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3 years ago

mr franks economy car can travel 420 miles on a 12 gallon tank of gas. determine how many miles he can travel on 8 gallons

Mathematics

1 answer:

S_A_V [24]3 years ago

3 0

Answer:

280 miles

Step-by-step explanation:

Divide 420 by 12 to find the unit rate of miles per gallon.

You get 35 miles per gallon

To find how many miles he can travel for 8 gallons, multiply 35 by 8.

You get 280 miles.

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The rectangle shown has a perimeter of 48 cm and the given area. Its length is 6 more than twice its width. Write and solve a sy

melamori03 [73]

Answer:

The length of the rectangle is 18 cm

The width of the rectangle is 6 cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of the rectangle is

$P=2(x+y)$

we have

$P=48\ cm$

$48=2(x+y)$ ------> equation A

$x=2y+6$ ------> equation B

Substitute equation B in equation A and solve for y

48=2(2y+6+y)

48=2(3y+6)

48=6y+12

6y=48-12

y=36/6=6 cm

Find the value of x

x=2(6)+6=18 cm

The area of the rectangle is

A=xy

A=18*6

A=108 cm^2

4 0

3 years ago

Which of these sets could represent the side lengths of a right triangle?

Jlenok [28]

Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

Now, in the given triplets:

(a) {4, 8, 12}

Here, $(4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94$

So, third side of the triangle 8.94 ≠ 12

Hence, {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10

Hence, {6, 8, 10} is a triplet.

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10 ≠ 15

Hence, {6, 8, 15} is NOT a triplet.

(d) {5, 7, 13}

Here, $(5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60$

So, third side of the triangle 8.60 ≠ 13

Hence, {5, 7, 13} is NOT a triplet.

4 0

3 years ago

5 1 The measure of Z1 = O 55 O62.5 110 5

Akimi4 [234]

Answer: 55

Step-by-step explanation:

Congruent angles intercept congruent chords, so since the circumference of a circle is 360 degrees, the arc angle 1 is inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

5 0

2 years ago

Help fast please!!!!!!!!

MArishka [77]

Step-by-step explanation:

The area is

${x}^{2} - 110x + 2800 \\ = {x}^{2} - 40x - 70x + 2800 \\ = x(x - 40) - 70(x - 40) \\ = (x - 40)(x - 70)$

Since the width is

$x - 40 \: (feet)$

Then, the length will be

$x - 70 \: (feet)$

4 0

3 years ago

Given the parent function of f(x)=x^4, what change will occur when the function is changed to f(-2x)?

Mekhanik [1.2K]

Answer:

Answer is 16x^4

Step-by-step explanation:

$given \: f(x) = {x}^{4} \\ to \: find: \: f( - 2x) \: \\ f( - 2x) = { (- 2x)}^{4} \\ = 16 {x}^{4}$

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION. 

7 0

3 years ago