Find the minimum maximum and domain and range of the functions h(x) = -x² + 4x - 2

Mathematics

1 answer:

Svet_ta [14]3 years ago

3 0

Domain (-infinity,infinity)

Min(?

max(2,2)

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Bella solves the equation 4(x + p) = 12, where p is a constant. He states that solution to the equation is x = -5. Determine the

liq [111]

Answer:

P=3

Step-by-step explanation:

To solve for p, we can simply substitute his answer in place of x, changing the equation to 4(-5+p)=12. Now we just have to solve it.

1. Apply the distributive property. We can do this by multiplying 4 by -5 and p. Our equation is now -20+4p=12

2. Add 20 on both sides. Since the 20 is negative, we would add it on both sides, canceling out the -20 and leaving us with the equation 4p=32.

3. Now divide 12 by 4. We want to get p alone by itself, so we divide both sides by 4, leaving us with the solution p=3.

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Step-by-step explanation:

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3 years ago

Find the height of a rectangular prism if the surface are is 288 square centimetres and the base has a length of 4 centimetres a

liraira [26]

The rectangular prism below is made up of 6 rectangular faces, and the faces opposite to each other are have an equal area.
The area of one of the faces is lxh or lh, and the area of the face opposite to it is also equal, so the area of those two equal faces is 2lh.
The area of the base of the prism is lxw, and the area of its opposite face is equal, so the area of those two equal faces is 2lw.
The area of the face in the left side of the prism is wxh, and the area of the face opposite to it is also equal, so their combined area is 2wh.
So, to find the total surface area of a rectangular prism, we’d add the sum of all the rectangular faces, so the formula of finding the surface area of a rectangular prism=
2lh+2lw+2wh
=2(lh+lw+wh)
Given,
Surface area of the rectangular prism=288 cm^2
2(lh+lw+wh)=288
2[4h+(4x9)+9h)]=288
4h+(4x9)+9h=288/2
4h+(4x9)+9h=144
13h+36=144
13h=144-36
13h=108
h=108/13
h=8.308 cm
Hope this helps!