Which angle is vertical to 2?

Value for (g⁰g)(1) = 17

Now, (g⁰g)(x) = g[g(x)]

let g(x) = 3x + 2

(g⁰g)(x) = g(3x + 2)

(g⁰g)(1) = g(5)

(g⁰g)(1) = 3(5) + 2

(g⁰g)(1) = 17

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The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex]  when f(x) = 16  is [tex]x=2^\frac{11}{3}[/tex] .

We have given a function [tex]f(x)=x\sqrt[3]{2}[/tex].        ....(1)

 Let y = f(x)

         [tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex]                         ......(2)

Swap the values of x and y, then the inverse is then

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

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

Comparing equation (2) and (3) , we get

      [tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]

It is given that f(x) = 16 on comparing it with equation (1) , we get

              [tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]

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Yes..............................

The number of T-shirts bought by the Brandywine Dance Team is 24.

The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.

First, the cost of the equipment is subtracted from the total cost spent by the team.  The remainder refers to the cost of the T-shirts.  Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.

The total amount spent = $644

The cost of the equipment = $356

The remainder after the equipment = $288 ($644 - $356)

Unit cost of T-shirts = $12

The number of T-shirts bought = 24 ($288/$12)

Thus, the Brandywine Dance Team bought 24 T-shirts.

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How many T-shirts were purchased by the Team?

Answer:

1. 5/12 in exact form and 0.416 in decimal form

2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.

On each "6" there's a - on top!

the answer is 71 miles far

Answer:

A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.

Step-by-step explanation:

A. The ratio of the number of boys to the number of girls is; 115:92

B. The same ratio using another form is; 115 to 92

C. The ratio of the number of boys to the number of adults is; 115:28

D. The same ratio using another form is; 115 to 28

We are told that there are 115 boys, 92 girls, and 28 adults. Thus;

Number of boys = 115

Number of girls = 92

Number of Adults = 28

Now, we want to find some ratios and they are;

A) The ratio of boys to the number of girls = 115 : 92

B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;

115 to 92

C) The ratio of the number of boys to the number of adults is;

115:28

D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28

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The side length of the square in centimeters is 13 centimeters

The area of a shape is the amount of space on the shape

The equation of the area of the square is given as

p² = 169

The area of a square is the product of its length

This means that we simply take the square root of both sides of the equation to determine the side length

Next, we take the square root of both sides of the equation

So, we have

√p² = √169

Evaluate the square roots

So, we have

p = 13

Hence, the side length of the square in centimeters is 13 centimeters

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The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

From the question, we are to determine the equation of the line that is perpendicular to the given equation.

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

That is,

If m₁ is the slope of one of the lines

and m₂ is the slope of the other line

Then,

m₁ = -1/m₂

First, we will determine the slope of the given line

The equation of the given line is

y = 3x - 9

Compare the equation to the general form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = 3

∴ The slope of the given line is 3

Thus,

The slope of the line that is perpendicular to this line is -1/3

Now,

To determine the equation this line,

We have that the line passes through the point (3, 1)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

m = -1/3

x₁ = 3

y₁ = 1

Putting the parameters into the equation,

y - 1 = -1/3(x - 3)

Expressing the equation in standard form

3(y -1) = -1(x - 3)

3y - 3 = -x + 3

3y + x = 3 + 3

x + 3y = 6

Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]

Answer (y2 -y1) / (x2 - x1)

hope this helps

Answer:

(y2 -y1) / (x2 - x1)

Step-by-step explanation:

Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.

Answer:

9 hours

Step-by-step explanation:

605 miles/11 hours = 55miles/hour

495 miles (time) = 495 / 55 =9
So, 9 hours

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

According to the given question:

Each block of horizontal  is 1/8 hr = 7.5 min

Each block of vertical is 10 km/hr

Time                     Velocity  (km/hr)

0 Min  ( 0 hr)               0

15 Min (1/4 hr)           50

45 Min (3/4 hr)           50

60 MIn  ( 1 hr)           100

90 Min  ( 3/2 hr)        100

120 Min ( 2hr)             0

The acceleration in first 15 minutes = (1/4 hr)  =  (50 - 0)/(1/4 - 0)  = 50/(1/4)

= 200  km/h²

The distance between the two cities =

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

Distance between two cities = 125 km

Average Speed of train during the journey = 125/2  = 62.5  km/hr

Therefore,

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

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Answer: 2169 rounded to the nearest hundred is 2200

Step-by-step explanation: Since 6 in the tenth place is greater than 5 the number in the hundred place which is 1 goes up to 2. That is how you get 2200

Here is the two-way table :

Felt tired        Did not feel tired               Total

Ate breakfast                    0.0714                0.7142                           0.7857

Did not eat breakfast        0.0714                0.1428                          0.2143                                  

Total                                  0.1428                 0.8572                                   1  

A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns. A conditional relative frequency is the ratio of the frequency of a class to the total frequency.  

People who ate breakfast and did not feel tired = 110 - 10 = 100

People who did not breakfast and did not feel tired = 30 - 10 = 20

                                              Felt tired        Did not feel tired               Total

Ate breakfast                          10                     100                                    110

Did not eat breakfast              10                      20                                     30

Total                                          20                    130                                     140

                                       Felt tired        Did not feel tired           Total

Ate breakfast                   10 / 140           100 / 140                       110 / 140

Did not eat breakfast      10  / 140          20 / 140                         30 / 140

Total                                20 / 140            130 / 140                         140 / 140

                                         Felt tired        Did not feel tired               Total

Ate breakfast                    0.0714                0.7142                           0.7857

Did not eat breakfast        0.0714                0.1428                          0.2143                                  

Total                                  0.1428                 0.8572                                   1  

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47576777...................

Step-by-step explanation:

GOOD RIGHT?

The function model will be -

Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.

1200/N ≤ 7.50

1200 / 7.50 ≤ N

N ≥ 1200/7.5

N ≥ 160

To keep the price per kid to no more than $7.50, there must be more than 160 participants.

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The students will have 316 yards of the courtyard

The number of yards left for the students can be calculated as follows;

A school dedicated 50% of the courtyard area for students to start a garden

= 50/100

= 0.5

The number of yards is 632, the number of yards left for the students can be calculated as follows

= 0.5 × 632

= 316

Hence 316 yards are left for the students

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Answer:

-5, 1/2, -0.45, -0.05 would be the solution

Answer:

C

Step-by-step explanation:

The radicands have at least one prime-factor that is not in common.

The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.

The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).

The total amount she earns can be represented by

y = 15x + 20

where y is her daily earnings and x is the number of bikes she assembles

If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).

domain : {x| 0 ≤ x ≤ 6}

where x is a whole number

Substituting the minimum and maximum value of x in the function.

y = 15(0) + 20     when x = 0

y = 20

y = 15(6) + 20     when x = 6

y = 110

range : $20 ≤ y ≤ $110

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Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]  .

We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex].        ....(1)

 Let y = f(x)

     [tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex]                         ......(2)

Swap the values of x and y, then the inverse is then

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

Comparing equation (2) and (3) , we get

   [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]

We can check that this is really an inverse function or not

Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex]    equation (1) , we get

[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]

As LHS = RHS  which means inverse function is correct .

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