Alexa wants to purchase some new supplies for making jewelry

Part A. Write an equation of a line that is perpendicular to the line y = 2/3x + 5 and passes through the point (4, 0).

fenix001 [56]

Answer:

$y = -\frac{3}{2}x+6$

Step-by-step explanation:

Given:

The given equation of the line $y = \frac{2}{3} x + 5$ that passes through the point (4, 0).

Part A.

The equation of the line.

$y=mx+c$ -----------(1)

Where:

m = Slope of the line

c = y-intercept

The given equation of the line.

$y = \frac{2}{3} x + 5$

Comparing the given equation with equation 1.

The slope of the line is $m=\frac{2}{3}$ and y-intercept $c = 5$

We know that the slope of the perpendicular line is $(-\frac{1}{m})$ .

So the slope of the perpendicular line is $(m=-\frac{1}{\frac{2}{3}}=-\frac{3}{2})$ .

Using point slope formula we write the equation of the perpendicular line that passes through the point (4, 0).

$y-y_{1} = m(x-x_{1}$

Now we substitute the slope of the perpendicular line $m=-\frac{3}{2}$ and $y_{1} = 0, x_{1}=4$ from point (4, 0) in above equation.

$y-0 = -\frac{3}{2}(x-4)$

$y = -\frac{3}{2}x-(-\frac{3}{2}\times 4)$

$y = -\frac{3}{2}x-(-3\times 2)$

$y = -\frac{3}{2}x-(-6)$

$y = -\frac{3}{2}x+6$

Therefore the perpendicular line equation is $y = -\frac{3}{2}x+6$ .

Part B.

1. The slope of the perpendicular line is $m=-\frac{3}{2}$ .

2. The y-intercept of the perpendicular line is 6.

3. The equation of the line $y = -\frac{3}{2}x+6$ is perpendicular to the equation of line $y = \frac{2}{3} x + 5$ .

6 0

3 years ago

1The first three figures in a pattern are shown here. What is the fourth

goldfiish [28.3K]

Answer:

D

Step-by-step explanation:

The pattern is each end of the figure is expanding by one. A and C are automatically out because there is nothing in the middle of any figure in the previous pattern. B is out because it is the same as figure three. D is correct because it follows the rule of the pattern by expanind outwards one block on each end.

4 0

3 years ago

Select the correct answer

IgorC [24]

Answer:

b

Step-by-step explanation:

a x (b + c) = (a x b) + (a x c)

6 0

3 years ago

Read 2 more answers

Can someone please please help me out I don’t understand this

MatroZZZ [7]

Answer:

Step-by-step explanation:

5 0

3 years ago

9 cm and the other leg measures 11 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

nasty-shy [4]

Answer:

14.2 cm

Step-by-step explanation:

The hypotenuse of a triangle is measured using the pythagorean theorem. This formula sums up the squares of both legs of the triangle which would give the squared value of the hypotenuse. Therefore, we can then square root that value to find the hypotenuse. This would be the following...

$9^{2} + 11^{2} = x^{2}$

81 + 121 = $x^{2}$

202 = $x^{2}$

14.21 = $x^{2}$

Finally, we can see that the value of the hypotenuse is 14.2 cm

8 0

3 years ago