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3 years ago

The answers to this question

Mathematics

1 answer:

Nana76 [90]3 years ago

7 0

A) f(x) = x - 4 , g(x) = x + 4
⇒ f( g(x) ) = x + 4 - 4 = x
g( f(x) ) = x - 4 + 4 = x
⇒ f and g are not inverses of each other
b) f(x) = -1/(3x) , x ≠ 0 ; g(x) = 1/(3x) , x ≠ 0
⇒ f( g(x) ) = -1/( 3*(1/(3x)) ) = -1/(1/x) = -x
g (f(x) ) = 1/( 3*(-1/(3x)) ) = 1/( -1/x) = -x
⇒ f and g <span>are not inverses of each other</span>

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3 years ago

The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk

ladessa [460]

1. The information given in the problem is:

- <span>The length of a rectangular garden is 8 feet longer than the width.
- </span><span>The garden is surrounded by a 4-foot sidewalk.
- The area of the sidewalk is 320 ft</span>².

2. So, the length of the rectangular garden is:

L1=8+W1

3. The formula for calculate the area of the sidewalk, is:

A2=L2xW2

"A2" is the area of the sidewalk (A2=320 ft²).

"L2" is the length of the sidewalk.

"W2" is the widht of the sidewalk.

4. The length of the sidewalk (L2) is:

L2=L1+4+4 (4 feet on each side)
L2=L1+8

5. When you substitute L1=8+W1 into the equation L2=L1+8, you obtain:

L2=8+W1+8
L2=W1+16

6. The widht of the sidewalk is:

W2=W1+4+4
W2=W1+8

7. Now, you must substitute the length and the widht of the sidewalk into the formula A2=L2xW2:

A2=L2xW2
A2=(W1+16)(W1+8)
320=W1²+16W1+8W1+128
W1²+16W1+8W1+128-320=0
W1²+16W1+8W1-192=0

8. When you solve the quadratic equation, you obtain the value of W1:

W1=16.97 ft

9. Finally, you must substitute the value of W1 into the formula L1=8+W1:

L1=8+W1
L1=8+16.97
L1=24.97 ft

10. Therefore, the dimensions of the garden are:

L1=24.97 ft
W1=16.97 ft

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In the problems below, f(x) = log₂x and

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Answer:

(1,0)

Step-by-step explanation:

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0)

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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 5 times the number o

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Mark and Don have 18 and 92 marbles respectively.

<h3>What is the solution of the equation?</h3>

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

Learn more about equation here:

brainly.com/question/2972832

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