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Bingel [31]
3 years ago
10

H(x) = x2 – 3

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

g(x)=x^2+1

Step-by-step explanation:

The given function is

h(x)=x^2-3

If a function translated vertically upward by p units, then we need to add p in the function value to get the new function.

It is given that if the graph of h is translated vertically upward by 4 units, it becomes the graph of a function g. So,

g(x)=h(x)+4

g(x)=x^2-3+4

On simplification, we get

g(x)=x^2+1

Therefore, the required function is g(x)=x^2+1.

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<span>It's 9, so we round up to 4.1</span>
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2 years ago
3) An open top box is to be constructed out of a 90 inch by 70 inch piece of cardboard by cutting squares out of the corners and
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Answer:

a) The volume in cubic inches is 36000

b) The volume in cubic feet is 125/6

c) The volume in cubic yard is 125/162

Step-by-step explanation:

* Lets study the information of the problem to solve it

- The dimensions of the piece of cardboard are 90 inches by 70 inches

- The side of the cutting square is 15 inches

- The squares are cutting from each corner

∴ Each dimension of the cardboard will decrease by 2 × 15 inches

∴ The new dimensions of the piece of cardboard are;

90 - (15 × 2) = 90 - 30 = 60 inches

70 - (2 × 15) = 70 - 30 = 40 inches

- The dimensions of the box will be:

# Length = 60 inches

# width = 40 inches

# height = 15 inches

- The volume of any box with three different dimensions is

V = Length × width × height

∵ The length = 60 inches

∵ The width = 40 inches

∵ The height = 15 inches

∴ V = 60 × 40 × 15 = 36000 inches³

a) The volume in cubic inches is 36000

* Now lets revise how to change from inch to feet

- 1 foot = 12 inches

∵ 1 foot = 12 inches

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∴ 1 foot³ = 1728 inches³

∵ The volume of the box is 36000 inches³

∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6  

b) The volume in cubic feet is 125/6

* Now lets revise how to change from feet to yard

- 1 yard = 3 feet

∵ 1 yard = 3 feet

∴ 1 yard³ = (3)³ feet³

∴ 1 yard³ = 27 feet³

∵ The volume of the box is 125/6 feet³

∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162  

c) The volume in cubic yard is 125/162

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I hope this helps! :)

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