Width of the bedroom in the blueprint = 1 * 1/12
Width of the bedroom in the blueprint = 1/12 ft
Therefore, the dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.
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Convert. If necessary, round to the nearest tenth.
(Recall: 1 gal. = 3.79 L.)
Igal. x 20 L.
a. 10.5
b. 5.8
C.
10.1
d.
5.3
Therefore, the answer rounding to the nearest tenth is d. 5.3.
To convert 1 gallon to liters, we multiply by the conversion factor of 3.79 L/gal.
1 gal. * 3.79 L/gal = 3.79 L
Now, to find the equivalent of 20 liters, we can set up a proportion:
1 gal / 3.79 L = x gal / 20 L
Cross-multiplying and solving for x, we get:
x = (1 gal / 3.79 L) * 20 L = 20 / 3.79 gal
Rounding to the nearest tenth, we have:
x ≈ 5.3
Therefore, the answer is d. 5.3.
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Give the equations of the asymptotic of f(x),g(x) and h(x)
The equation of the asymptote for function f(x) is y = 0.
The equation of the asymptote for function g(x) is x = a, where a is a constant.
The equation of the asymptote for function h(x) is y = mx + b, where m and b are constants.
For function f(x), the asymptote is y = 0 since the function approaches zero as x approaches positive or negative infinity.
For function g(x), the asymptote is a vertical line at x = a. This occurs when the function approaches a specific x-value but does not cross it.
For function h(x), the asymptote is a straight line represented by y = mx + b. This occurs when the function approaches a linear relationship as x approaches positive or negative infinity. The values of m and b depend on the slope and y-intercept of the asymptote, respectively.
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For the circle: (x+3)^2 + (y-4)^2 = 100, find the length of the diameter
The length of the diameter of the circle in this problem is given as follows:
20 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for this problem is given as follows:
(x + 3)² + (y - 4)² = 100.
Hence the measure of the radius is given as follows:
r = 10 units.
The diameter has a measure which is twice the radius, hence:
d = 2 x 10
d = 20 units.
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Rita has two lengths of rope that are 9 feet and 1 foot long. Jeremy says there is only one possible additional rope length Rita can get to form a
triangle, Rita disagrees.
Who do you agree with? Explain your reasoning.
I agree with Rita. Jeremy is incorrect in claiming that there is only one possible additional rope length for Rita to form a triangle.
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, Rita has two rope lengths of 9 feet and 1 foot. For a triangle to be formed, the sum of the two shorter sides must be greater than the longest side. However, in this case, 1 foot + 9 feet is greater than 9 feet, which satisfies the triangle inequality. Therefore, Rita can form a triangle with these two rope lengths.
Rita's disagreement is valid as there are multiple possible additional rope lengths she can obtain to form a triangle, not just one.
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Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth ₹140₹140₹, 140 each and a shuttlecock worth ₹80₹80₹, 80. He wants to have a profit of 25\%25%25, percent?
The selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
To determine the selling price for Calvin's badminton kit, including a desired profit of 25%, we need to calculate the cost price and add the profit margin.
The cost price of the badminton kit consists of two rackets worth ₹140 each and a shuttlecock worth ₹80. Let's calculate the total cost price:
Cost Price = (2 * ₹140) + ₹80 = ₹280 + ₹80 = ₹360
To find the selling price with a 25% profit margin, we need to add 25% of the cost price to the cost price:
Profit = 25% of ₹360 = (25/100) * ₹360 = ₹90
Selling Price = Cost Price + Profit = ₹360 + ₹90 = ₹450
Therefore, the selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
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Brandon is running errands for his mother. It is 1 4 mile from his house to the library and 2 3 mile from the library to the grocery store. Brandon claims that he walks a total of 11 12 mile if he goes from his house to the library to the grocery store. Which of the following shows whether Brandon is correct and why? A. Yes; the correct distance is 11 12 mile, because 1 4 2 3 = 3 12 8 12 = 11 12. B. No; the correct distance is 10 12 mile, because 1 4 2 3 = 4 12 6 12 = 10 12. C. No; the correct distance is 1 mile, because 1 4 2 3 = 4 12 8 12 = 12 12 = 1. D. No; the correct distance is 1 1 12 miles, because 1 4 2 3 = 4 12 9 12 = 13 12 = 1 1 12.
The correct answer is D. No; the correct distance is 1 1/12 miles, because 1/4 + 2/3 = 4/12 + 8/12 = 12/12 = 1 1/12.
To solve this problem, we first need to convert the mixed numbers to fractions. 1 4 = 4 12 and 2 3 = 8 12. Then, we can add the fractions together. 4 12 + 8 12 = 12 12 = 1 1 12.
Therefore, Brandon is incorrect. He walks a total of 1 1/12 miles, not 11 1/2 miles.
12. Zoë had 3 times as much money as her
3
brother. She spent of her money on a
new CD player. Now how many times as
much money as her brother does Zoë have?
Zoë has 2 times as much money as her brother now. Answer: Zoë has twice as much money as her brother.
Let's find out how much money Zoë had to begin with if she spent 1/3 of her money on a new CD player.Suppose Zoë's brother had $x. Since Zoë had 3 times as much money as her brother, she had $3x to begin with.She spent 1/3 of her money on a new CD player.1/3 of $3x = $xZoë now has $2x remaining after buying the CD player.Since $2x is twice the amount of money her brother has ($x), Zoë has twice as much money as her brother after buying the CD player.
Therefore, Zoë has 2 times as much money as her brother now. Answer: Zoë has twice as much money as her brother.
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At sea level, the air presses down on our bodies at 14.7
pounds per square inch (psi). When diving in the ocean,
the pressure increases. The equation y = 0.445x + 14.7,
where x is the number of feet a diver descends, represents
this situation.
a. Explain using the definition how you know the
relationship represented by the equation is a function.
We can conclude that the relationship represented by the given equation is a function. Moreover, the pressure increases as the diver descends below sea level, which is shown by the positive slope (0.445) of the equation.
The equation y = 0.445x + 14.7 represents a situation where a diver descends below sea level. This equation gives the pressure (y) of the water at a depth of x feet below sea level. Here, y is dependent on x. It means that the pressure at a given depth is dependent on that particular depth. Therefore, we can say that the given equation represents a function because for each value of x, there is only one corresponding value of y.
A function is defined as a relation that maps each input value (x) to exactly one output value (y). In other words, it is a set of ordered pairs (x, y), where each value of x is paired with a unique value of y. The equation given above satisfies this definition of a function because it represents a one-to-one relationship between the depth (x) and the pressure (y) of the water.
Therefore, we can conclude that the relationship represented by the given equation is a function. Moreover, the pressure increases as the diver descends below sea level, which is shown by the positive slope (0.445) of the equation.
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In preparation for the homecoming football game, members of the student body are painting the school rock. If Angela works alone, it will take
her 5 and one-half hours. If Brandon works alone it will take him 7 hours. If they work together, approximately how long will it take?
4
3
6. 25
125
When working together, it will take Angela and Brandon about 3 hours and 12 minutes to paint the school rock.
The answer is 3
Let's first assume that Angela can paint the school rock in x hours, then Brandon would be able to paint the school rock in y hours.Angela’s work rate: \frac{1}{x} of the rock per hour .
So, Angela’s work rate = [tex]$\frac{1}{5.5}$[/tex]and Brandon’s work rate = \frac{1}{7} Working together, Angela and Brandon’s work rate will be: \frac{1}{5.5} + \frac{1}{7} of the rock per hour [tex]$\frac{1}{5.5} + \frac{1}{7}$ = $\frac{0.1818 + 0.1429}{1}$ = $\frac{0.3247}{1}$[/tex] Working together, they will paint the rock in \frac{1}{0.3247} hours = 3.08 hours. Rounding off to the nearest minute, it will take them about 3 hours and 12 minutes .
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Jessie tried to solve an equation step by step. 1. 5b+9=111. 5b=3Step 1b=2Step 2\qquad\begin{aligned} 1. 5b+9&=11\\\\ \\ 1. 5b&=3&\green{\text{Step } 1}\\\\ \\ b&=2&\blue{\text{Step } 2}\\\\ \end{aligned}1. 5b+91. 5bb=11=3=2Step 1Step 2Find Jessie's mistake. Choose 1 answer:Choose 1 answer:(Choice A)AStep 1\green{\text{Step }1}Step 1start color #28ae7b, start text, S, t, e, p, space, end text, 1, end color #28ae7b(Choice B)BStep 2\blue{\text{Step }2}Step 2start color #6495ed, start text, S, t, e, p, space, end text, 2, end color #6495ed(Choice C)CJessie did not make a mistake
Jessie made a mistake in Step 1 of solving the equation. The correct equation should be 5b + 9 = 111 instead of 5b + 9 = 11.
In Step 1, Jessie mistakenly wrote the right-hand side of the equation as 11 instead of 111. The correct equation should be 5b + 9 = 111, not 5b + 9 = 11. This error occurred in the process of trying to isolate the variable b by subtracting 9 from both sides of the equation.
Step 2, where Jessie obtained 5b = 3, is correct. However, the mistake in Step 1 led to an incorrect starting point, which affected the subsequent steps.
Therefore, the correct answer is Choice A: Jessie made a mistake in Step 1.
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If a manufacturing company uses a single, weight-losing raw material to manufacture its finished product, then most likely the company will:_________.
i. Choose to outsource its labor component.
ii. Locate its manufacturing plant at the raw material site.
iii. Locate several manufacturing plants close to consumers.
iv. Use a ubiquitous raw material.
v. Agglomerate close to similar factories
Option B : Locate its manufacturing plant at the raw material site.
Given,
Weight losing raw material to manufacture its finished products .
Here,
Weight loss raw materials are those which loses their weight while production sugar, iron and steel, and aluminum that lose weight during production.
For example we can take the industries that require minerals for their production works .
Another example is of sugar industry which require weight losing raw material .
Thus the correct option will be B .
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A hiker whose eye level is 2m above the ground wants to find the heigh of a tree. He places a mirror horizontally on the ground 20m from the base of the tree, and find that if he stands at a point c, which is 4m from the mirror b, he can see the reflection of the top of the tree. How tall is the tree
The height of the tree is 12 meters.
To solve this problem, we can use similar triangles.
Let's denote the height of the tree as 'h'.
We have a right triangle formed by the hiker's line of sight, the mirror, and the reflected image of the top of the tree.
The vertical leg of this triangle is 'h', and the horizontal leg is the sum of the distance between the mirror and the base of the tree (20m) and the distance between the mirror and the hiker (4m).
So the horizontal leg is 20m + 4m = 24m.
Now, we can set up the proportion between the similar triangles:
(hiker's eye level)/(horizontal leg) = (reflected image height)/(vertical leg)
Plugging in the given values:
2 / 24 = 1 / h
Cross-multiplying:
2h = 24
Dividing both sides by 2:
h = 24 / 2
h = 12
Therefore, the height of the tree is 12 meters.
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There are 640 acres in a square mile, and 5280 feet in 1. 00 mile. What is the length in feet (to the nearest foot) of the side of a square having an area of 1. 00 acre?
The side lengt of the square is approximately 1839 feet.
How to find the side length?To find the length in feet of the side of a square with an area of 1.00 acre, we need to convert the acreage to square feet.
Given:
1 acre = 640 acres/mile² (640 acres in a square mile)
1 mile = 5280 feet (conversion factor from miles to feet)
To convert acres to square feet, we can multiply by the conversion factor:
1 acre = 640 acres/mile² * 1 mile² * 5280 feet
Simplifying the units:
1 acre = 640 * 5280 square feet
Now, to find the length of the side of the square, we can take the square root of the area:
Side length = √(1 acre * 640 * 5280 square feet)
Calculating:
Side length ≈ √(1 * 640 * 5280) ≈ √3379200 ≈ 1839.29 feet
Rounding to the nearest foot, the length of the side of the square with an area of 1.00 acre is approximately 1839 feet.
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Find the volume of a right circular cone that that that has a height of 13.8ft and a base with a radius of 7.8ft
The volume of the right circular cone with a height of 13.8ft and a base radius of 7.8ft is approximately 672.59 cubic feet.
1. The formula for the volume of a right circular cone is V = (1/3)πr²h, where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
2. Plug in the given values into the formula: V = (1/3)π(7.8ft)²(13.8ft).
3. Calculate the volume: V = (1/3)π(60.84ft²)(13.8ft).
4. Simplify the expression: V ≈ 7.484π(13.8ft).
5. Use the approximation π ≈ 3.14159: V ≈ 7.484(3.14159)(13.8ft).
6. Calculate the volume: V ≈ 293.48ft³.
7. Round the result to two decimal places: V ≈ 672.59 cubic feet.
Therefore, the volume of the given right circular cone is approximately 672.59 cubic feet.
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the scale on a map is stated as 1 : 250000to villages are 9 cm apart on the maphow far from each other are the two villages in kilometres
The two villages are approximately 225 kilometers apart.
The scale on the map is given as 1:250000, which means that 1 unit on the map represents 250,000 units in reality.
If the distance between the villages on the map is 9 cm, we can set up the following proportion:
1 cm / 250,000 km = 9 cm / x km
Cross-multiplying, we have:
1 * x km = 9 cm * 250,000 km
x km = 2,250,000 km / 1 cm
Simplifying the expression, we find:
x km = 225 km
Therefore, the two villages are approximately 225 kilometers apart.
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Luis created a spreadsheet of his expenses for three months. Which of Luis's expenses are variable expenses?
Expenses
rent
utility bill
car loan payment
insurance payment
Jan Feb Mar
$1,250. 00 $1,250. 00 $1,250. 00
$124. 11 $108. 72
$121. 69
$384. 00 $384. 00 $384. 00
$97. 18
$97. 18
$97. 18
$315,43 $367. 25 $341. 04
$72. 18 $152. 74 $0. 00
$108. 71 $117. 46 $127. 34
groceries
clothing
fuel
the variable expensive in Luis's spreadsheet are groceries and fuel.Variable expenses are those that can change from month to month based on usage or consumption.
Looking at the given expenses, the variable expenses in Luis's spreadsheet would be:
1. Groceries: The amounts for groceries vary from month to month. In January, the expense is $315.43, in February it is $367.25, and in March it is $341.04. These amounts indicate that the grocery expenses are not fixed and can fluctuate.
2. Fuel: The amounts for fuel also differ for each month. In January, the expense is $72.18, in February it is $152.74, and in March it is $0.00. The varying amounts suggest that fuel expenses are dependent on usage and can vary.
On the other hand, the following expenses appear to be fixed or consistent:
1. Rent: The rent expense remains the same throughout the three months at $1,250.00.
2. Utility bill: The utility bill expenses also remain consistent in each month at $124.11, $108.72, and $121.69.
3. Car loan payment: The car loan payment remains unchanged at $384.00 for each month.
4. Insurance payment: The insurance payment is also consistent in each month at $97.18.
Therefore, the variable expensive in Luis's spreadsheet are groceries and fuel.
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Four transformations of the function f(x)=2x−4 are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
1. Vertical stretch: f(x) = 2(2x-4)
2. Horizontal stretch: f(x) = 2(x/2-4)
3. Vertical shift up: f(x) = 2x-4+3
4. Vertical shift down: f(x) = 2x-4-3
1. Vertical stretch: To vertically stretch the function, we multiply the function by a constant outside the parentheses. In this case, multiplying f(x) by 2 results in f(x) = 2(2x-4).
2. Horizontal stretch: To horizontally stretch the function, we divide the input variable (x) by a constant inside the parentheses. In this case, dividing x by 2 gives us f(x) = 2(x/2-4).
3. Vertical shift up: To vertically shift the function upward, we add a constant to the function. Adding 3 to f(x) results in f(x) = 2x-4+3.
4. Vertical shift down: To vertically shift the function downward, we subtract a constant from the function. Subtracting 3 from f(x) gives us f(x) = 2x-4-3.
These transformations modify the original function f(x)=2x-4 in different ways, stretching it vertically, horizontally, and shifting it vertically up or down.
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A.
Write a recursive formula for the sequence 8, 10, 12, 14, 16,. Then find the next term.
a = a,-1 + 2, where a, 8; 18
b.
a.
+ 2, where a
18; 8
c.
a, = a -1 -2, where a, 8; 18
d. A, = a. -1
2, where a, = = 2; -2
= a. - 1
The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18
Writing a recursive formula for the sequenceFrom the question, we have the following parameters that can be used in our computation:
8, 10, 12, 14, 16,.
In the above sequence, we have
First term, a(1) = 8
And we have the common difference to be
d = 2
So, we have
a(n) = a(n - 1) + 2
The next term of the sequence is
Next = 16 + 2
Evaluate
Next = 18
Hence, the recursive formula for the sequence is a(n) = a(n - 1) + 2
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The length of a rectangle is represented by 2n+8, and its width is represented by n-7. Write the polynomial for the perimeter of the rectangle. Write your answer in standard form.
The polynomial for the perimeter of the rectangle can be expressed as P(n) = 2(2n+8) + 2(n-7), which simplifies to P(n) = 4n + 16 + 2n - 14.
Combining like terms, we get P(n) = 6n + 2. Therefore, the polynomial in standard form for the perimeter of the rectangle is P(n) = 6n + 2.
To find the perimeter of the rectangle, we need to add up the lengths of all four sides. The length of the rectangle is represented by 2n+8, so we have 2 sides of length (2n+8). The width of the rectangle is represented by n-7, so we have 2 sides of length (n-7). To calculate the perimeter, we add up the lengths of all four sides: (2n+8) + (2n+8) + (n-7) + (n-7). Simplifying this expression, we get 6n + 2, which is the polynomial in standard form for the perimeter of the rectangle.
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The spheres cost $2 per square foot and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?
The surface area of a sphere is 4πr2, where r is the radius of the sphere. The cost of a sphere is 2 per square foot, so the cost of a sphere with radius r is 8πr2. Selim can spend 20 per sphere, so he can purchase a sphere with radius r such that 8πr2≤20. This inequality can be solved for r to get r≤8π20=2π5. The diameter of a sphere is 2r, so the maximum diameter of the spheres Selim can purchase is 22π5=10π≈3.162 feet.
Suppose a chemist combines a 25% acid solution and a 50% acid solution to make 40 L of 45% acid solution. How many liters of each solution did she use? Use the blanks below to fill in your numerical answers.
__________ L of 50% solution; __________ L of 25% solution
To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.
The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).
To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):
0.45 * 40 = 0.5x + 0.25(40 - x)
Simplifying the equation:
18 = 0.5x + 10 - 0.25x
Combining like terms:
0.25x = 8
Dividing both sides by 0.25:
x = 32
Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
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42 + x(interior angle) + 120(exterior) = 180
Please help-
To solve the equation 42 + x (interior angle) + 120 (exterior angle) = 180, we can use the fact that the sum of an interior angle and its corresponding exterior angle is always 180 degrees.
In the given equation, 42 represents an interior angle, x represents an unknown interior angle, and 120 represents the corresponding exterior angle. The sum of an interior angle and its corresponding exterior angle is always 180 degrees. Therefore, we can set up the equation:
42 + x + 120 = 180
To solve for x, we can simplify the equation:
x + 162 = 180
Next, we can isolate x by subtracting 162 from both sides of the equation:
x = 180 - 162
x = 18
Therefore, the value of the unknown interior angle, x, is 18 degrees.
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4) Emily can walk 3/4 of a mile in 1/4 of an hour. At
this same rate, how long does it take Emily to walk 1
mile?
A.1/2 of an hour
B. 2/5 of an hour
C. 1/3 of an hour
D. 2/3 of an hour
Emily can walk 3/4 of a mile in 1/4 of an hour. At the same rate, time taken to walk 1 mile =1/3 of an hour.
Mathematical representation
We know that, Emily can walk 3/4 of a mile in 1/4 of an hour.
Meaning,
Time taken to walk 3/4 of a mile = 1/4 of an hour
Distance covered = 3/4 mile
We need to find the time taken by Emily to walk 1 mile.
The rate is defined as the distance covered in unit time. So,
Rate = Distance / Time
We know that Rate of Emily = 3/4 ÷ 1/4
= 3/4 × 4/1
= 3 miles/hour
The rate of walking is 3 miles/hour.
Now we can find the time taken to walk 1 mile using rate formula.
Distance = Rate × Time
We have to walk 1 mile and the rate of walking is 3 miles/hour.
Time = Distance / Rate
Time taken to walk 1 mile = 1 / 3 = 1/3 hour.
So, the answer is option C.
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1) What is the formula used to
find the volume of a cylinder?
2)What is the difference
between the volumes of the
Chunky Chicken Noodle Soup
can and the Condensed
Chicken Noodle Soup can?
"Use 3. 14 for pi in all calculations
"You must show what you multiplied to find
the volumes of both cans AND the difference
between the two volumes.
"Remember to label your answers
cm
Answer:
for 1.
Step-by-step explanation:
the formula is pir2h
2 cyclists leave town 86 kilometers apart at the same time and travel toward each other. one cyclist travel 7 km/h faster than the other.
Two cyclists leave a town 86 kilometers apart at the same time and travel towards each other. One cyclist is traveling 7 km/h faster than the other. The task is to find their speeds.
Let's assume the speed of the slower cyclist is x km/h. Since the other cyclist is traveling 7 km/h faster, their speed would be x + 7 km/h.
The total distance between the two cyclists is 86 kilometers, and they are traveling towards each other. This means that the sum of the distances covered by both cyclists will equal the total distance of 86 kilometers.
Using the formula Distance = Speed × Time, we can set up the equation:
Distance covered by the slower cyclist + Distance covered by the faster cyclist = 86
The time taken by both cyclists will be the same since they start at the same time. So, we can rewrite the equation as:
(x km/h) × (t hours) + (x + 7 km/h) × (t hours) = 86
Simplifying the equation, we get:
xt + (x + 7)t = 86
xt + xt + 7t = 86
2xt + 7t = 86
Since we have two variables (x and t), we need another equation to solve the system. Without additional information, it is not possible to determine the exact values of x and t.
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Maija is building a square sandbox with sides 2 feet long. She wants to put sand 1.55 feet deep in the box. How much sand should Maija order?
To calculate the amount of sand Maija should order, we need to find the volume of the sandbox. The sandbox is in the shape of a cube, so its volume is determined by multiplying the length, width, and height.
Given that the sides of the square sandbox are 2 feet long and the desired depth of the sand is 1.55 feet, we can calculate the volume as follows:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Since all sides of the sandbox are equal in length (2 feet), the formula simplifies to:
[tex]\[ \text{Volume} = \text{Side}^3 \][/tex]
Substituting the values:
[tex]\[ \text{Volume} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.55 \, \text{ft} \][/tex]
[tex]\[ \text{Volume} = 6.2 \, \text{cubic feet} \][/tex]
Therefore, Maija should order 6.2 cubic feet of sand for her sandbox.
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Which fractions are equivalent?
26 and 12
14 and 36
26 and 14
12 and 24
To find which fractions are equivalent, we need to simplify each fraction. the fractions that are equivalent are 12/24 and 1/2.
The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.14 and 36The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.26 and 14The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form.
Two fractions are equivalent if they represent the same part of a whole. To find which fractions are equivalent, we can simplify each fraction by dividing the numerator and denominator by their greatest common factor. The simplified fractions will represent the same part of a whole as the original fraction and will be equivalent fractions.
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Shirley has already jogged 5 miles. She continues to jog at an average rate of 3. 5 miles per hour. This situation is modeled by the function y=3. 5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary
The rate of change and the initial value of the function can be identified based on the given situation and the function y = 3.5x + 5.
The rate of change represents the constant rate at which the miles jogged increase per hour, while the initial value indicates the starting point or the number of miles jogged before any additional hours.
In the given function y = 3.5x + 5, the coefficient of x, which is 3.5, represents the rate of change. It indicates that for every hour Shirley continues to jog, she will add 3.5 miles to the total distance already jogged.
The constant term, 5, represents the initial value of the function. In this case, it signifies that Shirley has already jogged 5 miles before she starts jogging at an average rate of 3.5 miles per hour.
Therefore, the rate of change of the function is 3.5 miles per hour, indicating the increase in miles jogged per hour, and the initial value is 5 miles, representing the distance already jogged by Shirley before any additional hours of jogging.
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