I need help solving this practice math problem

What are the coordinates of point B on \overline{AC} such that AB = 1/2 BC

marta [7]

Answer:

C. $B(x,y) = \left(3,-\frac{16}{3} \right)$

Step-by-step explanation:

Let $A(x,y) = (6,-7)$ , $B(x,y) = (x,y)$ and $C(x,y) = (-3,-2)$ . From statement we know that $AB = \frac{1}{2}\cdot BC$ , which is equivalent to the following linear algebraic formula:

$B(x,y) -A(x,y) = \frac{1}{2}\cdot [C(x,y)-B(x,y)]$ (1)

$B(x,y)-A(x,y) = \frac{1}{2}\cdot C(x,y)-\frac{1}{2}\cdot B(x,y)$

$\frac{3}{2}\cdot B(x,y) = \frac{1}{2}\cdot C(x,y)+A(x,y)$

$B(x,y) = \frac{1}{3}\cdot C(x,y) +\frac{2}{3}\cdot A(x,y)$ (2)

Then, the coordinates of point B on AC are:

$B(x,y) = \frac{1}{3}\cdot (-3,-2)+\frac{2}{3}\cdot (6,-7)$

$B(x,y) = \left(-1, -\frac{2}{3}\right)+\left(4, -\frac{14}{3} \right)$

$B(x,y) = \left(3,-\frac{16}{3} \right)$

Which means that correct answer is C.

5 0

3 years ago

A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with

kvasek [131]

Answer:

We are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Step-by-step explanation:

95 % confidence means that we are 95 % confident that the the proportion of American voters who favor congressional term limits is 64 percent.

95 % confidence means that of all the sample about 95 % values are within in the given range.

And only 5% sample are not included in the given parameter.

Margin of error is the amount of miscalculation or difference in change of circumstances from the obtained data.

3% margin of error usually occurs when the data size is small.

As the data size increases the margin of error decreases.

So this statement tells us that we are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Margin of error= z *σ/√n→

This indicates that as the sample size decreases the margin of error increases and vice versa.

3 0

3 years ago

What is the solution of the equation?<br> -39.75 = 7.5m

kolezko [41]

Answer:

m = -5.3

Step-by-step explanation:

-39.75 = 7.5m

Divide both sides by 7.5 to get m alone

-39.75/7.5 = 7.5m/7.5