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adoni [48]
3 years ago
11

The equation of the line that goes through the points ( − 3 , − 9 ) and ( − 6 , − 3 ) can be written in the form y = m x + b

Mathematics
1 answer:
ivolga24 [154]3 years ago
8 0

Answer:

y=-2x-15

Step-by-step explanation:

y=mx+b.

m is the slope of the line. To find it we can do \frac{dy}{dx} which is the difference between the y-coordinates divided by the difference between the x-coordinates.

So: \frac{dy}{dx} =\frac{-9-(-3)}{-3-(-6)} =\frac{-6}{3} =-2. Now we have the slope, let's input a set of coordinates into the equation so that we can find the constant b.

-9=-2(-3)+b

b=-15 - Re-arranging to get b

Now re-write the equation as we have the constants.

y=-2x-15

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The degree of the polynomial function below is ____ <br> f(x)=-3x^5+4x-2
andreev551 [17]

Answer:

the degree of the polynomial is 5

4 0
3 years ago
A woman has a total of $9,000 to invest. She invests part of the money in an account that pays 7 % per year and
Volgvan

Answer:

Hi! I believe this is your answer:

$750

Step by step explanation:

interest + interest      = total interest

0.08*x   + 0.09*(9000-x) = 750    dollars

0.08x + 810 - 0.09x = 750

-0.01x = 750 - 810 = -60  ====>  x = %28-60%29%2F%28-0.01%29 = 6000.

Final answer:  

$6000 was invested at 8%.  The rest   9000-6000 = 3000 dollars were invested at 9%.

Check.   0.08*6000 + 0.09*3000 = 480 + 270 = 750 dollars.

6 0
2 years ago
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
ryzh [129]

First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

t=0\implies f(10,0)=155

t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299

t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
Please help!!! I will give brainliest but only if you try and help.
Slav-nsk [51]

Answer:

<h2>____</h2><h3>1260 </h3><h2>____</h2>

Since we have to predict, we can use ratios to help us solve this.

12 said yes out of 72 randomly chosen, SO,

if 210 would say yes (goes to play), how many is total??

12 is to 72 AS 210 is to HOW MUCH (let it be x)??

We can setup ratio, cross multiply, and solve for x:

= 12/72= 210/x

= 12x = 210*72

=12x = 15,120

=x = 15,120/12

<h2>=x =1260</h2>

8 0
3 years ago
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Nataly [62]
We are given a watermelon dropped at free fall from a building 320 meters above the sidewalk. Superman is headed down at 30 meters per second. We are asked to determine how fast is the watermelon going when it passes Superman. To solve for the final velocity of the watermelon, we will use one of the kinematic equations (free fall):

vf = vi + a*t

where vf is the final velocity
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            a is the acceleration, in this case, gravitational acceleration = 9.8m/s^2
            t is time

we also need to set-up another equation using the distance:

d = vf + vi / 2 * t

(1) 320 m = vf * t /2

(2) vf = 9.8 m/s^2 * t

From here, we have two equations and two unknown, thus we can solve the problem by substitution. 

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8 0
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