Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.

Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Final answer:

To find the two integers, we looked for factors of 12 and tested them to find a pair that summed to -7. We discovered that -3 and -4 are the two integers that meet both the sum and product conditions.

Explanation:

To find two integers whose sum is -7 and whose product is 12, we need to find two numbers that add up to -7 and multiply to give 12.

Let's denote the two numbers we are looking for as x and y. We have two equations:

x + y = -7 (Equation 1)

xy = 12 (Equation 2)

We can use various methods to solve these equations, such as factors of 12, trial and error, or a systematic approach like substitution or elimination, but in this case, factoring is the easiest. We look for two numbers that multiply to 12 (1x12, 2x6, 3x4) and also add up to a sum of -7. We can see that the pair of numbers that satisfies both conditions is -3 and -4, because (-3)+(-4) = -7, and (-3)x(-4) = 12.

Thus, the two integers are -3 and -4.

Final answer:

To find the number of old houses when the city has 3 new houses for every 9 old houses, set up a proportion. By cross-multiplying 3/9 = 21/x, we find that there are 63 old houses when there are 21 new houses.

Explanation:

The student asks how many old houses there would be if a city had 3 new houses for every 9 old houses, and there are 21 new houses. This is a problem of proportions that can be solved using a simple cross-multiplication method.

To solve for the number of old houses, set up a proportion with the numbers provided:

3 new houses / 9 old houses = 21 new houses / x old houses

Now, cross-multiply:

3x = 9 × 21

3x = 189

Divide both sides by 3 to find x:

x = 189 / 3

x = 63

So, there are 63 old houses in the city.

Molly has 6 balloons.

Since Ann has seven balloons and Molly has a set less of balloons, we need to determine the value of the set.

We can represent the number of balloons Molly has as a variable, let's say x. So, the equation becomes: x = 7 - 1.

To solve the equation, we subtract 1 from 7, giving us the answer: x = 6. Therefore, Molly has 6 balloons.

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The solution is Company A

The company which offers the better deal is Company A with 500 minutes of talk time with $ 49.99

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the the first company be = A

Let the second company be = B

Now , Company A offers

The total talk time by Company A = 500 minutes

The total amount of talk time = $ 49.99

So , the equation will be

The talk time per minute = total talk time by Company A /  total amount of talk time

Substituting the values in the equation , we get

The talk time per minute = 500 / 49.99

The talk time per minute = $ 10.00

Now , Company B offers

The total talk time by Company B = 480 minutes

The total amount of talk time = $ 44.99

So , the equation will be

The talk time per minute = total talk time by Company B /  total amount of talk time

Substituting the values in the equation , we get

The talk time per minute = 480 / 44.99

The talk time per minute = $ 10.66

Therefore , the value of talk time per minute of Company A is less than Company B

Hence , The company which offers the better deal is Company A with 500 minutes of talk time with $ 49.99

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For the function j(x)=-4/5x+7, the value of x that will make j(x) equal to -5 is 15.

The question asks us to find the value of x for the function j(x)=-4/5x+7 when j(x) is -5. To solve this problem, we can simply substitute j(x) with -5 in the function equation and solve for x.

So, -5 = -4/5x + 7. We can then rearrange this equation to leave x on one side, leading to -4/5x = -5 - 7, which simplifies to -4/5x = -12. To find x, we then divide both sides by -4/5, resulting in x = -12 / (-4/5) = 15.

Therefore, the solution is x = 15, and the given function j(x) will equal -5 when x is 15.

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The volume of a cube is given as 64 cubic mm then the side length of the cube is 4 mm.

The volume of a cube can be calculated as the cube of the sides of a given figure.

The volume of a cube =[tex]sides^3[/tex]

We have been given that the volume of a cube is 64 cubic mm. We need to find the side length of the cube.

The volume of a cube =[tex]sides^3[/tex]

                                 64  = [tex]sides^3[/tex]

Now we will take cube-root on both sides of the equation;

∛ 64 = ∛ [tex]sides^3[/tex]

∛ 4^3 = ∛ s^3

4 = s

Therefore, the side length of the cube is 4 mm.

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Answer:

470 nickels

Step-by-step explanation:

$23.50 ÷ 0.05 = 470

The required estimated value of the division of 4020 / 16 is 200.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

here,
As of the given question,
rounding of the number 4020 is 4000, as the digit 20 in ten place is less than 50.

Rounding of the number 16 is 20

Now,
Division = 4000 / 20 = 200

Thus, the required estimated value of the division of 4020 / 16 is 200.

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Final answer:

To estimate 4020 divided by 16, round 4020 to 4000 and 16 to 20, then divide the rounded numbers to get an estimate of 200.

Explanation:

Estimating 4020/ 16 by Rounding

To estimate 4020/ 16 by first rounding each number so that it has only one non-zero digit, we'll start by rounding 4020 and 16 to their most significant figures. We round 4020 to 4000 since the first non-zero digit is a 4 with three following zeros, making it the most significant figure. Similarly, we round 16 to 20 because the leading digit is a 1 which we can round up to a 2 followed by a zero.

Next, we perform the division with our rounded numbers: 4000/ 20 = 200. This is our estimated result after rounding the original numbers to one non-zero digit and performing simple division.

The estimated division is simpler and can be done without a calculator, which is helpful for quick approximations.

Answer:

b=(2x-3c)/a

Step-by-step explanation:

ab+3c=2x

ab=2x-3c

b=(2x-3c)/a

If U= -2.8

-6.4-4*-2.8=4.8

So the answer is B.

Hope this helps!