5.A Nathan decided he wanted to go to a theme park. The theme

The table below shows four systems of equations:

fredd [130]

System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1

This is the correct answer because not only is it true but it also follows the property of solving systems of equations with adding the equations. To prove that it is true:

2nd equation in system #2 = 1st equation in system #1 + 2(2nd equation in system #1)

10x − 7y = 18 == 4x − 5y = 2 + 2(3x − y = 8)
10x - 7y = 18 == 4x - 5y = 2 + 6x - 2y = 16
10x = 7y = 18 == 10x - 7y = 18

5 0

4 years ago

21. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2.

dybincka [34]

Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$

Step 2 of 2

Find the slope of first line.

$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$

And

$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$

Since, both slopes are reciprocal of each other.

Therefore, the lines are perpendicular.

6 0

2 years ago

Evaluate the expression for the given value of the variable(s). Show your work.

ch4aika [34]

I got -50 as my answer

4 0

3 years ago

The sum of three consecutive numbers is 117. What is the first of the three numbers?

Harrizon [31]

38+39+40 = 117.

So the first of the three numbers is 38.

3 0

4 years ago

Diane runs 10 miles in 55 minutes, how many minuets does she take per mile?

Brut [27]

Step-by-step explanation:

Hi!!

 It's simple, you can do it easily. 

no. of miles = 10 miles

time = 55 mins.

now,

no. of mins for 1 mile = no. of miles/ time

 = 10 /55

 =0.18181818 min.

so, she takes 0.181818 or 2/11 min per each mile.

Hope it helps...

5 0

4 years ago

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