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3 years ago

Find the inverse of the function.

Mathematics

1 answer:

Akimi4 [234]3 years ago

3 0

Answer:

Step-by-step explanation:

The inverse is found by interchanging the x and y values and solve the result for y.

I will use y for f(x)

y = 4x^2

Inverse

x = 4y^2 Divide by 4

x/4 = 4y^2 /4

x/4 = y^2 Take the square root of both sides.

sqrt(x/4) = sqrt(y^2)

y = sqrt(x/4)

g(x) = sqrt(x/4) If you have a very fussy teacher, the inverse function could be written as

g(x) = +/- sqrt(x)/2

I expect that if the question is computer marked, I would try g(x) = sqrt(x)/2 first.

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Alex collects coins that appreciate (increase in) value. At the store he has found three coins that he likes and can afford. Hel

Step2247 [10]

Answer:

Initial: 25 40 60

Year 10: 25.70 40.50 60.25

Year 20: 27.45 42.70 64.50

Step-by-step explanation:

7 0

3 years ago

PLEASE HELP

SVEN [57.7K]

Answer:

Son's Age: 11

Mary's Age: 33

Step-by-step explanation:

Let set Mary and her son as variables,

M = Mary's age

S = Mary's son age

Breakdown:

"Mary is three times as old as her son"

M = 3S

"In 12 years, Mary's age will be one less than twice her son's age"

M + 12 = 2(S + 12) - 1

we add 12 to both sides as it will be in 12 years for both

We know that M = 3S, so we plug this in

3S + 12 = 2(S + 12) - 1

Now solve for S (son's age),

3S + 12 - 12 = 2(S + 12) - 1 - 12

3S = 2(S + 12) - 13

3S = 2S + 24 - 13

3S - 2S = 2S - 2S + 24 - 13

S = 24 - 13

S = 11

To find Mary age, plug in her son age ,

M = 3S

M = 3(11)

M = 33

Learn more about Substitution here: brainly.com/question/22340165

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2 years ago

Natalie used 112 inches blue yarnas a border around her rectangular bulletin board. If the bulletin board is 36 inches wide, how

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3 years ago

A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probab

VashaNatasha [74]

Answer:

(a) P (Both vehicles are available at a given time) = 0.81

(b) P (Neither vehicles are available at a given time) = 0.01

Step-by-step explanation:

Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.

Given:

The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)

P (A) = P (B) = 0.90

(a)

Compute the probability that both vehicles are available at a given time as follows:

P (Both vehicles are available) = P (Vehicle 1 is available) ×

P (Vehicle 2 is available)

$P(A\cap B)=P(A)\times P(B)$

$=0.90\times0.90\\=0.81$

Thus, the probability that both vehicles are available at a given time is 0.81.

(b)

Compute the probability that neither vehicles are available at a given time as follows:

P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×

[1 - P (Vehicle 2 is available)]

$P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\$

$=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01$

Thus, the probability that neither vehicles are available at a given time is 0.01.

(c)

Compute the probability that at least one vehicle is available at a given time as follows:

P (At least one vehicle is available) = 1 - P (None of the vehicles are available)

$=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99$

Thus, the probability that at least one vehicle is available at a given time is 0.99.

6 0

3 years ago

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, 3).

cupoosta [38]

Answer:

$y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)$

$y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)$

Step-by-step explanation:

Hi there!

Point-slope form: $y-y_1=m(x-x_1)$ where $m$ is the slope and $(x_1,y_1)$ is a point that falls on the line

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-4, 7) and (5, 3):

$m=\frac{\displaystyle 3-7}{\displaystyle 5-(-4)}\\\\m=\frac{\displaystyle 3-7}{\displaystyle 5+4}\\\\m=\frac{\displaystyle -4}{\displaystyle 9}$

Therefore, the slope of the line is $-\frac{\displaystyle 4}{\displaystyle 9}$ . Plug this into $y-y_1=m(x-x_1)$ as $m$ :

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

2) Plug a point into $y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)$

Because we're given two points, there are two ways we can write this equation:

$y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x-(-4))\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)$

$y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)$

I hope this helps!

4 0

3 years ago