adding and subtracting polynomials​

The number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The period of a periodic function is 8 s

From the question:

8n = 30

n = 30/8

n = 3.75 cycles

Thus, the number of cycles of the periodic function is 3.75 cycles if the  period of a periodic function is 8 s option (G) 3.75 is correct.

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Answer:

a. -5 b. 23 c. 871 d. -5

Step-by-step explanation:

f(x) = x^2 + 6x and g(x) = x - 4

a). (fog)(3) = (x - 4)^2 + 6(x - 4)

= (3 - 4)^2 + 6(-1)

= 1 -6

= -5

b). (gof)(3) = ( x^2 + 6x) - 4

= (9 + 18) - 4

= 23

c). (fof)(3) = (x^2 + 6x)^2 + 6(x^2 + 6x)

= 27^2 + 27(6)

= 871

d). (gog)(3) = (x - 4) -4

= (3 - 4) - 4

= -5

Answer:

y=2x+25

Step-by-step explanation:

please if you like the answer rate it 5 stars and mark as brainliest

Answer:

C

Step-by-step explanation:

Speed is distance/time. We can solve for the highest speed by looking at each spot on the graph.

In a, the highest speed is 7/1, or 7. In b, it's 30/4, or 7.5. In c, it's 60/7, or about 8.57. In D, it's about the same, but since it's decreasing drastically, it will go to C.

Answer:

the person was moving the highest at C

since speed=gradient in distance time graphs so if you find each gradient c will be the highest being 30m/h while point A was 7.5m/h, b was stationery and point d was -20m/h, negative means it's decelerating. you could also guess that C has the highest speed since its the steepest line out of them all.

7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12

What is equation ?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

given equations

2x+3y=-5

5z-y = -12

we have to add these two equations

Add 2x and 5x to get 7x

Add the y's

3y + (-1y)  OR 3y - y      

Which gives you 2y

add the (-5 and -12)

-12 + (-5) or -12 - 5 giving you -15

7x+2y=-17

Hence ,7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12

the complete question is

What is the result of adding these two equations?

2x+3y= -5

5x - y = - 12

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The equation of the parabola that has the same shape as  [tex]f(x) = -8x^2[/tex], but with the vertex (4,9) is  [tex]f(x) = -8(x - 4)^2 + 9.[/tex]

The general equation of a parabola is given by

y = a(x – h)² + k

or x = a(y – k)² + h.

Here (h, k) denotes the vertex.

Now it is given that,

The parent function is [tex]f(x) = -8x^2[/tex]

The vertex of parabola is given as (4,9)

Thus, we have

h = 4

k = 9

Now since, the transformations form of a parabola is given as:

[tex]f(x) = a(b(x - h)) + k[/tex]

where:

a = vertical distance

b = horizontal distance

h = horizontal shift, x-coordinate of vertex

k = vertical shift, y-coordinate of vertex

Therefore, transformed equation of parabola is given as,

[tex]f(x) = -8(x - 4)^2 + 9[/tex]

this is the required equation of parabola with the vertex (4,9).

Thus, the required equation of the parabola that has vertex (4,9) is [tex]f(x) = -8(x - 4)^2 + 9[/tex].

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Answer:

63 3/4

Step-by-step explanation:

First:

convert any mixed numbers to fractions.

Then your initial equation becomes:

17/2 ÷ 2/15

Applying the fractions formula for divison,

= 17/2×15/2

= 255/4

Simplifying 255/4, the answer is = 63 3/4.

Hope this helps :)

Answer:

63.9

Step-by-Step Expectation:

8.5/0.133=63.9

The linear equation that we want to graph is:

y = (2/3)*x - 9

And its graph can be sen at the end of the answer.

First, we need to find the linear equation. We know that it passes through the point (6, - 5) and it has a slope of (2/3), then we can write:

y = (2/3)*x + b

To find the value of b, the y-intercept, we replace the values of the point:

-5 = (2/3)*6 + b

-5 = 4 + b

-5 - 4= b = -9

The linear equation is:

y = (2/3)*x - 9

And its graph can be seen in the image below:

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Answer:

the numbers are 27,28

Step-by-step explanation:

Let the numbers be x,x+1

The sum is 55

⟹x+x+1=55

2x+1=55

2x+54

x=27

So the numbers are 27,28

The required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.

What are the factors of an expression?

Any number or expression that completely divides another number or expression is called as the factor of an expression. These can be positive or negative depending upon the given expression.

Calculating the factor of expression. 4x² - 9

Given an expression, 4x² - 9

Terms of an expression are 4x², - 9

Further breaking the terms to factors, we obtain,

4, x, x, -3, 3

Hence, the required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.

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Answer:

y = (1/6)x - 11

Step-by-step explanation:

y = (1/6)x + 7; Point: (12, -9)

                                 (x₁, y₁)

y - y₁ = m (x - x₁)

y - (-9) = (1/6) (x - 12)

y + 9 = (1/6)x - 2

    -9              -9

y = (1/6)x - 11

I hope this helps!

The volume of water in the vase is 103.5π inches³.

Diameter (d) of Cylindrical vase = 6 inches

Radius (r) of Cylindrical vase = d/2 = 3 inches

Height (h) of Cylindrical vase = 12 inches

Volume of Cylindrical vase (V) = πr²h

                                                     = π × 3 × 3 × 12

                                                     = 108π inches³

As we know that at the bottom of the vase, there are 7 marbles,

and,  Diameter of Marbles = 3 inches

         Radius of Marbles = 1.5 inches

Marble is a shape of sphere, so

The Volume of Marble = 4/3 (πr³)

                                       = 4/3 ( π × 1.5 × 1.5 × 1.5)

                                       = 4/3 ( 3.375π)

                                       = 4.5π inces³

To find the volume of water in the vase, we have to subtract the volume marbles from the volume of cylindrical vase,

The volume of water in the vase = 108π inches³ - 4.5π inces³

                                                       = 103.5π inches³

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Answer:

n(3in)2(12in) - 7(4/3n(1.5in)3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: $43.33

Solution:

Sale price = Original Price x 1.20(discount)

Original price = Sales Price divided by discount

Therefore:

Original price = $52 / 1.2 = $43.33 dollars (just round)

[tex]\textit{since the roots are }-2\pm \sqrt{3}\implies \begin{cases} x=-2 + \sqrt{3}\implies&x+2-\sqrt{3}=0\\\\ x=-2 - \sqrt{3}\implies&x+2+\sqrt{3}=0 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]( ~~ x+2-\sqrt{3} ~~ )( ~~ x+2+\sqrt{3} ~~ )=\stackrel{y}{0} \\\\\\ \underset{\textit{difference of squares}}{( ~~ \underline{(x+2)}-\sqrt{3} ~~ )( ~~ \underline{(x+2)}+\sqrt{3} ~~ )}=y\implies (x+2)^2~~ - ~~(\sqrt{3})^2~~ = ~~y \\\\\\ (\stackrel{F~O~I~L}{x^2+4x+4})~~ - ~~(3)~~ = ~~y\implies {\LARGE \begin{array}{llll} x^2+4x+1=y \end{array}}[/tex]

Answer:

155 degrees

Step-by-step explanation:

It is halfway in between the 150 and 160 marks.

Answer:

-2x2 - 50

Step-by-step explanation:

First, you collect the like terms:

x2 - 3x2 + 5 x -8 -10

Do multiplication first:

x2 - 3x2 + (-40) - 10

Combine the terms:

-2x2 - 50

Answer:

5 star of you

Step-by-step explanation:

you are cool dictator

It should be noted that the slope shows that the rate of change in elevation rise at first but later reduced.

The total change in elevation is 10500 feet

It should be noted that from the table, the time and the elevation has been given.

Therefore, the total elevation will be the addition of all the values given. This will be 10500 feet.

Also, the slope shows that the rate of change in elevation rise at first but later reduced.

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Answer:

Hello! Here's the correct answer to your question:)

5y+23

An expression which is represented by the diagram (see attachment) is: A. -6 - (-1).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

By critically observing the diagram (see attachment), we can logically deduce the following information:

In this context, we can the diagram (see attachment) by using the following expression:

-6 - (-1)

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Answer: ob false

Step-by-step explanation: look at a calculator and it will show 8 is not a 5 is not 8 times five is 40 hope this helps

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x-6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so for a perpendicular line to that one then

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so we're really looking for the equation of a line whose slope is -2 and that it passes through (2 , -1)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{2}) \implies y +1= -2 (x -2) \\\\\\ y+1=-2x+4\implies {\LARGE \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

The results of the composition of two functions are listed below:

Let f and g be functions, with which we are asked to find the expressions of composite functions, where the input of one of the functions is substituted by the other function. The operation of composition is defined below:

f ° g (x) = f [g (x)]    

If we know that f(x) = x + 1 and g(x) = 2 · x + 5, then the resulting expression are shown below:

a) f ° g (x) = f [g (x)]

f ° g (x) = (2 · x + 5) + 1

f ° g (x) = 2 · x + 6

b) g ° f (x) = g [h (x)]

g ° f(x) = 2 · (x + 1) + 5

g ° f (x) = 2 · x + 7

c) f ° g (- 1) = f [g (- 1)]

f ° g (- 1) = 2 · (- 1) + 6

f ° g (- 1) = 4

d) g ° f (- 1) = g [f (- 1)]

g ° f (- 1) = 2 · (- 1) + 7

g ° f(- 1) = 5

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Answer:

4. Fixed and movable pulleys can be combined.

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{6}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2s = 6[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

s = 3[tex]\sqrt{2}[/tex]

The length of side s in the given square is 3√2 units. Therefore, option F is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given square, each sides measures s units and the diagonal measures 6 units.

We know that, sinθ=Opposite/Hypotenuse

Now, sin45°=s/6

1/√2 =s/6

s=6/√2

s=3√2

Therefore, option F is the correct answer.

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Answer:

Step-by-step explanation:

a. 4.2-2.8= 1.4

b. 72.1-45.6=26.5

c. 82.2-41.3-29.2=11.7

d.17.1-11.7-0.8=4.6

e.29.2-12.5-0.9=15.8

Answer: A. 1.428, B. 26.41, C. 11.686, D. 4.574, E. 15.77

Step-by-step explanation: These are the answers for all of them

The inverse of [tex]f(x) = \sqrt{x - 4}[/tex] is [tex]f^{-1}(x) = x^{2} +4[/tex] that is option G) is correct

According to the question we have been given the function which is :

                  [tex]f(x) = \sqrt{x - 4}[/tex]

To find the inverse of this function we will solve this step by step

First we will convert it into equation form

    [tex]y = \sqrt{x - 4}[/tex]

Then we will interchange the variables x and y

 [tex]x = \sqrt{y - 4}[/tex]

Then we will solve for y, we get

Taking square on both sides of the equation, we get

[tex]x^{2} = y - 4[/tex]

[tex]y = x^{2} + 4[/tex]

Now replacing variable y with [tex]f^{-1} (x)[/tex] , we get

[tex]f^{-1}(x)[/tex] = [tex]x^{2} +4[/tex]

Thus the inverse of [tex]f(x) = \sqrt{x -4}[/tex] is [tex]f^{-1} = x^{2} +4[/tex] that is option G) is correct

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Answer: 27

Step-by-step explanation:

The interval in which the function has positive average rate of change is x > √3

The function is given as

f(x) = x^3 - 9x

Differentiate the above function to determine the average rate of change

So, we have

f'(x) = 3x^2 - 9

Set the function to greater than 0

So, we have

3x^2 - 9 > 0

Add 9 to both sides

3x^2 > 9

Divide by 3

x^2 > 3

Take the square root of both sides

x > √3

Hence, the interval in which the function has positive average rate of change is x > √3

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