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Leto [7]
3 years ago
6

What is the minimum value of the function g(x) = x2 - 6x – 12? -21 3-21 3 3+21

Mathematics
1 answer:
balandron [24]3 years ago
4 0

Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

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This one is hard! try your best please.
user100 [1]

Answer:

1. 301.6 in^{3}

2. 576 in^{3}

3. 274.41 in^{3}

Step-by-step explanation:

We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and \frac{12}{3} =4. That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.

Then, you can find the volume of the box, because you know its dimentions are 12x12x4.

Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)

3 0
2 years ago
Zachary and his children went into a grocery store and will buy bananas and peaches.
stealth61 [152]

Answer:

0.5b + 1.5p ≤ 8

Step-by-step explanation:

The inequality function is as follows:

Let us assume the number of bananas acquired be b

And, the number of peaches acquired be p

Cost of each banana be $0.50

ANd, the cost of each peach be $1.50

Also the total would be $8

The possible values of banana is 0.5b

And, for peaches it would be 1.5p

So, the inequality function is

0.5b + 1.5p ≤ 8

7 0
3 years ago
(Look at screenshot)
True [87]

#1

Clear shown in graph

  • H(0)=5

#2

No

At. no where graph passes through origin so y intercept is not 0 at anywhere

#3

Domain is x values

  • Domain =[0,oo)

#4

Range is y values set

  • Range=[5,50]
8 0
2 years ago
for a different punch recipe, the equation,s=4c represents the number of cups of seltzer,s, that you need for,c, cups of cranber
asambeis [7]

Answer:

4

Step-by-step explanation:

If two variables are proportional then

y\propto x

y=kx    ...(i)

where, k is constant of proportionality.

The given equation is

s=4c       ...(ii)

where,

s = number of cups of seltzer.

c = cups of cranberry juice.

On comparing (i) and (ii), we get

Independent variable: x=c

Dependent variable: y=s

Constant of proportionality: k=4

Therefore, the constant of proportionality is 4.

8 0
3 years ago
A fish tank that measures 30 inches by 24 inches by 9 inches is filled with water 7/8 of its height. 2/3 of the water leaks out
kondaur [170]
6/5 would be the answer
4 0
3 years ago
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