Solve x2 + 2x + 5 = 4 by completing the square

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:

36

Step-by-step explanation:

Answer:36

Step-by-step explanation:

The probability that they are both white if the first sock is kept and second is drawn will be 8.33%.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

A drawer contains 4 black socks, 3 white socks, and 2 red socks.

One sock is drawn from the drawer and kept.

The second sock is drawn from the drawer.

The total number of the event will be

Total event = 9

Then the probability that they are both white will be

P = (3/9) (2/8)

P = (1/3)(1/4)

P = 1/12

P = 0.0833

P = 8.33%

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The probability of drawing two white socks from the drawer is 2/27.

To find the probability that both socks drawn are white, we need to find the probability of drawing a white sock on the first draw and then drawing another white sock on the second draw.

There are a total of 9 socks in the drawer (4 black, 3 white, and 2 red).

The probability of drawing a white sock on the first draw is 3/9 (3 white socks out of 9 total socks).

After replacing the first sock, the total number of socks remains the same, but the number of white socks decreases to 2. So the probability of drawing a white sock on the second draw is 2/9.

Now, to find the probability of both events happening, we multiply the probabilities together: P(First white sock) * P(Second white sock) = (3/9) * (2/9) = 6/81 = 2/27.

Therefore, the probability that both socks drawn are white is 2/27.

Answer:

3/28

Step-by-step explanation:

Given in the question that,

stack of cards have numbers (1, 1, 2, 2, 3, 3, 3, 4)

Total number of cards = 8

Number of card with 3 on them = 3

Number of card with 2 on them = 2

To find the probability that he pulls out a 3 first and then pulls out a 2, we will multiple the probability of having 3 with 2.

Probability of having 3 = 3/8

Probability of having 2 = 2/7 (without replacing)

3/8 x 2/7 = 3/28

Thus, the answer is 3/28

Answer:3/28

Step-by-step explanation:

Took test got it right

Answer:

[tex]\large\boxed{\dfrac{n^3}{8}\sqrt{15n}}[/tex]

Step-by-step explanation:

[tex]\sqrt{\dfrac{60n^{11}}{256n^4}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\ \text{and}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\sqrt{\dfrac{60}{256}n^{11-4}}=\dfrac{\sqrt{60n^7}}{\sqrt{256}}=\dfrac{\sqrt{4n^{6+1}\cdot15}}{16}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{\sqrt{4n^6\cdot15n}}{16}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{4n^{3\cdot2}}\cdot\sqrt{15n}}{16}\qquad\text{use}\ (a^n)^m=a^{nm}[/tex]

[tex]=\dfrac{\sqrt{4(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{\sqrt{4}\cdot\sqrt{(n^3)^2}\cdot\sqrt{15n}}{16}=\dfrac{2\!\!\!\!\diagup^1\sqrt{15n}}{16\!\!\!\!\!\diagup_8}=\dfrac{n^3\sqrt{15n}}{8}[/tex]

Answer:

f(2) = 0

Step-by-step explanation:

Function f(t) is defined in three different ways depending on the value of t.

For t = 8, function f(t) is -64/t.

For t = 10, function f(t) is 14 - t.

We are not asked about f(8) or f(10). We are asked about f(2). The third definition of function f(t) is for all values of t that are not 8 or 10. 2 is not 8 or 10, so use the third definition of function f(t) and plug in 2 for t.

f(t) = t^2 - 3t + 2 for t not equal to 8 or 10.

f(2) = 2^2 - 3(2) + 2

f(2) = 4 - 6 + 2

f(2) = 0

Answer:

4 quarts

Step-by-step explanation:

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:

Volume  = 40in^3

Step-by-step explanation:

The volume of a box is:

Volume = width x lenght x height

Where:

width: 4in

Length: 5in

Height = 2in

Then: Volume = width x lenght x height = 4in x 5in x 2in = 40in^3

ANSWER

The volume is 40 cubic inches.

EXPLANATION

The dimensions of the box are ,

width, w=4 inches

height, h=2 inches

and

length, l=5 inches

The box is a rectangular prism.

The formula for finding the volume of a rectangular prism is

[tex]V=l \times b \times h[/tex]

We substitute the values to get,

[tex]V=4\times 5 \times 2 = 40 {in}^{3} [/tex]

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

Answer:

D assuming the black dot means multiplied

Step-by-step explanation:

Answer is provided in the image attached.

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: 7

Step-by-step explanation:

mode is the most replicated number

Answer:

The mode is 7.. :)

Step-by-step explanation:

Answer:

Step-by-step explanation:1/3

Is the correct answer

Hello! :)

Suppose you have a fair coin: this means it has a 50% chance of landing heads up and a 50% chance of landing tails up. Suppose you flip it three times and these flips are independent. What is the probability that it lands heads up, then tails up, then heads up? So the answer is 1/8, or 12.5%.

Hope I helped and answered in time!

Good luck!

~ Destiny ^_^

Answer:

it is not C i did that so it might be B

Step-by-step explanation:

The approximate area that is shaded blue 77 in².

In this question we simply calculate area of circle where r=5 , and area of rectangle l = 2 and b = 1.

   Area of circle = πr²

                           = [tex]\frac{22 *5*5}{7}[/tex] = 78.57

Area of rectangle = l * b

                              2 * 1 = 2

 Then simply subtract area of rectangle to area of circle .

Area of shaded blue = 78.57 - 2

                                 = 76.57 ⇒ 77 in²

Therefore, The approximate area that is shaded blue 77 in².

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Answer:

y=1

Step-by-step explanation:

5y(2x-1)=y(x+2)+20, x=3

5y(2(3)-1)=y(3+2)+20

5y(6-1)=y(5)+20

5y(5)=5y+20

25y=5y+20

25y-5y=20

20y=20

y=20/20

y=1

5y(2x-1)=y(x+2)+20, x=3​

Step 1: Substitute x with 3

5y(2(3) - 1) = y(3 + 2) + 20

Step 2: Combine like terms in the parentheses

5y(6 - 1) = y(3 + 2) + 20

5y(5) = y(3 + 2) + 20

5y(5) = y(5) + 20

Step 2: Distribute the number outside the parentheses to the numbers inside the parentheses

25y  = 5y + 20

Step 3: Combine like terms by subtracting 5y to both sides

25y-5y  = (5y-5y) + 20

20y = 20

Step 4: Divide 20 to both sides to isolate y

[tex]\frac{20y}{20} = \frac{20}{20}[/tex]

y = 1

Check:

5(1) (2(3) - 1) = 1(3+2) + 20

5(6-1) = 1(5) + 20

5(5) = 5 + 20

25 = 25

Hope this helped!

Answer:

the inequality would be: 89+41+17.50x Is less than 200

Step-by-step explanation:

add all of the numbers together and the x with the 17.50. Add a less than inequality sign, then 200, which represents how much it would be for repairs

Answer:

[tex]130+17.50x \leq 200[/tex]

Step-by-step explanation:

The appliance repair company will repair his microwave for a service call fee of $89, a parts fee of $41, and a charge of $17.50 for every 15 minutes of labor.

If Josh spends $200 or more on repairs, he will replace the microwave.

Let x represents the number of 15-minute intervals of labor.

So, as per the scenario, the inequality becomes:

[tex]89+41+17.50x \leq 200[/tex]

=> [tex]130+17.50x \leq 200[/tex]

Solving for x

[tex]17.50x \leq 200-130[/tex]

[tex]17.50x \leq 70[/tex]

[tex]x \leq 4[/tex]

Hence, up to 4, 15 minutes interval that is one hour. the repair cost will be up to $200.

But after this it will cost more. Hence, Josh can opt for replacing after 4, 15 minutes intervals.

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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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:

where is the information about bob and paul?

Step-by-step explanation:

Answer:

2x + 4 = 3x + (–1)

Step-by-step explanation:

I just did it so i hope this helped

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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Basically you do

2 x 3.14 x 8 squared

= 401.92

Then you do

401.92 + 14 x 8

=513.93

Hope this helps :)

Answer:

The correct answer is option option B 606.32 yd²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the base radius and l is the lateral edge

To find lateral edge

l =  √(r²+ h²) =  √8² + 14²  = 16.12

To find the surface area of given cone

Here r = 8 yd and l = 16.12 yd

Surface area =  πrl + π r² = π * 8 * 16.12  + π8²

  = 606.32 yd²

Answer:

333

Step-by-step explanation:

divide the number of times the spinner is spun by how many sections there are the answer is 333

Answer:

333

Step-by-step explanation:

divide the number of times the spinner is spun by how many sections there are the answer is 333

hope this helps mark me brainliest

Answer:

Step-by-step explanation:

Bill and Ted are going to order t-shirts for there school clubs. The t-shirts will have the club logo printed on the front. Bill and Ted ask two local t-shirt companies to give them a price. * Patty's Printing charges $21.50 for each t-shirt. * Sandra's shirts has a one-time set up fee for $63 and then charges $18 for each t-sh

Patty's Printing= 21.5x

Sandra's Shirts = 63+ 18x

x=30

Patty's Printing: 21.50 (30) = 645

Sandra's Shirts = 63+ 18 (30) = 603

Sandra's Shirts

Answer:

y=3/7x

Step-by-step explanation:

Parallel means same slope.

y-y1=m(x-x1)

y-0=3/7(x-0)

y=3/7(x)+0

y=3/7x

Answer: The answer is y=3/7x

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=81\pi \end{cases}\implies 81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies \boxed{9=r}~\hspace{10em}\stackrel{\textit{diameter = twice the radius}}{18}[/tex]

[tex]

A=81\pi \\

A=\pi r^2 \\

81\pi=\pi r^2\Longrightarrow r^2=81

radius=\sqrt{81}=\boxed{9} \\

diameter=2radius = 2\cdot9=\boxed{18}

[/tex]

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:

1. rectangular prism

2. cylinder

3. cone

4. triangular pyramid

5. sphere

Step-by-step explanation:

There are 3,024 different ways the coach can choose players for first base, second base, third base, and shortstop from a team of 9 players.

Since the positions are distinct (first base, second base, third base, and shortstop), and each position can only be filled by one player, we can use the permutation formula to calculate the number of arrangements.

The coach has 9 players to choose from for the first position.

After selecting one player for first base, there remain 8 players for the second position, 7 players for the third position, and 6 players for shortstop.

The total number of different ways the coach can choose players for the four positions is obtained by multiplying these numbers:

9 x 8 x 7 x 6 = 3,024

Hence, there are 3,024 different ways.

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