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4 years ago

Find both unit rates and explain what each means: 250 miles on 8 gallons of fuel

Mathematics

1 answer:

My name is Ann [436]4 years ago

3 0

250 miles on 8 gallons of fuel
means 250 miles were traveled on 8 gallons, so an average of 250mi/8gal = 31.25 mpg

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Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

Last step: substitute the slope and y intercept into y=mx+b.

$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

3 0

4 years ago

What is the answer to 1935 divided by 54

Degger [83]

35.833

0 0 3 5. 8 3 3

5 4 1 9 3 5. 0 0 0

− 0

1 9

− 0

1 9 3

− 1 6 2

3 1 5

− 2 7 0

4 5 0

− 4 3 2

1 8 0

− 1 6 2

1 8 0

− 1 6 2

1 8

7 0

3 years ago

If a 25 in. by 32 in. window has a wooden frame 2 inches wide surrounding it, what is the total area of the window and frame?

d1i1m1o1n [39]

Answer:

1044 sq. inches

Step-by-step explanation:

The frame adds 2 inches on each side of the window, so the width becomes 29 in. and the length becomes 36 in.

Area = width × length

So the total area of the window and the frame is:

A = 29 × 36 = 1044 in²

7 0

3 years ago

Help please! Solve the system of equations.

Lelu [443]

2 * x = 2 * 3 = 6

9 * y = 9 * 2 = 18

18 + 6 = 24

x = 3

y = 2

7 0

3 years ago

Solve for x. 163 - x= -52 O A r = -215 B. X=-111 C. x = 111 D. x = 215

Eduardwww [97]

Answer:

Step-by-step explanation:

3 0

3 years ago