System of equations how to for this problem?

A parallelogram should have two pairs of parallel sides meaning the length of side AB should be the same as the length of side CD and the length of side AD should be the same as the length of side BC.

<u>First, lets see if line AB is parallel to line CD.</u>

Let's start by finding out the length of line AB.

Since we know x = 6 we will replace x with 6 in the expression:

7(6) + 2 = 42 + 2 = 44

Now that we know the length of line AB is 44, lets find the length of line CD by replacing x with its value of 6:

9(6) - 10 = 54 - 10 = 44

Now that we know the length of line CD is 44, we can see that line AB is parallel to line CD since they both have the same length of 44.

<u>Now, lets see if line BC is parallel to line AD.</u>

Let's start by finding out the length of line BC.

Since we know y = 8 we will replace y with 8 in the expression:

3(8) + 7 = 24 + 7 = 31

Now that we know the length of line BC is 31, lets find the length of line AD by replacing y with its value of 8:

5(8) - 9 = 40 - 9 = 31

Now that we know the length of line AD is 31, we can see that line BC is parallel to line AD since they both have the same length of 31.

<u>Conclusion</u>

ABCD is a parallelogram because it contains two parallel sides.

5 0

3 years ago

Janie bought 4 apples and 6 bananas. Each apple costs $0.40, and each banana costs $0.60. Enter an expression representing the t

baherus [9]

total cost = c

c =0.40(4) + 0.60(6)

c = 1.60 + 3.60

total cost = 5.20

3 0

3 years ago

Write the equation of the line parallel to 3x-y=7 that passes through point (-5, -3)

IceJOKER [234]

<h2>Answer:</h2>

$\boxed{y=3x+12}$

<h2>Step-by-step explanation:</h2>

In this problem we know the equation of a line, which is:

$3x-y=7$

We also can write this equation as:

$y=3x-7$

This line has a slope $m=3$ which is also the slope of the line we are looking for because they're parallel. We also have a point $(-5,-3)$ . Therefore, we can write this equation as follows:

$y-y_{0}=m(x-x_{0}) \\ \\ y-(-3)=3(x-(-5)) \\ \\ y+3=3(x+5) \\ \\ y+3=3x+15 \\ \\ \boxed{y=3x+12}$

From the figures below, the line in red is $3x-y=7$ while the line in blue is $y=3x+12$ and this line passes through the point (-5, -3)!

4 0

3 years ago

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