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4 years ago

11

What is the missing dimension of a rectangle or prism with the following dimensions and volume? Length 3 cm width 5 cm volume 45

cm3 height?Please help me find the height.

1 answer:

dem82 [27]4 years ago

7 0

You got the volume so the formula for finding a rectangular prism is l*w*h=x. l stands for length, w stands for width, h stand for height, and x stands for the total volume. Put the numbers in the formula so do 3*5*l=45 multiply the 3 and 5 and you will get 15*l=45 and divide by 15 on both sides (use a calculator if you can't do it in your head) and the answer should be 3.

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one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of

Zarrin [17]

Answer:

20 gallons were used from the tank with the octane rating of 80.

Step-by-step explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1) $x\times140 + y\times80 = 60\times120$

$140x+80y = 7200$

or $7x+4y = 360$ .........[3]

(2) $x + y = 60$

Now multiply equation (2) by 4

$4x + 4y = 240$ ...........[4]

Subtract (4) from (3)

$7x+4y-4x-4y=360-240$

$3x=120$

$x=\frac{120}{3}$

$x=40$

Put x in equation [4] we get,

$4(40) + 4y = 240$

$160 + 4y = 240$

$4y = 80$

$y=\frac{80}{4}$

$y=20$

Therefore, x=40 and y=20

So, 20 gallons were used from the tank with the octane rating of 80.

7 0

3 years ago

What are the domain and range of the exponential function below? F(x) = 3x + 2

skelet666 [1.2K]

The domain is 3 and range is 2

3 0

3 years ago

Read 2 more answers

What is the average rate of change of f over the interval [3,4]?

masya89 [10]

Answer:

4

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ 3, 4 ] , then

f(b) = f(4) = - 1 ← from table

f(a) = f(3) = - 5 ← from table , then

average rate of change = $\frac{-1-(-5)}{4-3}$ = $\frac{-1+5}{1}$ = 4

3 0

3 years ago

The house has a form of a rectangle with one side two and a half times as long as the other side.

Studentka2010 [4]

Answer:

A. (x*2.5)*x

B. (32*2.5)*32=2560

Step-by-step explanation:

4 0

3 years ago

Which expressions are equivalent??

Brilliant_brown [7]

<u>Given</u>:

The given expression is $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$

We need to determine the equivalent expression.

<u>Option A:</u> -1

Solving the expression, we get;

$\frac{3}{2} x+14-\frac{3}{2} x+15$

Simplifying, we get;

$14+15=29$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is not equivalent to -1.

Hence, Option A is not the correct answer.

<u>Option B</u>: 29

Solving the expression, we get;

$\frac{3}{2} x+14-\frac{3}{2} x+15$

Simplifying, we get;

$14+15=29$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to 29.

Hence, Option B is the correct answer.

<u>Option C</u>: $2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Let us rewrite the given expression.

$2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to $2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Thus, Option C is the correct answer.

<u>Option D</u>: $2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)$

Rewriting the expression, we get;

$2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Hence, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent not to $2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)$

Thus, Option D is not the correct answer.

<u>Option E:</u> $2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Multiplying the terms within the bracket, we get;

$2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Hence, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to $2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Thus, Option E is the correct answer.

4 0

3 years ago