if y-4 = x+5 and 2x+5 = x+12, then find the value of x and y

3 answers

To find the value of x and y, we can solve the system of equations.

1) y - 4 = x + 5
2) 2x + 5 = x + 12

Let's start by solving equation 2 for x:

2x + 5 = x + 12
Subtract x from both sides:
2x - x + 5 = x - x + 12
x + 5 = 12
Subtract 5 from both sides:
x = 12 - 5
x = 7

Now, let's substitute the value of x into equation 1 to find y:

y - 4 = 7 + 5
y - 4 = 12
Add 4 to both sides:
y = 12 + 4
y = 16

Therefore, the value of x is 7 and the value of y is 16.
LM¯¯¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD. If AB =50 and DC = 135, what is LM? Please show all work in order to recieve full credit for this problem
To find the length of LM, we first need to find the length of AD and BC, as LM is the midsegment connecting the midpoints of AD and BC.

In a trapezoid, the midsegment is parallel to the bases and is equal to the average of the lengths of the bases.

Given AB = 50 and DC = 135, we need to find AD and BC. Since AD and BC are parallel to AB and CD respectively, they have the same length.

AD = AB = 50
BC = DC = 135

Now, we can find the length of LM.

LM = (AD + BC)/2
LM = (50 + 135)/2
LM = 185/2
LM = 92.5

Therefore, the length of LM is 92.5.