Answer: See below
Step-by-step explanation:
1. (fоg)(x) means f of g(x). You would plug in g(x) into f(x).
(fоg)(x)=3(4x²-5)-3
(fоg)(x)=12x²-15-3
(fоg)(x)=12x²-18
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2. (gоf)(x) means g of f(x). You would plug in f(x) into g(x).
(gоf)(x)=4(3x-3)²-5
(gоf)(x)=4(9x²-18x+9)-5
(gоf)(x)=36x²-72x+36-5
(gоf)(x)=36x²-72x+31
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3. (fоg)(0) means f of g(0). You would plug in g(0) into f(x).
(fоg)(0)=3(-5)-3
(fоg)(0)=-15-3
(fоg)(0)=-18
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4. (gоf)(0) means g of f(0). You would plug in f(0) into g(x).
(gоf)(0)=4(-3)²-5
(gоf)(0)=4(9)-5
(gоf)(0)=36-5
(gоf)(0)=31
A rug is to fit in a room so that a border of even width is left on all four sides.
If the room is 16 feet by 25 feet and the area of the rug is 220 square feet, how wide will the border
:
Let x = the width of the border around the rug
then
(25-2x) by (16-2x) the dimensions of the rug
:
The area equation
(25-2x)*(16-2x) = 220 sq/ft
FOIL
400 - 50x - 32x + 4x^2 = 220
:
Arrange as a quadratic equation
4x^2 - 82x + 400 - 220 = 0
:
4x^2 - 82x + 180 = 0
Simplify, divide by 2
2x^2 - 41x + 90 = 0
Factor
(2x - 5)(x - 18) = 0
Two solutions
2x = 5
x = 2.5 ft
and
x = 18 ft, obviously this not the solution
;
Border will be 2.5 ft
:
:
Check this by finding the dimension of the rug, and then the area
(25 - 2(2.5))*(16 - 2(2.5)) =
(25 - 5) * (16 - 5) =
20 * 11 = 220
Answer:
1, 4, & 6
Step-by-step explanation:
1. is a fraction and fractions are rational numbers
2. 11 is not a perfect square so the answer should be a terminating decimal and terminating decimals are irrational numbers
3. is a terminating decimal and an irrational number
4. .23 is a decimal which is a rational number since it can be made into the fraction 23/100
5. is a terminating decimal which is an irrational number
6. is a fraction which is a rational number
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