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Phantasy [73]
3 years ago
14

Find the distance between the pair of points and then round your answer to the nearest tenth.

Mathematics
1 answer:
Travka [436]3 years ago
3 0

Answer:

d = 9.4 units (nearest tenth)

Step-by-step explanation:

Given the distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, distance between (-4, 5) and (4, 0) is calculated as follows:

Let (-4, 5) = (x_1, y_1)

(4, 0) = (x_2, y_2)

d = \sqrt{(4 - (-4))^2 + (0 - 5)^2}

d = \sqrt{(8)^2 + (- 5)^2}

d = \sqrt{64 + 25}

d = \sqrt{89}

d = 9.4 units (nearest tenth)

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Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9 ; (–6,
matrenka [14]

Answer:

y = - \frac{3}{2} x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{2}{3} x + 9 ← is in slope- intercept form

with slope m = \frac{2}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{2}{3} } = - \frac{3}{2}, thus

y = - \frac{3}{2} x + c ← is the partial equation

To find c substitute (- 6, 5) into the partial equation

5 = 9 + c ⇒ c = 5 - 9 = - 4

y = - \frac{3}{2} x - 4 ← equation of perpendicular line

5 0
3 years ago
Find the exact solutions of x2 − 3x − 5 = 0 using the quadratic formula. Show all work! 75 points please help!!!!!
noname [10]

Answer:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Step-by-step explanation:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0

<u>Given quadratic equation</u>:

x^2-3x-5=0

<u>Define the variables</u>:

\implies a=1, \quad b=-3, \quad c=-5

<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:

\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}

\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}

\implies x=\dfrac{3 \pm \sqrt{29}}{2}

Therefore, the exact solutions to the given <u>quadratic equation</u> are:

x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}

Learn more about the quadratic formula here:

brainly.com/question/27868610

brainly.com/question/27750885

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2 years ago
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slamgirl [31]
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noname [10]

Answer:

It's right :)

Explanation:

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