Given the linear equation r=-2. 5 t and t can only be a negative number, what quadrant will the r coordinate be located?.

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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The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18

From 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 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.

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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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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Mrs. Rodriguez sold 128.8 ounces of popcorn.We know that each bag of popcorn weighs 2.3 ounces. Therefore, to find out the total amount of popcorn Mrs. Rodriguez sold in 56 bags, we need to multiply 2.3 by 56. That is;2.3 × 56 = 128.8Therefore, there are 128.8 ounces of popcorn in 56 bags

We are given that Mrs. Rodriguez is selling popcorn at the snack stand. Each bag holds 2.3 ounces of popcorn. In one hour, she sold 56 bags of popcorn. Our task is to find out how many ounces of popcorn are in 56 bags.In order to find out how many ounces of popcorn are in 56 bags, we need to first find out the weight of one bag of popcorn. We are told that each bag holds 2.3 ounces of popcorn. So, we have:

Weight of one bag of popcorn = 2.3 ounces Now, we can use this information to calculate the total weight of popcorn Mrs. Rodriguez sold in 56 bags. To do this, we need to multiply the weight of one bag of popcorn (2.3 ounces) by the number of bags she sold (56). That is;Weight of 56 bags of popcorn = 2.3 × 56= 128.8Therefore, Mrs. Rodriguez sold 128.8 ounces of popcorn in one hour.

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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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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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The missing side lengths are x = 4 and y = 4.The correct answer choice is D) x = 4, y = 4.

To find the missing side lengths in a triangle, we can use trigonometric ratios. In this case, we are given the length of one side (8) and the measure of one angle (30 degrees), and we need to find the lengths of the other two sides (x and y).

In a right triangle, the trigonometric ratios can be used to relate the angles and side lengths. In this case, we are not given that the triangle is a right triangle, so we will assume it is not.

The sine ratio relates the ratio of the length of the side opposite an angle to the length of the hypotenuse. In this case, the side opposite the 30-degree angle is y, and the hypotenuse is 8. So we can write:

sin(30 degrees) = y/8

Using the known value of sin(30 degrees) = 1/2, we can solve for y:

1/2 = y/8

Cross-multiplying, we get:

y = 4

So we have found the length of side y to be 4.

To find the length of side x, we can use the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

Using the law of sines, we can write:

sin(30 degrees)/x = sin(angle opposite x)/8

Since we know the sine of 30 degrees is 1/2, we can rewrite the equation as:

(1/2)/x = sin(angle opposite x)/8

Since the angle opposite x is 180 degrees - 30 degrees = 150 degrees, we have:

(1/2)/x = sin(150 degrees)/8

Using the known value of sin(150 degrees) = 1/2, we can solve for x:

(1/2)/x = 1/2/8

Cross-multiplying, we get:

x = 4

So we have found the length of side x to be 4.

Therefore, the missing side lengths are x = 4 and y = 4.

The correct answer choice is D) x = 4, y = 4.

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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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To determine the measure of angle DAB, we need to use the congruence of quadrilaterals ABCD and AMCG.

Quadrilateral ABCD is congruent to quadrilateral AMCG.

Since the two quadrilaterals are congruent, their corresponding angles are equal. Therefore, we can write:

m∠DAB = m∠MAC

However, the measure of angle MAC is not given in the given information. Therefore, without additional information, we cannot determine the exact measure of angle DAB.

The options provided in the question do not correspond to the measure of angle DAB. Therefore, the correct answer cannot be determined based on the given information.

It is important to have additional information about the measures of angles or the side lengths in order to determine the measure of angle DAB accurately.

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Answer:

Step-by-step explanation:

To enlarge a 4x6 photo with a ratio of 2:3, we can multiply the dimensions of the photo by the enlargement ratio to find the new dimensions.

Original photo dimensions: 4 inches x 6 inches

Enlargement ratio: 2:3

To find the new dimensions, we can multiply the original dimensions by the enlargement ratio:

New width = 4 inches x 2 = 8 inches

New height = 6 inches x 3 = 18 inches

Therefore, the new dimensions of the enlarged photo would be 8 inches x 18 inches.

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.

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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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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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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Cindy has scores of 72, 82, 83 and 89 on her Biology tests. Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

Cindy's current average score in Biology is:

(72 + 82 + 83 + 89) / 4 = 81.5

Since the final exam counts as two tests, we can calculate the total number of points Cindy can earn in the course as follows:

Total points = 4 tests + 2 tests = 6 tests

To earn a C in the course, her average score must be between 77 and 84. Let's assume she needs to score x on her final exam to achieve a C. Then her total points would be:

Total points = 72 + 82 + 83 + 89 + x + x

Simplifying this equation, we get:

Total points = 326 + 2x

To earn a C, Cindy's average score must be between 77 and 84. Therefore, we can set up an inequality:

77 <= (326 + 2x) / 6 <= 84

Multiplying both sides by 6, we get:

462 <= 326 + 2x <= 504

Subtracting 326 from all sides, we get:

136 <= 2x <= 178

Dividing by 2, we get:

68 <= x <= 89

Therefore, Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

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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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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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This means that the expression 10x² + 2x - 8  completely factored as 2(5x - 2)(x + 2).

The correct factored form of the expression 10x² + 2x - 8 is:

2(5x - 2)(x + 2).

To factor the quadratic expression completely for common factors first that the coefficient 2 is a common factor in all three terms. After factoring out 2, left with (5x² + x - 4).

An factor the trinomial (5x² + x - 4). However, this trinomial cannot be factored further using integer coefficients.

So, the factored form of the expression is 2(5x - 2)(x + 2).

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Answer:

for 1.

Step-by-step explanation:

the formula is pir2h

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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The length of the diameter of the circle in this problem is given as follows:

20 units.

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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The inverse operation used to solve the equation x/7 = 5 is multiplication

Inverse operations are mathematical operations that reverse or undo each other. To isolate the variable, inverse operations are used. For example, addition and subtraction are inverse operations, as are multiplication and division.

In an equation, inverse operations can be used to solve for a variable. In order to solve the equation x/7 = 5, we will use inverse operations.The inverse operation of division is multiplication. So, we can isolate x by multiplying both sides of the equation by 7.x/7 = 5Multiplying both sides by 7 gives:x = 7 × 5x = 35Therefore, x = 35 is the solution to the equation.

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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 manufacturing company has determined that the daily revenue R(n) in thousands of dollars is given by the formula R(n) = 12n - 0.6n where n represents the number of palettes of product sold (0 < n < 500).

If the company wishes to make a revenue of 45 thousand dollars, we are supposed to find the number of palettes of product sold .Solution :Let us substitute the value of R(n) = 45 in the given equation and solve for n45 = 12n - 0.6n45 = 11.4n, n = 3.9474Hence, the manufacturing company has to sell either 3 or 4 palettes of product to make $45.000.

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The side lengt of the square is approximately 1839 feet.

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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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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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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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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