Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins 2 years younger than Lana. When the four sisters' ages are added together, the result is 45. If the youngest sister is n years old, what is n?

By definition, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.

The inverse or reciprocal function of f(x) is called another function f⁻¹(x) that satisfies: If f(x)=y , then f⁻¹(y)=x.

To build or calculate the inverse function of any function, one of the ways to do it is to interchange the variables x and y, and use a combination of algebraic methods in order to isolate the variable "y".

Being f(x)=y=4x, to calculate the inverse, in first place you interchange the variables x and y:

f(y)=x=4y

Isolating the variable y, you get:

h(x)=x÷4= [tex]\frac{1}{4}[/tex]x

Finally, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.

Learn more about the inverse of a function:

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Answer:

y=x+30

Step-by-step explanation:

use y2-y1/x2-x1 to find the slope

the y-int is 30 since looking at the answer choices

Answer:

y=x+30

Step-by-step explanation:

Answer:

17%

Step-by-step explanation:

12,750/75,000=0.17

Which means it's 17%

Brainliest please-

Answer:

I do believe that the answer is 0 solutions.

Step-by-step explanation:

x+10 =x+5

Subtract 5 from both sides, you get:

x+5=x

Subtract x from both sides, and you get:

5=0 which is NOT true. Also I maybe wrong, pls don't be mad at me.

Step-by-step explanation:

point (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4) .

Step-by-step explanation:

Given function f(x)=x(x-4)f(x)=x(x−4) also point (2+ c,y) is on the graph of f(x) ,

We have to find out of given point which point will also be on the graph of f(x).

Consider the given function f(x)=x(x-4)f(x)=x(x−4)

f(x)=x(x-4)f(x)=x(x−4) can be rewritten f(x)=x^2-4xf(x)=x

2

−4x

Now we substitute the given point (2+ c, y) in the function given ,

we have,

f(x)=y=x(x-4)f(x)=y=x(x−4)

put for x as 2+c , we have,

\Rightarrow y=(2+c)(2+c-4)⇒y=(2+c)(2+c−4)

Solve, we get

\Rightarrow y=(2+c)(c-2)⇒y=(2+c)(c−2)

Thus, both point (2+c, y) and (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4)

Thus, option (1) is correct.

Answer:

4. The expression has a value of 1/36 . True

5. An equivalent expression is (6)^5. (6)^- 7  True

Step-by-step explanation:

Not true. The 6 without an exponent is equivalent to the 6 having a 0 exponent.

6 · (6)^0 · (6)^–3

= 6.1.1/216

= 1/36

= (6)^-2

2. The sum of exponents is 2.  

False ( the sum of exponents is -2)

3.Multiply the exponents to solve the expression .

False when the bases are the same the exponents are added or subtracted.

4. The expression has a value of 1/36 .

True

5. An equivalent expression is (6)^5. (6)^- 7

True

Answer:

The last two answers d and e

Step-by-step explanation:

Answer:

y - 5 = 1/4 (x+1)

Step-by-step explanation:

y - 5 = 1/4 (x - (-1))

to simplify the problem you can change (x - (-1)) to (x+1) because subtracting a negative is the same as adding a positive

y - 5 = 1/4 (x+1)

and that is your final answer if you want to keep it in point slope formula

Answer:

(5,1)

(3,4)

(2,2)

(1,5)

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[tex]s(av) = \frac{∆x}{∆t} \\ [/tex]

[tex]s(av) = average \: \: speed[/tex]

[tex]∆x = covered \: \: distance[/tex]

[tex]∆t = time \: \: of \: \: the \: \: covered \: \: distance \\ [/tex]

_________________________________

[tex]s(av) = \frac{183}{3} \\ [/tex]

[tex]s(av) = 61 \: \: \frac{mile}{hour} [/tex]

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Answer:

plz mark brainliest

Step-by-step explanation:

16/3 or 5 1/3

Answer:

[tex]u=\frac{16}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

[tex]\frac{7}{6} =\frac{u+4}{8}[/tex]

Step 2: Solve for u

Step 3: Check

Plug in u into the original equation to verify it's a solution.

Here we see that 7/6 does indeed equal 7/6.

∴ [tex]u=\frac{16}{3}[/tex] is a solution of the equation.

Answer:

41.7

Step-by-step explanation:

[tex]10(2 + 3) - 8.3 \\ \\ = 10 (5) - 8.3 \\ \\ = 50 - 8.3 \\ \\ = 41.7[/tex]

I think 45

Step-by-step explanation:

120-30=90

90 pieces are gone and divide that by two for each friend

90÷2=45 so he has 45 friends?

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

There isn't anything to choose from.

However, if your expression is (1.5)^3, then the answer is 3.375. You can match this up to what choices you have.

1.5^3=3.375

1.5*1.5*1.5=3.375

Answer:

One expression is 3(1.5)

Step-by-step explanation:

Here"s why:

The order of multiplication doesn't matter. For example, 3 times 5 is 15 and 5 times 3 is also 15.

I hope this is somewhat you were looking for!!   :)

Answer:

43

Step-by-step explanation:

Answer: I dont know what the fill in the blank would be, but simply make any number not negative

Step-by-step explanation: Example |-3| = 3

there are always positive

Answer:

y=x+6 is the correct answer:)

Step-by-step explanation:

Answer:

True

Step-by Step Explanation:

Answer:

you cant have two variables

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

-22 is the quotient

Answer: -22

Hope this helps.

Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

Answer:its 7 because half of 14 cp=14 so pd =7

Step-by-step explanation:

Answer:

undefined slope

Step-by-step explanation:

This is a vertical line parallel to the y- axis.

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (- 5, - 6) ← 2 points on the line

m = [tex]\frac{-6+3}{-5+5}[/tex] = [tex]\frac{3}{0}[/tex]

Since division by zero is undefined then the slope is undefined.

Note that all vertical lines have an undefined slope

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Learn more probability about here:

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Answer:

Step-by-step explanation:

I'm 8th grade, G

For this problem, you can start by taking the 35 and dividing it by 5 to get 7. Then you need to take 300 and divide that by 5 to get the right proportions. Then you can take your new number from 300 and divide that by 7, and you should not be on the right path because I'm probably an idiot.

Sorry bout it

Answer:

hi

Step-by-step explanation: