How many solutions does 5x+17=4(3x-1) have?

Which equation represents a line that is perpendicular to line PQ?

valentinak56 [21]

Answer:

B. y=1/3x+4

Step-by-step explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is $\frac{y_2-y_1}{x_2-x_1}$ where ( $x_{1}$ $y_1$ ) and ( $x_2$ , $y_2$ ) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

x1=-8

y1=7

x2=-4

y2=-5

Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m= $\frac{(-5-7)}{(-4--8)}$

simplify

m= $\frac{-5-7}{-4+8}$

add

m=-12/4

divide

m=-3

So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!

3 0

4 years ago

Erin decided to divide 1,653 by 27 using partial quotient with multiples of 20. What are all the partial quotients Erin should s

podryga [215]

1,653÷27=61.2
61.2×20=1224

7 0

4 years ago

Read 2 more answers

If z1= 3+3i and z2=7(cos(5pi/9) + i sin (5pi/9)), then z1/z2= blank

mixas84 [53]

$z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill$

$\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill$

$\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill$

6 0

3 years ago

If 5-3(2a+1)=-4a+10, what is the value of a+2

AlekseyPX

Answer:

-2

<em>BRAINLIEST, PLEASE!</em>

Step-by-step explanation:

5 - 3(2a + 1) = -4a + 10

5 - 6a - 3 = -4a + 10

2 - 6a = -4a + 10

-2a = 8

a = -4

-4 + 2 = -2

5 0

3 years ago

Read 2 more answers

The number sentence 4x7=4x3 + 4x4 is an example of what property?

GarryVolchara [31]

It the property of distributive

8 0

3 years ago