Identify the question that is NOT statistical

Triangles PQR and RST are similar right triangles. Which proportion can be used to show that the slope of LaTeX: \overline{P

alukav5142 [94]

Question:

Triangles PQR and RST are similar right triangles. Which proportion can be used to show that the slope of PR is equal to the slope of RT?

Answer:

$\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}$

Step-by-step explanation:

See attachment for complete question

From the attachment, we have that:

$P = (-7,7)$

$Q = (-7,3)$

$R = (-4,3)$

$S = (-4,5)$

$T = (2,-5)$

First, we need to calculate the slope (m) of PQR

Here, we consider P and R

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$P(x_1,y_1) = (-7,7)$

$R(x_2,y_2) = (-4,3)$

$m = \frac{y_2 - y_1}{x_2 - x_1}$ becomes

$m = \frac{3 - 7}{-4 - (-7)}$ --------- (1)

Next, we calculate the slope (m) of RST

Here, we consider R and T

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$R(x_1,y_1) = (-4,3)$

$T (x_2,y_2)= (2,-5)$

$m = \frac{y_2 - y_1}{x_2 - x_1}$ becomes

$m = \frac{-5 - 3}{2 - (-4)}$ ---------- (2)

Next, we equate (1) and (2)

$\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}$

From the list of given options (see attachment), option A answers the question

4 0

2 years ago

Solve the equation identify extraneous solutions

PIT_PIT [208]

Answer:

Step-by-step explanation:

The goal to solving any equation is to have x = {something}. That means we need to get the x out from underneath that radical. It's a square root, so we can "undo" it by squaring. Square both sides because this is an equation. Squaring both sides gives you

$x^2=-3x+40$

Get everything on one side of the equals sign and set the quadratic equal to 0:

$x^2+3x-40=0$

Throw this into the quadratic formula to get that the solutions are x = 5 and -8. We need to see if only one works, both work, or neither work in the original equation.

Does $5=\sqrt{-3(5)+40}$ ?