Find the inverse of the given function.

Answer:

C, A, C

Hope This Helps!

Answer: OPTION C

Step-by-step explanation:

 To express a polynomial in Standard form, you need to see the exponent of each term of the polynomial and then order the polynomial from highest exponent to lowest exponent.

Therefore, for the polynomial  [tex]5a^2 + 3a^3 + 1[/tex], you get:

  [tex]3a^3 +5a^2 +1[/tex]

The highest exponent gives you the degree of the polynomial. In this case, the highest exponent is 3, then it is a polynomial of degree 3 or a cubic polynomial.

When a polynomial has three terms, is called "trinomial". Since this polynomial has three terms, it is a trinomial.

Therefore, the you can classify it as:

Cubic trinomial

Answer:

C

Step-by-step explanation:

Answer:

g(n) = 2n+49

Step-by-step explanation:

Since g(1) = 51, then g(1)+2=g(2) or g(2)=53. So the formula for g(n) is

g(n) = 49+2n

The explicit formula for g(n) will be g(n) = 2n + 49.

Functions are found all across mathematics and are required for the creation of complex relationships.

g(1) = 51 and g(n) = g(n – 1) + 2

Since g(1) = 51, then g(1) + 2= g(2) or g(2) = 53.

So the formula for g(n) will be

g(n) = 49 + 2n

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Answer:

The mean will decrease.

Answer:

The correct option is B.

Step-by-step explanation:

From the given dot plot we can create a frequency table.

  x                   f

 1.5                 2

  2                  1

 2.5                3

  3                  1

 3.5                2

  4                   1

This data can be written as

1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4

The mean of the data is

[tex]Mean=\frac{\sum x}{n}=\frac{1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{10}=2.65[/tex]

The number of terms is 10 which is an even number. So, the median of the data is

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{5th+6th}{2}=\frac{2.5+2.5}{2}=2.5[/tex]

If next student presents a monologue that is about 0.5 minutes long, then the new data is

0.5, 1.5, 1.5, 2, 2.5, 2.5, 2.5, 3, 3.5, 3.5, 4

The mean of the new data is

[tex]Mean=\frac{\sum x}{n}=\frac{0.5+1.5+1.5+2+2.5+2.5+2.5+3+3.5+3.5+4}{11}=2.4545..\approx 2.45[/tex]

The number of terms is 11 which is an odd number. So, the median of the new data is

[tex]Median=(\frac{n+1}{2})th=6th=2.5[/tex]

Median of given data and new data is same but the mean of new data is less than the mean of original data. It means the mean will decrease.

Therefore the correct option is B.

The 3rd one.....................

Answer:

Fourth option

Step-by-step explanation:

An m×n matrix is a matrix with m rows (horizontal lines) and n columns (vertical lines).

By definition, the multiplication of two matrices [tex]m_1[/tex]×[tex]n_1[/tex] and [tex]m_2[/tex]×[tex]n_2[/tex] can be done only if:

[tex]n_1 = m_2[/tex]

In the first option:

[tex]n_1 = 2\\m_2 = 1[/tex]

In the second option

[tex]n_1 = 1\\m_2 = 2[/tex]

In the third option

[tex]n_1 = 2\\m_2 = 1[/tex]

In the fourth option

[tex]n_1 = 1\\m_2 = 1[/tex]

[tex]n_1 = m_2[/tex] Multiplication can be done

Answer:

Option A. 6.247°

Step-by-step explanation:

we know that

1°=60'

1'=60"

we have

6° 14' 48"

Convert to decimal form

Convert seconds to minutes

48"=48/60=0.8'

so

6° 14' 48"=6° + 14' +0.8'=6° 14.8'

Convert minutes to degrees

14.8'=14.8/60=0.247°

so

6° 14.8' =6° + 0.247°=6.247°

Answer:

6.247

Step-by-step explanation:

12,450 so yeah your welcome have a fantasist day

Answer:

[tex]\frac{24}{5}[/tex]

Step-by-step explanation:

To evaluate division of fractions, that is

[tex]\frac{9}{-5}[/tex] ÷ [tex]\frac{-3}{8}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down

[tex]\frac{9}{-5}[/tex] × [tex]\frac{8}{-3}[/tex] ( cancel the 9 and 3) giving

[tex]\frac{3}{-5}[/tex] × [tex]\frac{8}{-1}[/tex]

= [tex]\frac{3(8)}{-5(-1)}[/tex] = [tex]\frac{24}{5}[/tex]

To simplify a complex fraction, multiply both the numerator and the denominator by the same factor to eliminate fraction in the denominator, cancel common factors and follow rules of algebra to maintain equality.

To evaluate and simplify a complex fraction, we can use a strategy that involves multiplying the numerator and denominator by the same factor. For example, if our complex fraction had a denominator of 1/2, we could multiply both the numerator and the denominator by 2 to eliminate the fraction in the denominator. This approach ensures the units or variables cancel out where appropriate, leaving us with a simpler expression. When working with fractions, common factors can be identified and cancelled to simplify the fraction further. Always remember that fractions represent division, so when simplifying, divide the digit term of the numerator by that of the denominator and subtract the exponentials accordingly. This process is governed by the rules of algebra, maintaining the equality of the expression.

Answer:

The correct answer is option B).  108°

Step-by-step explanation:

Points to remember

Sum of angles of hexagon is 720°

From the figure we can see a hexagon.

To find the m<B

m<B = 720 - ( m<A + m< C + m<D + m<E + m<F)

  = 720 - ( 170 + 133 + 102 + 117 + 90)

  = 720 - 612

  = 108°

Therefore m<B = 108° Option B is the correct answer

Answer:

B. 108 degrees

Step-by-step explanation:

Step 1: Find the total area. Since it is a square all the sides are 12 ft so multiply 12 by 12

12 x 12 = 144

^^^This is the total area including the area around the pool. We just need the are of the pool

Step 2: Outside of the pool there are four little 2 ft by 2 ft squares that aren't part of pool, and therefore won't need to be covered. The area of these 2 ft by 2 ft square is 4ft (2 times 2 is 4). Since there are 4 of these squares we multiply 4 by 4 to get 16. This means that 16 ft of the 144 ft we found previously are not part of the pool and we must subtract 16 from 144 to get the total pool area

144 - 16 = 128

This means that the area of the pool is 128 ft

Hope this helped and made sense! Let me know!

Answer:

128

Step-by-step explanation:

Answer:

V = 3533

Step-by-step explanation:

Volume of a cylinder is given by

V = pi r^2 h

Using 3.14 for pi

V = (3.14) (7.5)^2 * 20

V = 3532.5

To the nearest whole number

V = 3533

Rewrite both fractions so they have a common denominator:

-3/6 = -21/42

-5/7 = -30/42

Now you have -21/42 - 30/42

Now subtract to get:

-51/42 which reduces to -17/14 = -1 3/14

The simplification of the expression is,-17/14. The simplification is done by applying the mathematical operation step by step.

Simplification usually entails doing out the expression's pending processes.

The given expression is

(-3/6) –(5/7)

The LCM of the 6 and 7 is 42 so  rewrite the equation as;

(-3×7)/42 – (5×6)/7

(-21/42)-30/42

-51/42

Divide by 3 from the numerator and denominator we get;

-17/14

Hence, the simplification of the expression is,-17/14

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For this case we must find the inverse of the following function:

[tex]f (x) = \sqrt [3] {x + 12}[/tex]

For this, we follow the steps below:

Replace f (x) with y:

[tex]y = \sqrt [3] {x + 12}[/tex]

We exchange the variables:

[tex]x = \sqrt [3] {y + 12}[/tex]

We solve the equation for "and":

[tex]\sqrt [3] {y + 12} = x[/tex]

We raise both sides of the equation to the cube to eliminate the root:

[tex](\sqrt [3] {y + 12}) = x ^ 3\\y + 12 = x ^ 3[/tex]

We subtract 12 on both sides of the equation:

[tex]y = x ^ 3-12[/tex]

Thus, the inverse function is:

[tex]f ^ {- 1} = x ^ 3-12[/tex]

Answer:

Option B

Option: B is the correct answer.

       B.    [tex]f^{-1}(x)=x^3-12[/tex]

The inverse function f(x) is calculated in the following steps.

The function f(x) is given by:

[tex]f(x)=\sqrt[3]{x+12}[/tex]

Now, we keep:

[tex]f(x)=y\\\\i.e.\\\\y=\sqrt[3]{x+12}[/tex]

Now, we interchange x and y

[tex]x=\sqrt[3]{y+12}[/tex]

Now, on taking cube on both side of the equation we have:

[tex]y+12=x^3\\\\i.e.\\\\y=x^3-12[/tex]

i.e.

[tex]f^{-1}(x)=x^3-12[/tex]

Answer:

[tex]V=152\pi in^{2}[/tex] in terms or pi

[tex]V=477.52in^{2}[/tex] simplified

Step-by-step explanation:

To solve this, we are using the Cylinder's volume formula:

[tex]V=\pi r^{2} h[/tex]

where

[tex]V[/tex] is the volume of the cylinder

[tex]r[/tex] is the radius of the cylinder

Remember that radius is half the diameter, so we can divide the diameter of our cylinder by 2 to find its radius: [tex]r=\frac{d}{2} =\frac{8in}{2} =4in[/tex]. Now, 9 1/2 inches is 9 and a half inches, so [tex]h=9.5in[/tex].

Replacing values:

[tex]V=\pi (4in)^{2} (9.5in)[/tex]

[tex]V=\pi (16in^{2})(9.5in)[/tex]

[tex]V=152\pi in^{2}[/tex]

[tex]V=477.52in^{2}[/tex]

We can conclude that the volume of our cylinder is [tex]V=152\pi in^{2}[/tex] in terms of pi, or [tex]V=477.52in^{2}[/tex] simplified.

Answer:

[tex]V=477.5in^3[/tex]

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula;

[tex]V=\pi r^2h[/tex]

where the radius is half of the diameter of the circle.

[tex]r=\frac{8}{2} =4in.[/tex]

The height of the cylinder is

[tex]h=9\frac{1}{2}=\frac{19}{2}in.[/tex]

We substitute the values into the formula to obtain;

[tex]V=\pi\times 4^2\times \frac{19}{2}[/tex]

[tex]V=477.5in^3[/tex]

correct to the nearest tenth

Answer:

Polygon Y's area is one ninth (1/9) of Polygon X's area

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

In this problem

Let

z-----> the scale factor

a-----> Polygon Y's area

b----> Polygon X's area

[tex]z^{2}=\frac{a}{b}[/tex]

we have

[tex]z=\frac{1}{3}[/tex]

substitute

[tex](\frac{1}{3})^{2}=\frac{a}{b}[/tex]

[tex]\frac{1}{9}=\frac{a}{b}[/tex]

[tex]a=\frac{1}{9}b[/tex]

therefore

Polygon Y's area is one ninth (1/9) of Polygon X's area

Answer:

1/9

Step-by-step explanation:

(x-5)(2x-1) (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have  as solution set.

Answer:

well i got some HOPE THIS WILL HELP

Step-by-step explanation:

To find the solution set of a factored quadratic equation, you should set each one of the factors equal to zero and solve for .

Lets take our first quadratic equation (x+1/2)(x-5)=0 and apply this. First we are our factors equal to zero  and ; next we are going to sole for  in each factor to find the solution set:

and , so the solution set for the quadratic equation (x+1/2)(x-5)=0 is 

Lets do the same for our next one (x-5)(2x-1)=0

and

So, the solution set for the quadratic equation (x-5)(2x-1)=0 is 

Next one (x+5)(2x-1)=0

and 

So, the solution set for the quadratic equation (x+5)(2x-1)=0 is 

Next one (-2x+1)(-x+5)=0

and

So, the solution set for the quadratic equation (-2x+1)(-x+5)=0 is : therefore, we are going the select this one.

Next one (x+1/2)(x+5)=0

and

So, the solution set for the quadratic equation (x+1/2)(x+5)=0 is 

Finally, our last one (-2x+1)(x-5)=0

and

So, the solution set for the quadratic equation (-2x+1)(x-5)=0 is ; this is also a correct answer, make sure to select this one too.

We can conclude that both (-2x+1)(-x+5)=0 and (-2x+1)(x-5)=0 quadratic equation have  as solution set.

Answer:

3

Step-by-step explanation:

The mean absolute deviation of the data set is approximately 3.09.

The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between observations in a data set and their mean.

To calculate the MAD, you first need to find the mean of the data set. In this case, the mean is 31.375.

Then, you calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).

Once you have calculated the absolute deviation of each data point, you find the average of those absolute deviations. This is the mean absolute deviation.

In the example data set, the mean absolute deviation is approximately 3.

Find the mean of the data set: (21 + 22 + 24 + 26 + 27 + 28 + 20 + 30) / 8 = 31.375

Calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).

Add up the absolute deviations of all the data points. In this case, the sum of the absolute deviations is 24.75.

Divide the sum of the absolute deviations by the number of data points to find the mean absolute deviation. In this case, the mean absolute deviation is 24.75 / 8 = 3.09375.

Therefore, the mean absolute deviation of the data set is approximately 3.09.

The complete question is:What is the mean absolute deviation of the data set?

(21, 22, 24, 26, 27, 28, 20, 303

2

3

6

22

Ik for s fact the awnser not a

Answer:

B) [tex]-5x + 2y + 1 > 0[/tex]

Step-by-step explanation:

Given point is (-2,-1)

to find out which inequality satisfies this point we plug in x and y value of the given point in each inequality

A) [tex]5x - 2y + 1 > 0[/tex]

x=-2 and y=-1

[tex]5(-2) - 2(-1) + 1 > 0[/tex]

[tex]-10+2+1>0[/tex]

[tex]-7>0[/tex] is False

B) -5x + 2y + 1 > 0

[tex]-5(-2) +2(-1) + 1 > 0[/tex]

[tex]10-2+1>0[/tex]

[tex]9>0[/tex] is True

C) -2x + 5y - 1 > 0

[tex]-2(-2) +5(-1) -1 > 0[/tex]

[tex]4-5-1>0[/tex]

[tex]-2>0[/tex] is False

D) 2x + 5y - 1 > 0

[tex]2(-2) +5(-1) - 1 > 0[/tex]

[tex]-4-5-1>0[/tex]

[tex]-10>0[/tex] is False

Answer:

Step-by-step explanation:

To find the arithmetical mean, add all the numbers togther and divide by the number of numbers.

The sum of all the numbers is ... 59.

There are 7 numbers.

59/7 which is about 8.43 is the arithmetic mean.

Arithmetic mean is 8.42 (Approximately)

Given that;

Values = 8,10,10,10,6,7,8

Find:

Arithmetic mean

Computation:

Arithmetic mean = Sum of all number / Number of term

Arithmetic mean = [8 + 10 + 10 + 10 + 6 + 7 + 8] / 7

Arithmetic mean = 59 / 7

Arithmetic mean = 8.42 (Approximately)

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ANSWER

Yes

EXPLANATION

The given relation is

2x-5y=-15

We solve for y to obtain:

-5y=-2x-15

Divide through by -5.

[tex]y = \frac{2}{5}x + 3[/tex]

This is linear relation.

There is a positive linear relationship between the two variables x and y.

Also we can see that the highest degree of the variables is unity.

Hence it represents a linear relationship between x and y.

Answer:

Part 1) The system is solved using elimination

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) The system is solved using substitution

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) The system is solved by graphing

The graph in the attached figure

Step-by-step explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

[tex]-36x-24y=-78.6[/tex] -------> equation C

Multiply the equation B by 4 both sides

[tex]16x+24y=54.8[/tex] -------> equation D

Adds equation C and equation D

[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]

Substitute the value of x in the equation A

[tex]6(1.19)+4y=13.10[/tex]

[tex]4y=5.96[/tex]

[tex]y=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex]    

[tex]4y=-6x+13.10[/tex]

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  

[tex]6y=-4x+13.70[/tex]

[tex]y=-(4/6)x+13.70/6[/tex]

[tex]y=--0.67x+2.28[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]-0.67x+2.28=-1.5x+3.275[/tex]

[tex]1.5x-0.67x=3.275-2.28[/tex]

[tex]0.83x=0.995[/tex]

[tex]x=1.19[/tex]

Find the value of y

Substitute the value of x in the equation A

[tex]y=-1.5(1.19)+3.275=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) Solve the system by graphing

we have

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point [tex](1.19,1.49)[/tex]

see the attached figure

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Answer:

1) The system of linear equations is equal to

b+t=15  and 2b+3t=38

2) The number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8

Step-by-step explanation:

Let

b----> the number of bicycles ordered​

t----> the number of tricycles ordered​

we know that

b+t=15 -----> equation A

2b+3t=38 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (7,8)

see the attached figure

therefore

The number of bicycles ordered​ was 7

The number of tricycles ordered​ was 8

The number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8.

Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.

Let, the number of tricycles and b represent the number of bicycles ordered​.

A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.

[tex]\rm b+t=15[/tex]

The number of wheels for all the tricycles and bicycles totaled 38.

[tex]\rm 2b+3t=38[/tex]

From equation 1

[tex]\rm b+t=15\\\\b=15-t[/tex]

Substitute the value of b in equation 2

[tex]\rm 2b+3t=38\\\\ 2(15-t)+3t=38\\\\30-2t+3t=38\\\\t=38-30\\\\t=8[/tex]

Substitute the value of t in equation 1

[tex]\rm b+t=15\\\\b=15-t\\\\ b = 15-8\\\\b=7[/tex]

Hence, the number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8.

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Answer:

1. rectangular prism

2. cylinder

3. cone

4. triangular pyramid

5. sphere

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^2-4x-5=x^2+x-5x-5=x(x+1)-5(x+1)=(x+1)(x-5)[/tex]

Answer:

$25

Step-by-step explanation:

i have an odd method of solving these types of equations

25x=100

x=4

340/4 = 85

85 x 3 = 255

Answer:

13.6

Step-by-step explanation:

so i did 340 devided by 25 and thats how i got it i hope this is helpful

For this case, when making the division of polynomials, we must build a quotient that when multiplied by the divisor of the same as the terms of the dividend, the sign is changed and they are eliminated until reaching the remainder of the division.

It must be fulfilled that:

[tex]Dividend = Quotient * Divider + Remainder[/tex]

When observing the attached figure, the quotient is:

[tex]x ^ 2-2x-3[/tex]

Answer:

[tex]x ^ 2-2x-3[/tex]

See attached image

[tex]4.5x(2 - 6) \\ \\ 1. \: 4.5x \times - 4 \\ 2. \: = - 18x[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{You could solve this equation by distributing}[/tex]

[tex]\text{The Algebraic I formula for distribution is: a(b + c) = ab + ac}[/tex]

[tex]\text{4.5x(2 - 6)}\\\text{4.5x(2) = 9x}\\\text{4.5x(-6)= -27x}[/tex]

[tex]\text{Combine like terms: 9x - 27x = ?}[/tex]

[tex]\text{Solve that}\uparrow\text{you should get the rest of -18x}[/tex]

[tex]\boxed{\boxed{\text{Answer: -18x}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

B. The temperatures were more consistent in Cape Town

Step-by-step explanation:

A low standard deviation indicates less variation away from the mean.

Since Cape Town has a lower standard deviation than Three Rivers, it is more consistent

The value 1/5 becuse you simplify

Answer:

165=z

Step-by-step explanation:

99/3 = z/5

We can solve this using cross products.

99*5 = 3z

495 = 3z

Divide each side by 3

495/3 = 3z/3

165 = z

here is your answer young man/lady

The mode is 12, the median is 18.5, the mean is 23.6667, and the range is 26.

The mode is 12 because it appears twice in the list. The median is 18.5 because it is the middle value when the numbers are arranged in ascending order. The mean is 23.6667 which is the sum of all the numbers divided by the total count. The range is 26 which is obtained by subtracting the smallest value (12) from the largest value (38).

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