Question

suppose m is the mid - point of xy. if my = 5x + 12 and xy = 58, find the value of x and my. write your answers as integers or decimals (not as fractions).

Explanation:

Step1: Recall mid - point property

Since M is the mid - point of XY, then $XY = 2MY$.

Step2: Substitute given values

We know that $XY = 58$ and $MY=5x + 12$. So, $58 = 2(5x + 12)$.

Step3: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we get $58=10x + 24$.

Step4: Solve for x

Subtract 24 from both sides: $58−24 = 10x+24 - 24$, which simplifies to $34 = 10x$. Then divide both sides by 10: $x=\frac{34}{10}=3.4$.

Step5: Find the value of MY

Substitute $x = 3.4$ into the expression for MY: $MY=5(3.4)+12$. First, calculate $5\times3.4 = 17$, then $MY=17 + 12=29$.

Answer:

$x = 3.4$, $MY = 29$