After Charlie ate 2/3 of the remaining cake, he divided the rest equally among his 3 friends. What fraction of the pan of cake did each friend get? Write an expression and show all of your work.

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

A function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.

Here,

Given :

f(x) = 3x²-3x - 8

g(x) = -x - 7

To find : fog)(-8)= ?

Thus,

We find

=> F(g(x)) => 3g(x)² -3g(x) - 8

=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8

At x =-8

=> 3(-8-7)² - 3(-8-7)-8

=> 3(225)-3(15) -8

=> 675 - 45 -8

=> 622

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

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quadrilateral with both pairs of opposite sides congruent

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.

So, the option  I only is correct

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solving sin ( 4x ) = √3 / 2 , the value of x is 15°

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

For angle of 30° and 60°

sin 30° = 1/2

cos 60° = √3/2

tan60° = √3

for angle 60 °

sin60° = √3/2

cos 60° = 1/2

tan60° = 1/√3

since sin(4x) = √3/2

and sin 60° = √3/2

sin60° = sin(4x)

this means 60° = 4x

divide both sides 4

x = 60/4

x = 15°

therefore the value of x is 15°

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If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;

the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;

the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is

⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]

substituting the values ,

we get the equation as ;

⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]

taking LCM as 4 and 6 as 12 and solving further  ,

we get ;

⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .

Therefore , the fraction of fruit  punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The given question is incomplete , the complete question is

About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .

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Answer:

96π or 301.59 in³

Step-by-step explanation:

V(cone) = 1/3πr²h

= 1/3·π·6²·8

= 96π or 301.59

Answer:

301.58  

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

slope, m = (y₂ - y₁)/(x₂ - x₁)

plug in the values, and we get m = (3 - (-1))/((3 - 2) = 4

As x increases by 1, y increases by 4.

-1

Step-by-step explanation:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Answer:

See graph below

Step-by-step explanation:

The equation r=5cosθ basically means the graph is going to be a circle with a radius of 5/2=2.5 to the right on the horizontal axis since it's cosine.

To graph the function r=5cosθ, we graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ and a radius of 2.5

The function is given as:

r=5cosθ

The above means that, we want to graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ.

The radius r is calculated using;

r = 5/2

r = 2.5

Hence, the graph of r=5cosθ has a radius of 2.5

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Answer:

c and d

Step-by-step explanation:

Answer: You plug in y as 0 into your equation.

Step-by-step explanation:

Do the above thing OK.

Answer:

Jack has 8 and his brother has 17

Step-by-step explanation:

j = # jack has

b = # brother has

j + b = 25

b = 1 + 2j  (brother has one more than twice the amount jack has)

j + 1 + 2j = 25

3j = 24

j = 8

b = 25-8 or 17

Answer:

y=(this is a fraction) 4/3 times x-3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(3x+2)(x-4)

3x^2-12x+2x-8

3x^2-10x-8=0

The length BC of the right triangle is 18 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:

Therefore, using proportion because triangle ABC is similar to triangle BDC.

x / 36 = 9 / x

cross multiply

x × x = 36 × 9

x² = 324

square root both sides of the equation

x = √324

x = 18 units

Therefore,

BC = 18 units

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Answer:

Sorry I don't know this one, I got 5.32

Step-by-step explanation:

Answer:

<ABC and <CB both add up to 90 degrees and fit in the angle <ABD so they could be 45 degrees, or one could be 20 degrees while the other is 70, they just have to add up to 90 degrees

Step-by-step explanation:

The slope and the y-intercept of the given data table will be option A) Slope= -0.0018, y-intercept = 212

The y-intercept of any linear equation is the point at which the line or the curve intersects the vertical i.e the Y- axis.

To find this intercept, the value of x is taken to be 0 in the model, since on the Y-axis, the value of x is 0.

Here from the given table, we need to check the boiling point or the value of Y for which the value of the altitude or the x value is 0

Hence we get the y-intercept as 212° F.

Now, the formula for slope

= change in y/ change in x

here we will take any two data rows and divide the difference in boiling points by the difference in altitudes.

Taking the first 2 rows gives us

Slope = -0.9/500

= -0.0018

Hence we choose option A) Slope = -0.0018, y-intercept = 212

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Complete Question

The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y-intercept of the line that models this situation?

A. Slope= -0.0018, y-intercept = 212

B. Slope= 0.0018, y-intercept =-212

C. Slope =212, y- intercept= 0.0018

D. Slope=-212, y-intercept = 0.0018

a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

What is histogram ?

A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.

a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram

b) For this one the class width is given to be the following: class with = 10 .  See the attachment for table

c)  See the attachment for the graph

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Answer:

4,800

Step-by-step explanation:

6,000/5

1,200x4

4,800

Therefore , the solution of the given problem of probability comes out to be  thus brand A is more prefer by the person as probability of B IS 0.43.

A probability is a number that represents the likelihood that a certain event will occur. Probabilities may be expressed as percentages

range from 0% to 100% or from 0 to 1.

Here,

Given :

Which brand of pasta do Texas and California prefer

Because brand B is preferred by 45 persons in Texas, the answer would be A.

There are 105 persons that favor brand B overall.

=> 45/105

=> 15/ 35

=> 0.42857...

So ,

rounded it would be 0.43,

thus brand A is more prefer by the person

Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.

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r=13/2

After I solved it it was kinda easy

Answer:

r=13/2

Step-by-step explanation:

Answer:

could you just give the

Step-by-step explanation:

equation so I could try to solve it

Answer:

The answer is 22.4

Answer: JNL

Step-by-step explanation: We can give angle 1 another name by using 3 letters which include the letter of the vertex point in the middle, and two other letters of the two rays that meet at the vertex point.

Answer:

where is the question????

Answer:

where

Step-by-step explanation:

Answer:

Are you asking for it from miles to inches?

If so it would be 20

Step-by-step explanation:

600/30=20

Hope this helps <3

Answer:I think it would be 20 inches that is if your supposed to do 600÷30

Step-by-step explanation:uhh I hope this is right good luck tho

Answer:

24

Step-by-step explanation:

To answer this you simply need to divide 6 by 1/4

or

6÷1/4

which is also equivalent to 6*4

this will get you 24