Question

1 fill in the blank 1 point

1. find the weighted average if the weight of point m is 6 and the weight of point o is 4.

the weighted average is type your answer.
2 fill in the blank 1 point

1. if the weighted average of point n and q is - 1.75. if the weight of point n is 7 times the weight of point q. find point q.

Explanation:

Step1: Recall weighted - average formula

The formula for the weighted average $W$ of two numbers $x_1$ and $x_2$ with weights $w_1$ and $w_2$ is $W=\frac{w_1x_1 + w_2x_2}{w_1 + w_2}$.

Step2: Identify values for the first problem

For the first problem, assume $x_M=- 2$ (co - ordinate of point $M$), $w_M = 6$, $x_O=3$ (co - ordinate of point $O$), $w_O = 4$. Then $W=\frac{6\times(-2)+4\times3}{6 + 4}$.

Step3: Calculate the first weighted average

First, calculate the numerator: $6\times(-2)+4\times3=-12 + 12=0$. Then, divide by the denominator: $\frac{0}{10}=0$.

Step4: Set up equation for the second problem

Let the weight of point $Q$ be $w$, then the weight of point $N$ is $7w$. Let the co - ordinate of point $N=-4$ and the co - ordinate of point $Q$ be $x_Q$. The weighted average formula gives $-1.75=\frac{7w\times(-4)+w\times x_Q}{7w+w}$.

Step5: Simplify the second - problem equation

The denominator $7w + w=8w$. The equation becomes $-1.75=\frac{-28w+w x_Q}{8w}$. Since $w
eq0$ (because if $w = 0$, there is no non - trivial weighted average), we can cancel out $w$ from the numerator and denominator. So, $-1.75=\frac{-28 + x_Q}{8}$.

Step6: Solve for $x_Q$

Multiply both sides of the equation by $8$: $-1.75\times8=-28 + x_Q$. $-14=-28 + x_Q$. Add $28$ to both sides: $x_Q=-14 + 28 = 14$.

Answer:

1. $0$
2. $14$