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KengaRu [80]
3 years ago
5

2) A car travels 100 km with 7.4 liters of gas. How much gas is required for a 1322 km trip?

Mathematics
1 answer:
Mademuasel [1]3 years ago
5 0

Answer:

97.8 liters

Step-by-step explanation:

We use proportions:

If 7.4 liters are needed for 100 km, then we can write the rate:

7.4 L / 100 km  which should equal the rate for the x number of liters needed for a 1322 km trip:

7.4 L / 100 km = x / 1322 km

solving for "x" by multiplying both sides by 1322:

x = 97.828 liters

which we may be able to round to 97.8 liters

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What best describes the distance between two points with coordinates (2,-3) and (-4,2)
Fed [463]

Answer:

Option c (7.8) is the correct alternative.

Step-by-step explanation:

The given points are:

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The distance between two points will be:

= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

On substituting the values, we get

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Step-by-step explanation:

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Find the value of x in the<br> following parallelogram:<br> 3<br> 5x - 6<br> 3x - 2<br> x = [?]
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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,
omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

<u>Pyramid A</u>

s = 4 -- base sides

V = 36 -- Volume

<u>Pyramid B</u>

s = 6 --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

V = \frac{1}{3} * B * h

Where B represents the area of the base equilateral triangle, and it is calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

B = \frac{1}{2} * s^2 * sin(60)

B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}

B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}

B = 4\sqrt 3

The height is calculated from:

V = \frac{1}{3} * B * h

This gives:

36 = \frac{1}{3} * 4\sqrt 3 * h

Make h the subject

h = \frac{3 * 36}{4\sqrt 3}

h = \frac{3 * 9}{\sqrt 3}

h = \frac{27}{\sqrt 3}

To calculate the volume of pyramid B, we make use of:

V = \frac{1}{3} * B * h

Since the heights of both pyramids are the same, we can make use of:

h = \frac{27}{\sqrt 3}

The base area B, is then calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where

s = 6

So:

B = \frac{1}{2} * 6^2 * sin(60)

B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}

B = 9\sqrt 3

So:

V = \frac{1}{3} * B * h

Where

B = 9\sqrt 3 and h = \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9 * 27

V = 81

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