(5x–7)–5(7x–12)+7=0
Help please

Answer:

[tex] g ( x ) * f ( x ) = ( x + 9 ) ^ 2 [/tex]

Step-by-step explanation:

We are given the following two functions and we are to find [tex]g(x) * f(x)[/tex]:

[tex]f(x)=x2-81[/tex]

[tex]g(x)=(x - 9)^{-1} ( x + 9)[/tex]

[tex]g(x)*f(x)=x^{-81} * \frac{x+9}{x-9}[/tex]

[tex]g ( x ) * f ( x ) =\frac{(x+9)(x-9)(x+9)}{x-9}[/tex]

[tex] g ( x ) * f ( x ) = ( x + 9 ) ( x + 9 ) [/tex]

[tex]  g ( x ) * f ( x ) =( x + 9 ) ^ 2 [/tex]

For this case we have the following fusions:

[tex]f (x) = x ^ 2-81\\g (x) = (x-9) ^ {- 1} * (x + 9)[/tex]

We can rewrite g (x) as:

According to the following power property:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Also:

If we factor f (x) we have:

[tex]f (x) = (x + 9) (x-9)[/tex]

We must find:

[tex]f (x) * g (x) = (x + 9) (x-9) * \frac {(x + 9)} {(x-9)}[/tex]

We simplify common terms in numerator and denominator:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

ANswer:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

[tex]\bf \begin{cases} R(x)=58x-0.4x^2\\ C(x)=2x+14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ P(x)\implies \stackrel{revenue}{R(x)}-\stackrel{costs}{C(x)}\implies (58x-0.4x^2)-(2x+14) \\\\\\ (58x-0.4x^2)-2x-14\implies 58x-0.4x^2-2x-14 \\\\\\ 56x-0.4x^2-14\implies \boxed{-0.4x^2+56x-14} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf R(80)\implies 58(80)-0.4(80)^2\implies R(80)=4640-2560\implies \boxed{R(80)=2080} \\\\[-0.35em] ~\dotfill\\\\ C(80)=2(80)+14\implies C(80)=160+14\implies \boxed{C(80)=174} \\\\[-0.35em] ~\dotfill\\\\ P(80)=-0.4(80)^2+56(80)-14 \\\\\\ P(80)=-2560+4480-14\implies \boxed{P(80)=1906}[/tex]

The profit function P(x) is 56x - 0.4x² - 14. When we plug x=80 into the equations, we find that R(80) = 3680, C(80) = 174, and P(80) = 3506.

To solve the student's question, firstly we use the provided data. The profit function P(x) can be expressed as the difference between the revenue function R(x) and the cost function C(x).

To find P(x), we subtract the equation for C(x) from the equation for R(x). So, P(x) = R(x) - C(x) = (58x - 0.4x²) - (2x + 14) = 56x - 0.4x² - 14.

To answer the second part of the question, we substitute x=80 into the equations for R, C, and P.
Therefore R(80) = 58×80 - 0.4×80² = 3680, C(80) = 2×80 + 14 = 174, and P(80) = 56×80 - 0.4×80² - 14 = 3506.

https://brainly.com/question/33158589

#SPJ6

Answer:

B is the correct answer.

Step-by-step explanation:

Apex

Answer:

Quotient: [tex]2x^2-2x+2[/tex]

B is correct

Step-by-step explanation:

Given: The format of synthetic division.

We take first number at bottom row and multiply with -3, write the result below second number (4) and then simplify (4-6=-2)

Repeat the process at end.

At last we get 0 (Remainder)

Last number of last row shows remainder and rest are coefficient of quotient.

Synthetic Division: Please find attachment.

-3 | 2       4          -4         6 |

             -6           6        -6

     2      -2           2         0

last row : 2   -2    2  

Initially we had 4 terms ( three degree polynomial)

Quotient must have two degree polynomial.

Quotient: [tex]2x^2-2x+2[/tex]

Answer:

C

Step-by-step explanation:

Firstly, we know that the function must be negative due to its shape. This means that the answer cannot be B

Next we can use the equation [tex]x=\frac{-b}{2a}[/tex] that is used in order to find the vertex of the parabola.

A)

[tex]f(x)=-x^2+6x+7\\a=-1,b=6,c=7\\\\x=\frac{-6}{-2} \\x=3[/tex]

As the vertex is at x=3 on the graph, this one could be a contender.

C)

[tex]f(x)=-x^2+6x-7\\a=-1,b=6, c=-7\\\\x=\frac{-6}{-2} \\\\x=3[/tex]

This also could be the equation

D)

[tex]f(x)=-x^2-6x-7\\\\a=-1, b=-6, c=-7\\\\x=\frac{6}{-2} \\\\x=-3[/tex]

This rules option D out.

For this last step, we can look at where the zeroes would be for each equation. (These values are irrational, so we cannot look at specific number)

A)

[tex]f(x)=-(x^2-6x-7)[/tex]

As this equation has a negative value for c, this means that one zero must be positive and the other must be negative.

This means that option A can be ruled out

C)

[tex]f(x)=-(x^2-6x+7)[/tex]

As this equation has a positive value for c, this means that both of the zeroes must be positive. This means that it is the only one that fits all of the criteria.

Answer:

The answer is 32.45

Step-by-step explanation:

Answer:

18x + 27

Step-by-step explanation:

Distribute

-9(-2x-3)

18x + 27

Solution

18x + 27

Answer:

18x + 27

Step-by-step explanation:

- (8) * - (5 ) is = + 40

-----------------------------

-9( - 2x -3)

(-9*-2) + (-9*-3)

(18x )+(27)

18x + 27

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 9 and d = - 2, hence

[tex]a_{n}[/tex] = 9 -2(n - 1) = 9 - 2n + 2 = - 2n + 11

[tex]a_{n}[/tex] = - 2n + 11 ← n th term formula

Answer:

Option D is correct.

Step-by-step explanation:

Previous Balance Method uses the "previous" balance, that is, the balance from the month before.

Here, it is given that the  opening balance of one of her 30-day billing cycles was $2990. This means this was previous month amount or previous balance.

So, Annette will be charged the interest on $2990.

Hence, option D is correct.

Answer:

D.

Step-by-step explanation:

Foil is an acronym that stands for:

First

Outside

Inside

Last

First:

(w + x )(w + x ) = [tex]w^{2}[/tex]

Outside:

(w + x )(w + x ) = wx

Inside:

(w + x )(w + x ) = wx

Last:

(w + x )(w + x ) = [tex]x^{2}[/tex]

so...

[tex]w^{2}[/tex] + wx + wx + [tex]x^{2}[/tex]

[tex]w^{2} +x^{2} + 2xw[/tex]

Hope this helped!

Answer: [tex]x^2+2wx+w^2[/tex]

Step-by-step explanation:

Given the expression [tex](w + x )(w + x )[/tex] , which indicates the multiplication of two binomials, you can simplify it with FOIL:

Multiply:

The first terms (w by w).

The outside terms  (w by x).

The inside terms together (x by w).

The last terms together (x by x).

Then, you get:

[tex](w + x )(w + x )=(w)(w)+(w)(x)+(x)(w)+(x)(x)=w^2+wx+wx+x^2[/tex]

Adding like terms, you get:

[tex]x^2+2wx+w^2[/tex]

Answer:

2.5

Step-by-step explanation:

lower quartile.

3, 4, 5, 5, 6, 6, 7, 7, 8

median = 6

lower quartile 1/4th position

(4+5)/2 = 4.5

Upper quartile 3/4th position

(7+7)/2 = 7

Interquartile range = upper quartile - lower quartile

                                = 7 - 4.5

                                 = 2.5

Answer:

Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5

Step-by-step explanation:

Before we calculate interquartile range, you should understand that:

Interquartile range is the range between Q3 and Q1 of a dataset i.e Q3 - Q1

Where,

Q1 is the middle value in the first half of the data set and

Q3 is the middle value in the second half of the data set.

So to calculate the interquartile range we find the Q3 and Q1

5, 6, 7, 3, 4, 5, 6, 8, 7

So in the data set to find Q1 and Q3, we rearrange the dataset and divide it into First half and second half.

3, 4, 5, 5, 6, 6, 7, 7, 8

First half = 3, 4, 5, 5

Second half = 6, 7, 7, 8

So

Q1 = (4+5)/2 = 4.5

Q3 = (7+7)/2 = 7

Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5

Answer:

b

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Answer:

The linear inequality is [tex]y > \cfrac 23 x+3[/tex], which is the third option.

Step-by-step explanation:

In order to determine the inequality, we need to first identify the line equation associated to it, to do that we can identify a couple of points and get the slope then the line equation.

Identifying points and finding slope.

From the segmented line we can tell that it crosses the points (0,3) and (3, 5), thus we can find the slope using

[tex]m = \cfrac{y_2-y_1}{x_2-x_1}[/tex]

Replacing the points we get

[tex]m= \cfrac{5-3}{3-0}[/tex]

[tex]m = \cfrac 23[/tex]

Writing the line equation.

Now that we have the slope m, and a point (0,3) we can find the line equation using,

[tex]y-y_1 = m(x-x_1)[/tex]

Replacing the point and slope we get

[tex]y-3 = \cfrac 23 (x-0)[/tex]

Simplifying and solving for y we get

[tex]y = \cfrac 23 x+3[/tex]

Writing the inequality.

Notice that the associated line is a segmented line, so the linear inequality does not contain it that is why we only need to use greater than or less symbols.

Then we can tell that the shaded area is above the segmented line so we can conclude that the linear inequality is

[tex]y > \cfrac 23 x+3[/tex],

And that is the third option.

Answer:

222 Calls

Step-by-step explanation:

We are given four values and the mean of the given data, so in order to find the fifth value, we will use the formula for mean. The formula for mean is:

Mean=(∑x)/n

Here n is the total number of values which is 5

Let x_5 be the number of calls for Thornbury

Putting the values of mean and the data given

273=(244+353+235+311+x_5)/5

273*5=1143+x_5

1365=1143+x_5

x_5=1365-1143

x_5=222 Calls

So the number of police calls in Thornbury is 222 ..  

Answer:

[tex]222[/tex]                                                              - written in [tex]2/24/2021[/tex]

Step-by-step explanation:

The answer is [tex]222[/tex] because...

First Step:

Multiply the mean by how many numbers in total there are, including the [tex]?[/tex] mark: [tex]273[/tex] * [tex]5=1365[/tex]

Second Step:

Add up all the numbers, not including the [tex]?[/tex] mark: [tex]244+353+235+311=1143[/tex]

Third Step:

Now subtract those numbers: [tex]1365-1143=222[/tex]

Fourth Step/Final answer:

Now we know that the answer is [tex]222[/tex]

Answer:

The third side is approximately 31.6 inches long.

Step-by-step explanation:

When given the lengths of two sides of a right triangle, you can easily use Pythagorean Theorem (a2+b2=c2; a or b being the legs, c being the hypotenuse) to find the length of the third side. Since the legs (10 in. and 30 in.) are already given to us, we can simply insert the numbers into Pythagorean Theorem and solve for the third side! It should look a little something like this: 102+302=c2, then solve for the squares to get 100+900=c2, then add the two side lengths to get to 1,000=c2, then find the square root of both sides (now, since the c is already being squared, they will cancel out to just c, but you will get the actual square root of 1,000). Should all go well, you should get an answer of 31.6227766017, which just so happens to round out to 31.6. And with that, we have our final no-longer-missing side length of 31.6 inches.

Hope this helped!

Calculate half the base by multiplying the length of a side ( 60 cm) by the fraction of the ratio from the base to the vertex ( 5/12).

Then multiply that by 2 for the width of the base.

60 x 5/12 = 300/12 = 25 cm.

Full width = 25 x 2 = 50 cm.

Answer:

Full width = 25 x 2 = 50

Answer:

The answer is D.35.5 got it right on plato

Step-by-step explanation:

The expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5

Supposing that the considered random variable is discrete, we get:

[tex]\text{Mean} = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]

where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values

and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]

The probability distribution of Y is given as:

Y = y   f(y) = P(Y = y)

10            0.10

20           0.25

30           0.05

40           0.30

50           0.20

60           0.10

Thus, the expectation (also called expected value) of y is calculated as:

[tex]E(Y) = \sum_{\forall y_i} f(y_i)y_i \\\\E(Y) = 10 \times 0.1 + 20\times 0.25 + 30 \times 0.05 + 40 \times 0.3 + 50 \times 0.2 + 60 \times 0.1\\\\E(Y) = 1 + 5 + 1.5 + 12 + 10 + 6 = 35.5[/tex]

Thus, the expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5

Learn more about expectation of a random variable here:

https://brainly.com/question/4515179

A random variable can be either discrete or continuous. It is discrete it can assume only a finite number of values, or a countable infinity of values at most.

It is continuous if it can assume values in an interval, or in general, an uncountable infinity of values.

That being said, we have:

Option A is a discrete random variable, because the number of heads in 5 throws can be 0, 1, 2, 3, 4 or 5. So, we have finitely many possible values.

Option B is a discrete random variable, because the number you roll on a die is either1, 2, 3, 4, 5 or 6. So, we have finitely many possible values.

Option C is a discrete random variable, because if there are n students in a class, the number of boys is an integer between 0 and n. So, we have finitely many possible values.

Option D is finally a continuous random variable, because the height of a 10-year-old can be any number (in a suitable range of course).

Final answer:

The example of a continuous random variable is D. Height of 10-year-olds, as height is a measured quantity that can have various values on a continuous scale.

Explanation:

When considering which of these is an example of a continuous random variable, it is important to understand the difference between discrete and continuous random variables. A discrete random variable consists of countable values, such as the number of heads when flipping a coin, whereas a continuous random variable includes values that are measured on a continuous scale, such as weight or height. Therefore, the correct answer to the student's question is D. Height of 10-year-olds because height is measured rather than counted, and it can take on a theoretically infinite number of values within a range.

The tree is 27 feet tall. In order to find that out you know that because it is occurring at the same time of day, the two shadows are proportional to each other. Then set up two fractions like I did in the image and cross multiply to find x. Hope this helps!

Answer:

C

Step-by-step explanation:

To find the percent of adults who use toothpaste, we divide the number of adults who use toothpaste by the total adults.

0.08/0.75

The answer is about 11 percent, so C is the true statement.

Answer:

C is right on Ap ex!

Step-by-step explanation:

That answer is right, I don't know why that person commented wrong, but they must have been doing a different question!

Answer:

The value of 2 in 270,413 is 10,000x greater than the value of 2 in 419,427.

Step-by-step explanation:

The value of 2 in 270,413 is 200,000.

The value of 2 in 419,427 is 20

Divide the two numbers together to find your answer:

200,000/20 = 10,000

The value of 2 in 270,413 is 10,000x greater than the value of 2 in 419,427.

~

Hence ,value of 2  is [tex]10^{4}[/tex] time grater than value in 419,427

Place value of digit in number is  place at which it is placed .

Given

number one =  270413

Place value of 2= 200,000

number two =419,427

place value of 2= 20

Difference in place value of 2 in 200000 and 20 is of 2 x 10000

Hence  value of 2 is greater by [tex]10^{4}[/tex] in numbers .

Learn more about place value of numbers

https://brainly.com/question/12386995

#SPJ2

Answer:

1.  6x

2. -3x + 2

3. -4x - 4

4. 4x + 11

5. -8x + 9

6. -14x - 18

Step-by-step explanation:

1. Finding sum of -3x+9x

As both the terms have different signs, the terms will be subtracted and the sign in the answer will be of the larger terms (the term with greater coefficient)

So the answer of -3x+9x is 6x

2. Finding the sum of -7x and 4x + 2

For sum,

-7x + (4x+2)

= -7x + 4x + 2

= -3x + 2

3. Finding the difference when 6x is subtracted from 2x - 4

= 2x - 4 - (6x)

= 2x - 4 - 6x

= 2x - 6x - 4

= -4x - 4

4. Finding the difference when -3x - 7 is subtracted from x + 4

= (x+4) - (-3x-7)

= x + 4 + 3x + 7

= x + 3x + 4 + 7

= 4x + 11

5. Finding the result when 13x + 2 is subtracted from 11 + 5x

= (11 + 5x) - (13x + 2)

= 11 + 5x - 13x - 2

= 5x - 13x + 11 - 2

= -8x + 9

6. Finding the result when -18x - 4 is added to 4x - 14

= (4x - 14) + (-18x - 4)

= 4x - 14 - 18x -4

= 4x - 18x - 14 - 4

= -14x - 18

..

Answer:

3456

Step-by-step explanation:

the given equation is: [tex](3^{2} 8) (4^{2} 3)[/tex]

= (9 × 8) (16 × 3)

= (72) (48)

= 3456

Answer:

c. time

Step-by-step explanation:

time is always the independent variable because you can't control it

The independent variable among the option is time.

An independent variable is defines as the variable that is changed or controlled in a scientific experiment.

Independent variables are stand alone variables. They are not dependent on any other variables.

Therefore, time is usually controlled in any experiment. Therefore, time is the independent variables among the option.

learn more on independent variables here: https://brainly.com/question/1479694

#SPJ9

Answer:

30 mph

Step-by-step explanation:

The average speed = Total distance / Total Time

Distance at 45 m/hr.

t = 20 minutes = 20/60 = 1/3 hour.

r = rate = 45 miles / hour

d = r * t

d = 45 * 1/3 = 15 miles.

Average Speed going home.

t =  30 minutes

t = 30 min / 60 min // hour = 1/2 hours

r = 15 miles / 1/2 = 15 * 2 =  30 miles / hr.

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

therefore

|3| = 3 and |-3| = -(-3) = 3

Answer:

Graph 1 is the correct representation of absolute value of -3.            

Step-by-step explanation:

Absolute value of a number is the measure of positive distance on a number line from zero to that number.

It is denoted by:

[tex]\mid c \mid = c, \text{if c} > 0\\ ~~~~~ = -c, \text{if c} < 0[/tex]

So, the absolute value of -3 =

[tex]\mid -3 \mid = 3[/tex]

The correct representation of the absolute value option 1.

As the graph in option 1 represents the positive distance between zero and -3.

Answer:

DATA GATHERING

Step-by-step explanation:

AC would be the sum of ab plus bc.

AC = 9 + 12 = 21

Answer:

A.

9 centimeters

B.

12 centimeters

C.

15 centimeters

D.

18 centimeters

heres the answer choices, i need this too!!

Step-by-step explanation:

Answer: it will take 1.25 hours

Step-by-step explanation:

It

It will take the teacher 1.25 hours to print 6,000 pages.

To calculate how long it will take to print 6,000 pages with a copy machine that can print 80 sheets per minute, we need to divide the total number of pages by the rate of printing per minute to find out the time in minutes, and then convert that time into hours if necessary.

Step 1: Divide the total number of pages by the printing speed to find the time in minutes.

Total pages: 6,000

Printing speed: 80 pages/minute

Time calculation: 6,000 pages divided by 80 pages/minute = 75 minutes

Step 2: Convert minutes into hours by dividing by 60 since there are 60 minutes in an hour.

Conversion to hours: 75 minutes divided by 60 minutes/hour = 1.25 hours

Therefore, it will take the teacher 1.25 hours to print 6,000 pages.

Answer:

The distance is 9 (Sorry if i'm wrong)

Answer:

square root of 85

Step-by-step explanation:

(7+2)^2 + (9-7)^2

(9)^2+(2)^2

81+4

Square root of 85

The Volume is approximately 226

To find the volume of the cylindrical barrel with a height of 8 feet and a diameter of 6 feet, use the formula V = πr²h where r is the radius and h is the height. The approximate volume is approximately 226.08 cubic feet.

The approximate volume of the cylindrical barrel can be calculated using the formula V = πr²h.

Given that the diameter is 6 feet, the radius (r) would be half of the diameter, which is 3 feet. The height (h) is 8 feet.

Substitute the values into the formula to find the volume: V ≈ 3.14 × (3)² × 8 ≈ 226.08 cubic feet.