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Answers

Answer 1

Answer:

Answer:

a. $f^-^1(x)=(x)/(4) +3$

b. $f(-9)=-48$

c. $f^-^1(-9)=(3)/(4)$

Step-by-step explanation:

In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.

$f^-^1(x)=4x-12$

$y=4x-12$

$x=4y-12$

$x+12=4y$

$(x)/(4) +3=y$

$f^-^1(x)=(x)/(4) +3$

In b, all you have to do is plug in -9 into f(x).

$f(9)=4(9)-12$

$f(9)=-48$

In c, you plug in -9 into inverse function f.

$f^-^1(-9)=(3)/(4)$

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Which number line represents the solutions to |x + 4| = 2?

Answers

Answer:

The solution is represented by the first number line, wich has the solutions x=-6 and x=-2.

Step-by-step explanation:

We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is

$|x+4|=2$

when we clear out the absolute value, we will have two possible solutions:

$x+4=2$

and

$-(x+4)=2$

now we clear x from both equations

$x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2$

$-(x+4)=2 \Leftrightarrow -x-4=2 \Leftrightarrow -2-4=x \Leftrightarrow x=-6$

Then, we have that x=-2 and x=-4 are the solutions for the equation, and therefore the number line that represents the solution is the first one, where the points -6 and -2 are highlighted.

the first number line

given | x + 4 | = 2

removing the bars from the absolute value gives

x + 4 = 2 or x + 4 = - 2

x = 2 - 4 or x = - 2 - 4

x = - 2 and x = - 6 ← solutions

these are indicated on the number line by a solid circle at - 2, - 6

A rectangular prism is 3 meters long, 4 meters wide, and has a total surface area of 94 square meters. What is its height?3 m
4 m
5 m
6 m

Answers

S = 2lw + 3lh + 2wh
94 = 2(3)(4) + 2(3)(h) + 2(4)(h)
94 = 2(12) + 2(3h) + 2(4h)
94 = 24 + 16h + 8h
94 = 24 + 14h
- 24 - 24
70 = 14h
14 14
5 = h

The answer is C.

Answer: answer is C

Step-by-step explanation:

In? gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For? example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is? 3, the odds of winning are 2:3(Note; if the odds of winning are 2/3, the propability of sucess is2/5)The odds of event occuring are 1:6. Find (a) the propability that the event will occur,(b) propability that the event will not occur.

(a)The propability that event will occur is....(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED.)

(b)The propability thet the event will not occur is...(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED)

Answers

Answer:

A) The probability that the event will occur $=(1)/(7)$

B)The probability that the event will not occur = $(6)/(7)$

Step-by-step explanation:

We are given that The odds of event occurring are 1:6.

So, Number of successful events = 1

Number of unsuccessful events = 6

So, Total events = 6+1=7

a)the probability that the event will occur= $\frac{\text{Favorable event}}{\text{Total event}}$

The probability that the event will occur $=(1)/(7)$

b)The probability that the event will not occur = $\frac{\text{Favorable event}}{\text{Total event}}$

The probability that the event will not occur = $(6)/(7)$

Quarterly withdrawls of $650 for 6 years; interest rate is 4.5% compounded quarterly.Find the amount necessary to fund the given withdrawls.

Answers

Answer:

The amount needed to finance this level of withdrawals is $ 9422.06

Step-by-step explanation:

For a fixed amount periodically withdrawn, during $n$ periods, with an interest rate $i$ , there is a present value of:

$V_(p) = A [(1- (1 + i) ^(- n))/(i)]$ . From where,

$V_(p) = 650 [(1- (1 + 0.045)^(-24))/(0.045)] = 9422.06$

The amount needed to finance this level of withdrawals is $ 9422.0609

A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13 hours round your answer to the nearest whole number