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LekaFEV [45]
2 years ago
6

What is the standard form for the quadratic function? g(x) = (x + 1)^2– 2

Mathematics
1 answer:
zloy xaker [14]2 years ago
3 0

Answer: g(x)=x^2+x-1

Step-by-step explanation:

(x+1)^2-2

x^2+2*1*x+1^2-2\\x^2+2x+1-2\\x^2+x-1

You might be interested in
3.If the ratio of lynx to mountain lions and wolverines in the park is 2:3:1.So for every 2 lynx, there are 3 mountain lions and
Zolol [24]
A.  The ratio of lynx to mountain lions to wolverines is 2:3:1.

Thus, there are 2 lynx in the ratio.  If there were 6 lynx, we would have to multiply all of the numbers in the ratio by 3 (because 6/2 = 3) to keep the ratio in the same proportion.  

Therefore, because there is 1 wolverine in the ratio, and 1 * 3 = 3, if there were 6 lynx, there would be 3 wolverines.

b. We can use the same ideas that we had in part a to help us in part b.
There are 3 mountain lions in the ratio, but there are 15 mountain lions in the problem.  Thus, the multiplier is 5, because 15/3=5.

Therefore, because there are 2 lynx in the ratio, and 2*5 = 10, if there were 15 mountain lions, there would be 10 lynx.

c.  There is one wolverine in the ratio, but there are 10 wolverines in the problem.  Thus, the multiplier is 10, because 10/1 = 10

Therefore, because there are 3 mountain lions in the ratio, and 3 * 10 = 30, if there were 10 wolverines in the park, then there would be 30 mountain lions.

d.  The total number of lynx, mountain lions, and wolverines is 30.
To find out how many of each animal there should be, we must make an equation using the ratio and the variable x. 

2x + 3x + 1x = 30

This equation means that the total number of animals together is 30, which is true.  Now let's simplify by combining like terms.

6x = 30

Finally, we can simplify by dividing both sides by the coefficient of x, or 6.

x = 5

Thus, going back to our original equation, we know that the amount of lynx is 2x, mountain lions is 3x, and wolverines is 1x.

Lynx = 2x = 2(5) = 10 lynx
Mountain Lion = 3x = 3(5) = 15 mountain lions
Wolverines = 1x = 1(5) = 5 wolverines

Hope this helps! :)

7 0
3 years ago
Find the volume of the solid generated when R​ (shaded region) is revolved about the given line. x=6−3sec y​, x=6​, y= π 3​, and
Dmitrij [34]

Answer:

V=9\pi\sqrt{3}

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

V=\int\limits^b_a {\pi r^{2}} \, dy

where:

r=6-(6-3 sec(y))

r=3 sec(y)

a=0

b=\frac{\pi}{3}

so the volume becomes:

V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy

This can be simplified to:

V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy

and the integral can be rewritten like this:

V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy

which is a standard integral so we solve it to:

V=9\pi[tan y]\limits^\frac{\pi}{3}_0

so we get:

V=9\pi[tan \frac{\pi}{3} - tan 0]

which yields:

V=9\pi\sqrt{3}]

6 0
3 years ago
marys age is 2 upon 3 that of peters age. two years ago marys age was 1 upon 2 of whats peters age will be in 5years time. how o
Nitella [24]

Answer:

the Peter age be 27

Step-by-step explanation:

Let assume peter be

And, then mary is 2p ÷ 3

So

The equation would be  

2p ÷ 3  - 2 = 1 ÷ 2 (p + 5)

4p - 12 = 3p + 15

p = 27

So Peter age be 27

And, the mary age is

= 2 (27) ÷ 3

= 18

Hence, the Peter age be 27

4 0
2 years ago
The kinetic energy of a moving object, E joules, is directly proportional to the square
Mariulka [41]

Answer:

1/4

Step-by-step explanation:

8 0
3 years ago
Angles use the diagram at the right (HELP PLEASE)
Helga [31]
I need help to because ye this is hard
6 0
2 years ago
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