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3 years ago

Sophia uses 8 gallons of gas to drive 204 miles at the same rate how many miles can Sophia drive using 18 gallons of gas

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

8 0

Answer:

Sophia can drive 3672 miles using 18 galloons of gas.

Step-by-step explanation:

204 x 18 = 3672.

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What are the vertices of A'B'C if ABC is dilated by a scale factor of 2?

malfutka [58]

The vertices of A'B'C' if A(0, 10), B(8, 6), C(4, 2) is dilated by a scale factor of 2 are;

C. A'(0, 20), B'(16, 12), C'(8, 4)

<h3>Which method can be used to find the vertices of A'B'C'?</h3>

Given that triangle ABC is dilated by a scale factor of 2, we have;

A'B' = 2 × AB

A'C' = 2 × AC

B'C' = 2 × BC

Length of AB = √((8-0)^2 + (6-10)^2) = 4•√5

Length of AC = √((4-0)^2 + (2-10)^2) = 4•√5

Length of BC = √((8-4)^2 + (6-2)^2) = 4•√2

By multiplying the given coordinates by the scale factor, we have;

A' = 2 × (0, 10) = (0, 20)

B' = 2 × (8, 6) = (16, 12)

C' = 2 × (4, 2) = (8, 4)

A'B' = √((16-0)^2 + (12-20)^2) = 8•√5

A'C' = √((8-0)^2 + (4-20)^2) = 8•√5

B'C' = √((16-8)^2 + (12-4)^2) = 8•√2

Therefore when we have;

A'(0, 20), B'(16, 12), C'(8, 4), we get;

A'B' = 2 × AB

A'C' = 2 × AC
B'C' = 2 × BC

The correct option is therefore;

C. A'(0, 20), B'(16, 12), C'(8, 4)

Learn more about finding the distance between points on the coordinate plane here:

brainly.com/question/7243416

#SPJ1

5 0

2 years ago

Which property is shown in the sentence below? 15(x - 2) = (x - 2)15

Volgvan

The answer is communative. hope that helped

7 0

3 years ago

Mark the statements that are true.

qaws [65]

Answer:

Hi there!

The correct choices are: A, B, C

Step-by-step explanation:

π in radians equals to 180°

A is correct because 180/3 = 60

C is correct because 180/4 = 45

7 0

3 years ago

The larger of two numbers is 10 less than 5 times the smaller.their sum is 146 .find the smaller number

ExtremeBDS [4]

For this problem, you would have to use a system of equations. Hope this helps!

5 0

3 years ago

A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol

k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

<u>Given the following data:</u>

Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

$W = 3 + L$ ......equation 1

$H = 4 + L$ ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

$Volume = length * width * height$ .....equation 3.

Substituting the values into equation, we have;

$224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}$

Rearranging the polynomial, we have;

$L^{3} + 7L^{2} + 12L - 224 = 0$

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

$(x - 3) = 0\\x = 3$

$P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0$

We would try with 4;

$P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0$

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

3 0

3 years ago