1.Draw Angle POQ of measure 75° and find its line of symmetry<br><br> Pls answer with steps

The number of cases of a new disease can be modeled by the quadratic regression equation y = –2x2 + 36x + 6, where x represents

nirvana33 [79]

Since x represents the year, year 15 will be 15 years.

Plug in "15" as your "x"

y = -2(15)^2 + 36(15) + 6

15^2 = 225 (Exponents come before multiplication)

y = -2(225) + 36(15) + 6

y = -450 + 540 + 6

y = 90 + 6

y = 96

<em>The answer is B</em>

3 0

3 years ago

Find the point(s) of intersection (if any) of the plane and the line. Also, determine whether the line lies in the plane. 2x - 2

s2008m [1.1K]

Answer:

the intersection is the point P=(x,y,z)=(8,9,14) and the line does not lie in the plane

Step-by-step explanation:

from the equation of the line

x - 1/2 = y + (3/2)/-1 = (z + 1) / 2 = t (parameter)

then the parametric equation of the line is

x= 1/2 +t

y = (3/2) + t

z = (-1) + 2*t

therefore from the equation of the plane

2x - 2y + z = 12

2*(1/2 +t) - 2[(3/2) + t] + [(-1) + 2*t] = 12

1+2*t - 3 -2*t -1 + 2*t = 12

-3 + 2*t = 12

t= 15/2

therefore there is only one intersection of the line with the plane ( then the line does not lie in the plane , since there would be infinite intersection points). The intersection is

x= 1/2 +t = 1/2 +15/2 = 8

y = (3/2) + t = (3/2) + 15/2 = 9

z = (-1) + 2*t = (-1) + 2*15/2 = 14

thus the intersection point P=(x,y,z)=(8,9,14)

7 0

3 years ago

Ice cream shop is open within the month of june,july and august The shop served 100 fewer customers than they did in july They s

Julli [10]

The number of customers served in the ice cream shop in June, July and August are 125, 25 and 250 customers respectively

<h3>How to write and solve equation?</h3>

let

June = x
July = x - 100
August = 2x
Total customers = 400

Total = June + July + August

400 = x + (x- 100) + 2x

400 = x + x - 100 + 2x

400 = 4x - 100

400 + 100 = 4x

500 = 4x

x = 500/4

x = 125

So,

June = x

= 125 customers

July = x - 100

125 - 100

= 25 customers

August = 2x

= 2(125)

= 250 customers

Learn more about equation:

brainly.com/question/2972832

#SPJ1

5 0

2 years ago

Find the exact value of sin(cos^-1(4/5))

boyakko [2]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2762144

_______________

Let $\mathsf{\theta=cos^{-1}\!\left(\dfrac{4}{5}\right).}$

$\mathsf{0\le \theta\le\pi,}$ because that is the range of the inverse cosine funcition.

Also,

$\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}$

Square both sides and apply the fundamental trigonometric identity:

$\mathsf{(5\,cos\,\theta)^2=4^2}\\\\
\mathsf{5^2\,cos^2\,\theta=4^2}\\\\
\mathsf{25\,cos^2\,\theta=16\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{25\cdot (1-sin^2\,\theta)=16}$

$\mathsf{25-25\,sin^2\,\theta=16}\\\\
\mathsf{25-16=25\,sin^2\,\theta}\\\\
\mathsf{9=25\,sin^2\,\theta}\\\\
\mathsf{sin^2\,\theta=\dfrac{9}{25}}
$

$\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{9}{25}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{3^2}{5^2}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{3}{5}}$

But $\mathsf{0\le \theta\le\pi,}$ which means $\theta$ lies either in the 1st or the 2nd quadrant. So $\mathsf{sin\,\theta}$ is a positive number:

$\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\
\therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>

3 0

3 years ago

Read 2 more answers

How to find when,<br>y=-1/3x - 3<br>

Montano1993 [528]

The -3 would be where your line crosses the y-axis, so you would plot your point at -3. your slope will always be counted as rise/run, basically meaning you would count along the y-axis a certain amount of times, in this case -1, and along the x-axis a certain amount of times, here would be three. your next plot point would be (3,-4) and so on. hope this helped!

7 0

2 years ago

1.Draw Angle POQ of measure 75° and find its line of symmetry Pls answer with steps