Evaluate this exponential expression. 4^5

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

Learn more about function here:

https://brainly.com/question/29633660

#SPJ1

Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

The balance in the account after 30 years will be $91,745.06, the total amount of money put into the account will be $54,000 and  the total interest earned will be $37,745.06.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for the future value of an annuity to answer these questions:

FV = PMT(((1 + r)ⁿ - 1) / r)

a. To find how much will be in the account in 30 years, we need to calculate the future value of the annuity after 30 years of monthly deposits.

There are 12 months in a year, the number of months is:

n = 30 years × 12 months/year = 360 months

The monthly interest rate is:

r = 3% / 12 = 0.0025

Substituting the given values into the formula, we get:

FV = $150 × (((1 + 0.0025)³⁶⁰ - 1) / 0.0025)

= $91,745.06

b. To find the total amount of money put into the account, we need to multiply the monthly payment by the number of months:

Total amount = $150/month × 360 months
= $54,000

c. To find the total interest earned, we need to subtract the total amount of money put into the account from the future value of the annuity:

Total interest = $91,745.06 - $54,000

= $37,745.06

Therefore, the balance in the account after 30 years will be  $91,745.06, the total amount of money put into the account will be $54,000 and  the total interest earned will be $37,745.06.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ2

We can expand

\(f(x,y,z) = xy\ln(yz) = xy \ln(y) + xy\ln(z)\)

Then using the product and chain rules,

\(\dfrac{\partial f}{\partial x} = y\ln(y) + y\ln(z) + \boxed{y\ln(yz)}\)

\(\dfrac{\partial f}{\partial y} = x\ln(y) + \dfrac{xy}y + x\ln(z) = \boxed{x\ln(yz) + x}\)

\(\dfrac{\partial f}{\partial z} = \boxed{\dfrac{xy}z}\)

The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

To learn more about inequality;

brainly.com/question/28823603

#SPJ1

Answer:

A. -4 and 4

B. No solution.

Step-by-step explanation:

The given equation is

\(\dfrac{3}{x+4}+\dfrac{2}{x-4}=\dfrac{16}{(x+4)(x-4)}\)

A.

Equate the denominators equal to 0 to find the restrictions on the variable.

\(x+4=0\Rightarrow x=-4\)

\(x-4=0\Rightarrow x=4\)

Therefore, \(x\neq -4,4\).

B.

We have,

\(\dfrac{3}{x+4}+\dfrac{2}{x-4}=\dfrac{16}{(x+4)(x-4)}\)

\(\dfrac{3(x-4)+2(x+4)}{(x+4)(x-4)}=\dfrac{16}{(x+4)(x-4)}\)

Multiply both sides by (x-4)(x+4).

\(3x-12+2x+8=16\)

\(5x-4=16\)

Add 4 on both sides.

\(5x=16+4\)

\(5x=20\)

Divide both sides by 5.

\(x=4\)

Here the solution is x=4 but it is the restricted value.

Therefore, the given equation has no solution.

For the given rational equation, we have that:

The rational equation given in this problem is:

\(\frac{3}{x + 4} + \frac{2}{x - 4} = \frac{16}{(x + 4)(x - 4)}\)

Then, applying the least common factor:

\(\frac{3(x - 4) + 2(x + 4)}{(x + 4)(x - 4)} = \frac{16}{(x + 4)(x - 4)}\)

\(\frac{5x - 4}{(x + 4)(x - 4)} - \frac{16}{(x + 4)(x - 4)} = 0\)

\(\frac{5x - 20}{(x + 4)(x - 4)} = 0\)

Item a:

The denominator cannot be zero, hence:

\((x + 4)(x - 4) \neq 0\)

\(x \neq -4\)

\(x \neq 4\)

The values of the variable that make(s) the denominators zero are x = -4 and x = 4.

Item b:

\(5x - 20 = 0\)

\(5x = 20\)

\(x = \frac{20}{5}\)

\(x = 4\)

However, x = 4 makes the denominator zero, hence the equation has no solution.

You can learn more about rational functions at https://brainly.com/question/13136492

1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

read more about the construction of numbers at:

https://brainly.in/question/55819681

Answer:

A. Shifted 3 unit right and 2 unit down

Step-by-step explanation:

Let's determine the reason for the answer.

We will use a reference point, only one point to determine the reason.

Because the both shape are identical.

Let's use point A

The position of A is 2 on the y axis and 1 on the x axis

While the position of A' is 0 on the y axis and 4 on the X asis

Let's know how many units where moved from the position.

A' -A

For X axis

4-1= 3

For y axis

0-2= 2(we need only the magnitude)

So its 2 units Down and 3 unit right

Answer:

(x,5)

Step-by-step explanation:

If the line is horizontal, the y values cannot change.  So, for a line of infinite length, there are infinite possible values for x but only a single value for y.  Any ordered pair in which the y value is 5 is an acceptable answer.

The expression using the common factor is 1/12xy(x² + 5y)

From the question, we have the following parameters that can be used in our computation:

1/12 x^3 y + 5/12 xy^2

Rewrite properly

So, we have

1/12x³y + 5/12xy²

Factor out 1/12 from the expression

So, we have the following representation

1/12(x³y + 5xy²)

Factor out x from the expression

So, we have the following representation

1/12x(x²y + 5y²)

Factor out y from the expression

So, we have the following representation

1/12xy(x² + 5y)

Hence, the expression is (c) 1/12xy(x² + 5y)

Read more about common factor:

brainly.com/question/25266652

#SPJ1

Answer:The expression using the common factor is 1/12xy(x² + 5y)

Step-by-step explanation:

The amount of the down payment and the mortgage amount are $61440 and $194560

From the question, we have the following parameters that can be used in our computation:

Buy a $256,000 home with a down payment of 24%

This means that

down payment = 24% * 256,000

So, we have

down payment = 61440

Next, we have

mortgage amount = (1 - 24%) * 256,000

So, we have

mortgage amount = 194560

Hence, the mortgage amount is 194560

Read more about percentage at

https://brainly.com/question/24877689

#SPJ1

The sentences that is written in subjunctive mood is C. I wish you'd turn the lights off when you leave the room.

The subjunctive mood  can be regarded as the hypothetical scenario  that is been used in English, it can can be considered as the one that is been used to express a wish.

In some cases be used in the process of making  that recommendation, or demand, in the option C it can be seen that it is used to express wishes and this is the reason why it is been considered as a  subjunctive mood.

Learn more about mood at:

https://brainly.com/question/760210

#SPJ1

Answer: I wish you'd turn the lights off when you leave the room.

Answer:

d

Step-by-step explanation:

i took the test

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Learn more about monthly installment at https://brainly.com/question/3260195

#SPJ1

Answer: -2 and 4

Step-by-step explanation:

\(f(x) = \frac{-2x+2}{2x+4}\)            g(x) = -2x+8

Question asks what the domain is if we had f(x) ÷ g(x)

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4}\)  ÷                  >When dividing fractions, keep the first

                                                      Change the sign, flip the second fraction

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4} * \frac{1}{-2x+8}\)        

\(\frac{f(x)}{g(x)} = \frac{-2x+2}{(2x+4)(-2x+8)}\)          

> you can never get a 0 on the bottom of division so that is where the exception of what x cannot be.

2x+4 = 0

2x= -4

x =  -2

and

-2x+8 = =

-2x = -8

x = 4

So x cannot be -2 and 4

is this what u need.....

The AA similarity postulate states that two triangles are similar if they have 2 congruent angles. Looking at the image we can see that we have 2 lengths and one angle, but the AA similarity postulate states that we need 2 angles, then no, we cannot use AA similarity postulate to prove that they are similar. because there is only one known angle measure.

So what can we use to prove that the triangle is similar? Here, we can use SAS (side, angle, side). Anyway, the final answer is: No, because there is only one known angle measure.

The question asks for horizontal distance, the ball starts at (0,4) and lands at (14,0) so it's displacement is 14 right 4 down

Answer:

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Step-by-step explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

Answer:

Step-by-step explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

Answer: 11,12,149

Step-by-step explanation:

Answer

Its 11, 12, 149

Step-by-step explanation

Square foot of 11 = 3.31662479036

Square foot of 12 = 3.46410161514

Square foot of 149 = 12.2065556157

Answer:

$13.86

Step-by-step explanation:

Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86

Hopefully this helps- let me know if you have any questions!

Answer:

Okay I got youuu

Step-by-step explanation:

From the point Z go 5 right and 3 units up (5,3), and label it Z'. Do this for L and X, too.

The final answer is Z'(2,3) X'(5,0) L'(3,-1)! Hope this helps!

The experimental probability of the next balloon sold being green is 4/15.

Probability is a crucial concept in the field of mathematics that is used to measure the likelihood of an event happening.

According to the information given, the number of green balloons sold is 20, and the total number of balloons sold is the sum of all the colors, which is:

20 + 17 + 12 + 19 + 7 = 75

Now we can use these numbers to calculate the experimental probability of a green balloon being sold:

Experimental probability of a green balloon being sold = Number of green balloons sold / Total number of balloons sold

Experimental probability of a green balloon being sold = 20 / 75

Experimental probability of a green balloon being sold = 4/15

This means that if we randomly select a balloon from the store, the likelihood of it being green is 4 out of 15 or approximately 0.27 or 27%.

To know more about probability here

https://brainly.com/question/11234923

#SPJ1

Answer:

4/15

Step-by-step explanation:

Answer:

It's 11:55

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

please leave a rate and a like hope it helped

Answer:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.

Answer:

According to the estimate, there are 320 foxes in the area

Step-by-step explanation:

This is the mark-recapture method for estimating a  population,

For this, we have the formula,

N = (M*C)/R

Where N is the total population,

M is the number of animals captured (and then marked) the first time,

C is the number of animals captured on the 2nd try

R is the number of Marked animals captured on the 2nd try

So, in our case,

He catches 80 foxes, marks them

M = 80

he catches 36 foxes a few days later,

C = 36

He finds that 9 are marked

R = 9

So,

N = (36)(80)/9

N = 4(80)

N = 320

There are 320 foxes in the area

Answer: (-2,3)

Step-by-step explanation:

2x-5y=-19    (1)

-3x+y=9       (2)

2x-5y=-19     (3)

y=3x+9          (4)

2x-5(3x+9)=-19

2x-15x-45=-19

-13x=-19+45

-13x=26

Divide both parts of the equation by -13:

x=-2

Substitute the value of x=-2 into equation (4):

y=3(-2)+9

y=-6+9

y=3

Thus, (-2,3)

Answer:

9:103° is the answer because of vertically opposite angle

10: 119° is the answer because of alternate angle

Hope it helps you...

Step-by-step explanation:

mark me brainliest

The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵

From the question, we have the following parameters that can be used in our computation:

1/7log(x - 1) = 3log(2)

3 ln(w + 6) = 5 ln(6)

Solving the equation (1), we have the following equation

1/7log(x - 1) = 3log(2)

Multiply both sides of the equation by 7

So, we have the following representation

log(x - 1) = 21log(2)

Apply the power rule of logarithm

log(x - 1) = log(2)²¹

By comparison, we have

x - 1 = (2)²¹

Evaluate the exponent

x - 1 = 2097152

So, we have

x = 2097153

Solving the equation (2), we have the following equation

3 ln(w + 6) = 5 ln(6)

Multiply both sides of the equation by 1/3

So, we have the following representation

ln(w + 6) = 5/3 ln(6)

Apply the power rule of logarithm

ln(w + 6) = ln(6)³/⁵

By comparison, we have

w + 6 = (6)³/⁵

So, we have

w = (6)⁻²/⁵

Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵

Read more about equations at

https://brainly.com/question/2476251

#SPJ1