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artcher [175]
3 years ago
8

3. Which rate is faster? A: 60 feet in 90 seconds or B: 60 inches in 5 seconds​

Mathematics
1 answer:
Marianna [84]3 years ago
8 0

Answer:60 inches in 5 seconds

Step-by-step explanation:

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Mark is six years older than his brother Sam. The sum of their ages is 30. Let 'a' be Sam's age.
svlad2 [7]

Answer:

a = 12 years

Step-by-step explanation:

Mark is 6 years older than his brother Sam. Now, we are asked to represent Sam’s age by a. This means that if Sam is a years old, Mark is (a + 6) years old.

The sum of their ages is 30, this means that when we add their ages together, we get the sum of thirty.

Mathematically this means a + a + 6 = 30

2a + 6 = 30

This is the equation needed to get a. To get a , we proceed to solve the equation to completion.

2a = 30 - 6

2a = 24

a = 24/2

a = 12

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3 years ago
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Pentagon PQRST and its reflection, pentagon P'Q'R'S'T', are shown in the coordinate plane below:
bagirrra123 [75]
Answer: Choice A) x = 0

The line x = 0 lines up perfectly with the y axis. So the line of reflection is the y axis. 
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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
3 years ago
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