Problem 10
The two functions <u>are inverses</u> of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).
Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.
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Problem 11
y = a(6)^(t/2)
y = a( 6^(1/2) )^t
y = a(2.4494897)^t
y = a( b )^t
where b = 6^(1/2) = 2.4494897 approximately
Set b equal to 1+r and solve for r
1+r = 2.4494897
r = 2.4494897-1
r = 1.4494897
This rounds to about r = 1.45
The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately
Answers:
The equation is roughly y = a(1 + 1.4494897)^t
The growth rate is approximately 145%
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Problem 12
You have the correct answer. Nice work.
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Problem 13
You are very close to the correct answer. However, you're missing the base of the log.
The answer should be . So you'll need to write in a small "49" under the log.
The general rule is that exponential equations in the form are equivalent to the log version of . For each equation, b is the base. The idea of logs is to isolate the exponent.
Answer:
B) 8 cm
Step-by-step explanation:
Hello, I can help you with this
according to the question
The length of a rectangle is 3 cm greater than the width of the rectangle.
convert this into algebraic terms
Step 1
do the eqution
Let
W,width
L,Length
The length of a rectangle(L) is(=) 3 cm greater than the width (W+3) of the rectangle.
note:3 cm greater than the width (W+3) means that you need add 3 to the width to obtain the length
L=W+3 equation(1)
the area of the rectangle is 40 square cm
Let
A,Area
Area= 40 cm
A=40
also,A=L*W
40=L*W equation(2)
Step 2
solve the equations
L=W+3 equation(1)
40=L*W equation(2)
replace the value of L from equaiton (1) into equation (2)
we are looking for a distance, so we need the positive valur only.
Step 3
Now, replace the value of W into equation (1) to obtain the length
L=W+3 equation(1)
L=5+3
L=8
so, the length is 8 cm, B) 8 cm
Have a nice day.
Answer:
the answer is c hope this helps