The total number of degrees in the center is 360°. if all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles? 54° 72° 108° 144°

Answer:

Step-by-step explanation:

Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x).  That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).

See the attached image.  The table shows how the values of y change for each value of x used in the respective function.  Plot those new values to produce the graph.

Answer:

[tex]\fbox {tan A = 0.5333}[/tex]

Step-by-step explanation:

tan A = opposite side of ∠A / hypotenuse

tan A = 8 / 15

tan A = 0.5333

Answer:

tan A = perpendicular/ base

tan A = 8/15

tan A=0.5333

Step-by-step explanation:

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Answer:

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

What is the equation for this situation?

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Step-by-step explanation:

This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given expression

y = x + 5.5

The possible values are

x = It is expected x is equal to 0 or greater to it

since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

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Answer:

$189

Step-by-step explanation:

35% of 140 = 49

140 + 149 = 189

Tom's total saving this year is $189.

It is a 35 percent increased saving from last year's $140.

Percentages are fractional values where the denominator is fixed to be 100.

To convert percentage into number, we multiply by 100.

In the question, we are informed that Tom was able to save 35% more this year than he did last year.

We are asked if he saved $140 last year, then how much did he save this year.

The increase in Tom's savings = 35% of last year's savings,

or, the increase = 35/100 * 140 (To convert percentage into quantity, we divide by 100).

or, the increase = $49.

Therefore, Tom's total savings this year = Last year's savings + Increase,

or, Tom's total saving this year = $140 + $49 = $189.

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Answer:

[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]

Explanation:

Foil method: (a + b)(c + d) = ac + ad + bc + bd

Solving steps:

[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]

[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]

[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]

[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]

[tex]1 +2\sqrt{7}[/tex]

option b) 1 + 2√7

Foil property method :-

[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]

then, on substituting the values,

[tex]\sf⇒ \:  \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]

[tex]\sf⇒ \:  \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]

Step-by-step explanation:

f(x) = y = 64x³ - 1

y + 1 = 64x³

(y + 1)/64 = x³

[tex]x = \sqrt[3]{(y + 1) \div 64} [/tex]

[tex]x = \sqrt[3]{y + 1} \div 4[/tex]

that is the actual inverse function to calculate the original x value for a given y value of the original function.

but to make it a "normal" function, we need to rename the variables (x to y, y to x) :

[tex]y = \sqrt[3]{x + 1} \div 4[/tex]

this is now f^-1(x)

but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...

Answer: B

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)=(2x+1)-(x^{2}-7)=2x+1-x^{2}+7=\boxed{-x^{2}+2x+8}[/tex]

The paint that the farmer needs to paint his Silo will cost $152.75.

To calculate the value of the total paint that the farmer will require, we must carry out the following procedure:

1. Identify the area you need to paint

2. Find how many cans of paint he needs.

That is, he will need 13 cans of paint.

3. Find the price of 13 cans of paint.

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-11, -6, -7 and -6.1 are the answers

The inequality is r lesser than or equal to -6

The value of cosine theta (cosθ) for the given triangle is determined as 4.58/5.

For a given sine value of a triangle, the remaining side length of the triangle can be calculated as follows;

sinθ = opp/hypo = 2/5

b² = 5² - 2²

b² = 21

b = 4.58

Value of cosine θ

Cosθ = adj/hypo

Cosθ = 4.58/5

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The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

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The attached graph represents the graph of f(x) = (x - 1)^2 - 2

The equation is given as:

f(x) = (x - 1)^2 - 2

Next, we set x to -2, -1, 0, 1 and 2.

So, we have:

f(-2) = (-2 - 1)^2 - 2 = 7

f(-1) = (-1 - 1)^2 - 2 = 2

f(0) = (0 - 1)^2 - 2 = -1

f(1) = (1 - 1)^2 - 2 = -2

f(2) = (2 - 1)^2 - 2 = -1

This means that the table of values is

x      f(x)

-2    7

-1    2

0    -1

1     -2

2    -1

Next, we plot the above points and connect them.

See attachment for the graph of f(x) = (x - 1)^2 - 2

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Answer:

See below

Step-by-step explanation:

The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .

a = adult tickets         cost = 15 a

c = children's tickets    <=== this is equal to 20 - a    

                  cost for children's tickets equals   10(20 - a)

15 a + 10c   =   225           rememeber c = 20 -a <===put that in

15 a      + 10 ( 20 -a)   = 225    solve for a

15a + 200 - 10 a = 225

5 a = 25

a = 5   tix                 then     c = 20 - a =  15   tix

Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.

So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!

So your final answer is 3/4.


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Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]

Step-by-step explanation:

[tex]\textsf {Question 9}[/tex]

[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]

[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]

[tex]\mathsf {15b + 4}[/tex]

[tex]\textsf {Question 10}[/tex]

[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]

[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]

[tex]\mathsf {4y + 6}[/tex]

[tex]\textsf {Question 11}[/tex]

[tex]\mathsf {8(r + 9) + 7r}[/tex]

[tex]\mathsf {8r + 8(9) + 7r}[/tex]

[tex]\mathsf {8r + 7r + 72}[/tex]

[tex]\mathsf {15r + 72}[/tex]

[tex]\textsf {Question 12}[/tex]

[tex]\mathsf {10(3n + 2 + 10n)}[/tex]

[tex]\mathsf {10(13n + 2)}[/tex]

[tex]\mathsf {10(13n) + 10(2)}[/tex]

[tex]\mathsf {130n + 20}[/tex]

The polynomial within the numerator is 9x²+45x+54.

Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.

A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let's take the polynomial within the numerator is k.

So, rewrite the given expression as

[tex]\frac{k}{3x^2+15x+18}=3[/tex]

or it also can be written as

[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]

Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire

k=3(3x²+15x+18)

Simplify the above expression,

k=9x²+45x+54

Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.

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Answer:a

Step-by-step explanation:

The constant of proportionality is 0.1

Find the constant of proportionality (r)in the equation y=rx.

r =

x    y

14  1.4

16  1.6

21  2.1

The equation is given as:

y = rx

When x = 14 and y = 1.4, we have:

1.4 = r * 14

Divide both sides by 14

r = 0.1

Hence, the constant of proportionality is 0.1

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Answer:

y = 1.5x + 1

Step-by-step explanation:

→ Choose 2 points

( 2 , 4 ) ( -2 , -2 )

→ Find the gradient

-6 ÷ -4 = 1.5

→ Write into format

y = 1.5x + c

→ Substitute in ( 2 , 4 )

4 = 3 + c

→ Minus 3 from both sides

1 = c

y = 1.5x + 1

Answer:

10

Step-by-step explanation:

By the geometric mean theorem,

[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]

Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [

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Answer:

2 pi : 1

Step-by-step explanation:

for every one unit of radius, there are two pi units in the circumference!

The area of the surface of the pool is 7322.64 m².

The area of rectangle is product of length and its breadth.

i.e., length * breadth

Given: Length = 100 m, Width = 52 m and Diameter = 52 m

Area of rectangle,

= 100 × 52

= 5200 m²

Now,

Area of semicircle = 1/2 × πr²

=1/2 × 3.14 × 26²

= 1061.32 m²

Hence, area of the surface of the pool is

= 1061.32 + 1061.32 + 5200

= 7322.64 m²

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5200 square meters, 1061, 7322

Answer:

D) 20

Step-by-step explanation:

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Answer:

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Answer:

Let the cost of orange be X and cost of cherry be y

3x + 9y = 78

8x + 4y = 58

Solving equation using elimination method

multiplying eq 1 with 8 and eq 2 with 3

8(3x + 9y ) = 78(8)

3( 8x + 4y) = 3(58)

24x + 72 y = 624

24x + 12y = 174

subtracting,

60 y = 450

y = 7.5

3x + 9(7.5) = 78

3x + 67.5 = 78

3x = 78 - 67.5

3x = 10.5

x = 3.5

In insurance, in a 100/300 policy, it should be noted that up to $100,000 bodily injury per single person injured in the accident will be covered.

An insurance coverage simply means the amount of risk or liability for an individual.

In this case, in a 100/300 policy, up to $100,000 bodily injury per single person injured in the accident will be covered.

Also,an amount up to $300,000 in total will be for bodily injuries per accident. Finally, there's a $100,000 for damages to the property of others.

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Answer: 6 ft

Step-by-step explanation:

[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]

The square root contains two same numbers and the cubic root contains three same numbers.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The square root contains two same numbers and the cubic root contains three same numbers.

For an example:-

√9 = [tex]\sqrt{3\times 3}[/tex] =  3 as we can see in the example the value of the square root of 9 is 3 it consists of two threes in the roots.

∛27 = [tex]\sqrt[3]{3\times 3\times 3}[/tex] = 3 here we have found that 27 contains 3 times 3 so the cube root of 27 will be equal to 3.

Therefore square root contains two same numbers and the cubic root contains three same numbers.

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The average rate of change in h(t) is 6.

It is a measure of how much the function changed per unit, on average, over that interval.

h(t) = 3 + 70t - 16t²

Average rate of change

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2

h(1) = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2

h(3) = 69

Average rate of change = Δh / Δt

=[h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6.

Hence, the rate of change is 6.

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