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3 years ago

5

Write an equation of a line in point-slope and slope intercept form that passes through the point (1, -8) and is perpendicular t

o the line: 2x-4y = -11

1 answer:

prisoha [69]3 years ago

3 0

Answer:

11y-2x= -90

Step-by-step explanation:

for the point (1,-8)

x=1 and y= -8

for the equation,

2x -4y= -11

x= -1/m

m= -1/x

x = -1/ (-11/2 )

m= 2/11

so for the equation,

y-y1= m(x- x1)

y- -8=2/11(x-1)

11(y+8)= 2(x-1)

11y +88= 2x-2

11y-2x= -90

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Prove that :( 1 + 1/<img src="https://tex.z-dn.net/?f=tan%5E%7B2%7DA" id="TexFormula1" title="tan^{2}A" alt="tan^{2}A" align="ab

Aliun [14]

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

$\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}$

<u>Right part:</u>

$\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}$

Since simplified left and right parts are the same, then the equality is true.

3 0

3 years ago

Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by p = 130e0.0205t,wh

svetoff [14.1K]

Answer: a) 236,000.

b) 2021

Step-by-step explanation:

Given : Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by $p = 130e^{0.0205t}$ (1)

where t = 0 corresponds to 1980.

Then , for 2009

t= 2009-1980=29

a. ⇒The population of Phoenix in 2009 = $p = 130e^{0.0205(29)}$

$p = 130e^{0.5945}$

$p =130(1.81212465608)=235.57620529\approx236$

Hence, the population of Orlando in 2009 was about 236,000.

b) Substitute p= 300 in (1) , we get

$300 = 130e^{0.0205t}$

$2.3077= e^{0.0205t}$ (Divide both sides by 130)

Taking Natural log on both sides,

$\ln(2.3077) = 0.0205t\\\\\Rightarrow\ t=\dfrac{\ln(2.3077)}{0.0205}$

$t=\dfrac{0.836251357528}{0.0205}=40.7927491477\approx41$

Hence, The year Orlando will have a population of 300,000 =1980+41 =2021

6 0

3 years ago

The sale price of the new car was $14,500. The sales tax rate was 6.5 percent. What was the sale tax on the car?

elixir [45]

$942.50.

$14,500 x 0.065 = $942.50

6.5% = 0.065

3 0

3 years ago

Which is the graph of y= [X] - 2?

Vera_Pavlovna [14]

Answer:

The third one from left

8 0

3 years ago

Read 2 more answers

Donna is running around a track.It takes her 3 1/2 minutes to run 1/4 of a lap.If she keeps running at the same speed,how long w

meriva

Answer:

70 minutes

Step-by-step explanation:

3 1/2 ÷1/4= 14 ×5= 70

so you first make 3 1/2 to an improper fraction, then you find the greatest common denominator between 7/2 and 1/4 which is 4, so you multiple 7/2 by 2 and get 14/4 and divide that by 1/4 and get 14minutes now multiply that by 5 laps and receive 70 minutes.

6 0

3 years ago