Question
In parallelogram MNOP
, the diagonals MO
and NP
intersect at point L
. ML=x+7
and LO=2x−10
. What is the value of x?
(1 point)
Responses
x=24
x equals 24
x=−3
x equals negative 3
x=17
x equals 17
x=−7
, the diagonals MO
and NP
intersect at point L
. ML=x+7
and LO=2x−10
. What is the value of x?
(1 point)
Responses
x=24
x equals 24
x=−3
x equals negative 3
x=17
x equals 17
x=−7
Answers
GPT-4o mini
In a parallelogram, the diagonals bisect each other. This means that the lengths of segments ML and LO are equal.
So, we can set up the equation:
\[ ML = LO \]
Given:
\[ ML = x + 7 \]
\[ LO = 2x - 10 \]
Setting these equal to each other:
\[ x + 7 = 2x - 10 \]
Now, let's solve for \( x \):
1. Subtract \( x \) from both sides:
\[ 7 = x - 10 \]
2. Add 10 to both sides:
\[ 17 = x \]
So, the value of \( x \) is \( 17 \).
Therefore, the correct response is:
**x=17** or **x equals 17**.
So, we can set up the equation:
\[ ML = LO \]
Given:
\[ ML = x + 7 \]
\[ LO = 2x - 10 \]
Setting these equal to each other:
\[ x + 7 = 2x - 10 \]
Now, let's solve for \( x \):
1. Subtract \( x \) from both sides:
\[ 7 = x - 10 \]
2. Add 10 to both sides:
\[ 17 = x \]
So, the value of \( x \) is \( 17 \).
Therefore, the correct response is:
**x=17** or **x equals 17**.