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4 years ago

9

Zach's car travels 21 miles on 1 gallon of gas. Write an equation to represent the relationship between the gas Zach's car uses

and the distance he travels. Then solve the equation to see how far Zach's travels on a trip if he uses 16 gallons of gas

1 answer:

Allisa [31]4 years ago

5 0

Answer:

Zach's car can travel 336 miles on 16 gallons of gas

Step-by-step explanation:

21 miles per 1 gallon is a ratio of 21:1 or a fraction of $\frac{21}{1}$ . You can now set up a ratio/fraction to see how many miles 16 gallons is. If 1 gallon of gas can take a car 21 miles, then set up a fraction $\frac{21}{1} \frac{x}{16}$ . Cross multiply. 21 x 16 = 336. 336 divided by 1 equals 336 so the answer is Zach's car can travel 336 miles on 16 gallons of gas.

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Write in slope-intercept form an equation of the line that passes through the points (−1,12) and (1,2).

zzz [600]

Answer:

$y=-5x+7$

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

the points (−1,12) and (1,2)

substitute

$m=\frac{2-12}{1+1}$

$m=\frac{-10}{2}$

$m=-5$

step 2

we know that

The equation of the line in slope intercept form is equl to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=-5$

$point\ (1,2)$

substitute in the linear equation and solve for b

$2=-5(1)+b$

$b=2+5=7$

therefore

$y=-5x+7$

4 0

3 years ago

To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x

Fiesta28 [93]

Given function is

$f(x)=\left\{\begin{matrix}3x+k & x\leq -4 \\ kx^2-5 & x> -4\end{matrix}\right.$

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

$kx^2-5$

so RHD= $k(-4)^2-5$

Now set both equal

$k(-4)^2-5=3(-4)+k$

$16k-5=-12+k$

$16k-k=-12+5$

$15k=-7$

$k=-\frac{7}{15}$

k=-0.47

<u>Hence final answer is -0.47.</u>

7 0

3 years ago

Audryn left a $12 tip on a $68.73 restaurant bill. What percent tip did she leave? Round to the nearest tenth of a percent.

Andrew [12]

Well, if we take 68.73 as the 100%, how much is 12 of it in percentage?

well $\bf \begin{array}{ccllll}
amount&\%\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
68.73&100\\
12&x
\end{array}\implies \cfrac{68.73}{12}=\cfrac{100}{x}$

solve for "x"

3 0

3 years ago

Read 2 more answers

Which expression is a difference of squares with a factor of 2x5?

Sedbober [7]

Answer:

${( \sqrt{3.5} })^{2} - {( \sqrt{1.5} )}^{2}$

Step-by-step explanation:

The difference of two squares identity is

${x}^{2} - {y}^{2} = (x - y)(x + y)$

When we let

$\sqrt{3.5}$

and

$\sqrt{1.5}$

, we get:

${( \sqrt{3.5} )}^{2} - {( \sqrt{1.5}) }^{2} = (3.5 - 1.5)(3.5 + 1.5)$

This will simplify to give us the required factors

${( \sqrt{3.5} )}^{2} - {( \sqrt{1.5}) }^{2} =2 \times 5$

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4 years ago

42/4 as a improper fraction

makkiz [27]

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3 0

3 years ago

Read 2 more answers