Helen drove from the restaurant to the toy store, which

anzhelika [568]

Answer is C
14.2+6.5(p+3q)-4.05q
14.2+6.5p+19.5q-4.05q
14.2+6.5p+15.45q→6.5p+15.45q+14.2
so the answer is C

7 0

1 year ago

If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?A.

Svetlanka [38]

Answer:

C. 40

Step-by-step explanation:

Let us say there are x 7's and y 77's.

We have been given that each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350. We are asked to find the value of n.

Since the sum of all numbers is 350, so we can represent this information in an equation as:

$7x+77y=350$

The only integer solutions for the equation $7x+77y=350$ are 10, 20, 30, 40, 50 .

So, there can be these many terms: 10 or 20 or 30 or 40 or 50 .

The given option only contains 40, so 40 would be the answer. For 40 terms to be there, there has to be 39 sevens and 1 seventy-seven.

Let us verify our answer.

$7x+77y=350$

$7(39)+77(1)=350$

$273+77=350$

$350=350$

Therefore, the total terms (n) could be equal to 40 and option C is the correct choice.

8 0

2 years ago

What is the result of substituting for y in the bottom equation?

zhenek [66]

Answer:

(A) $x + 3= x^2 + 2x-4$

Step-by-step explanation:

Given the equations:

$y = x + 3\\y= x^2 + 2x-4$

Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.

Substitution of y into $y=x^2 + 2x-4$ gives us:

$x + 3= x^2 + 2x-4$

The correct option is A.

6 0

2 years ago

A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. After a storm, the linear dimensions of th

QveST [7]

we know that

the volume of a cone is equal to

$V= \frac{1}{3} \pi r^{2}h$

in this problem

the radius is equal to

$r= \frac{112}{2}= 56ft$

1) Find the height of the cone before the storm

Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) Find the volume before the storm

$V= \frac{1}{3}*\pi* 56^{2}*33$

$V=34,496\pi\ ft^{3}$

3) Find the volume after the storm

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

so

r=(56/3) ft

h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

$V= 1,277.63\pi\ ft^{3}$

4) Find how this change affect the volume of the pile

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

the answer part a) is

The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

Part b) Estimate the number of lane miles that were covered with salt

5) Find the amount of salt that was used during the storm

$=34,496 \pi - 1,277.63 \pi \\= 33.218.37 \pi \\= 104,358.59\ ft^{3}$

6) Find the pounds of road salt used

$104,358.59*80=8,348,687.2\ pounds$

7) Find the number of lane miles that were covered with salt

$8,348,687.2/350=23,853.39 \ lane\ miles$

therefore

the answer part b) is

the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

Part c) How many lane miles can be covered with the remaining salt? Round your answer to the nearest lane mile

the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) Find the pounds of road salt

$4,013.79*80=321,103.20\ pounds$

9) Find the number of lane miles

$321,103.20/350=917.44 \ lane\ miles$

therefore

the answer part c) is

the number of lane miles is $917 \ lane\ miles$

7 0

2 years ago

One week, Claire earned $272.00 at her job when she worked for 17 hours. If she is paid the same hourly wage, how many hours wou

DochEvi [55]

Answer: 448 hours

Step-by-step explanation:

272 divided by 17 = hourly wage

hourly wage= 16$

448 divided by 16 = 28 weeks

28 x 16= 448 hours

4 0

2 years ago

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