Multiply. Write your answer as a fraction in lowest terms.

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:

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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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]

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 solution of the given equation by rounding off it to the nearest ten-thousandth is 1.0000.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: 5³x = 125

As given equation is 5³x = 125      —- 1

We know that 5³ = 125

So, equation 1 becomes,

125x = 125

x = 1

Hence, the solution of the given equation in nearest ten thousandth is 1.0000.

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The area that can be watered by the pipe of length 500 inches is approximately 18.03 square yards, when the length of the pipe is 800 inches the area watered is approximately 46.16 square yards and when the length of pipe is 1300 inches the area watered is approximately 121.89 square yards as calculated by the given function.

A function is defined as a relation between the dependent variable and the independent variable.

The length of the pipe is given by the function L=117.75√A where A is the area of the lawn that can be watered.

Now to calculate the area that can be watered using a particular length of pipe we have to find the inverse of the given function.

Given L=117.75√A

Squaring both sides we get

L²=13865.0625 × A

or , A=L²÷13865.0625

Now given length L=500 inches

Substituting the values we get:

A=(500)²÷13865.0625

A=18.0309...

A≈18.03 square yards

Hence the area that can be watered is approximately 64.68 square yards.

Similarly for length 800 inches

Area watered= (800)²÷13865.0625=46.159 square yards.

≈46.16 square yards

Similarly for length 1300 inches

Area watered=1300²÷13865.0625=121.889 square yards

≈121.89 square yards

Therefore the area that can be watered by the pipe of length 500 inches is approximately 18.03 square yards, when the length of the pipe is 800 inches the area watered is 46.16 square yards and when the length of pipe is 1300 inches the area watered is 121.89 square yards.

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Answer:

155 degrees

Step-by-step explanation:

It is halfway in between the 150 and 160 marks.

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)

The value of the composite function (h⁰ g)(x) calculated by  function operation is  -x-10 .

A function is defined as the relation between element of two sets, domain and range. A function is usually denoted using f, g or h .

A algebraic function is defined as y=g(x) such that each element y is related to a single value of x.

(h ∘ g)(x) is also written as h[g(x)] is called a composite function where which means the value of x=g(x) will be substituted in the function h(x).

Composite function is a process that joins two functions to create a third, unique function.

The output of one function becomes the input of another function in h of g of x.

Given functions are:

g(x)=1/2 x+7  and h(x)=-2 x+4

Therefore (h ∘ g)(x)=h[g(x)]

=h(1/2 x+7)

=-2(1/2 x+7)+4

=-x-14+4

=-x-10

Hence the value of the function operation  (h⁰ g)(x) is  -x-10 .

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The inverse of function y = x² / 5 is y = √5x.

given that the function is y = x² / 5

A function that can reverse into another function is known as an inverse function or anti function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.

[tex]x = \frac{ {y}^{2} }{5} \\ 5x = {y}^{2} \\ y = \sqrt{5x} [/tex]

Hence, the inverse of function y = x² / 5 is y = √5x.

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The polynomial that cannot be factored in the real number system is x²+4.

Factorization or factoring in mathematics is the process of expressing a number or other mathematical object as the sum of many factors, which are often smaller or simpler objects of the same type. For instance, the polynomial x² - 4 and the integer 15 can both be factored by the number 3×5.

By checking options

option a x²-3x+2 can be factorized as (x-2)(x-1) by using the sum and product rule.

option b x² +4 cannot be factorized.

option c 4x²-1 can be factorized by using property a²-b²=(a-b)(a+b)

             as (2x-1)(2x+1)

option d  2 x² y-2 x y² can be factored by treating x and y as being equivalent to -2xy(x-y)

Therefore, the polynomial that cannot be factored in the real number system is x²+4.

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Answer: y = -1/2

Step-by-step explanation:

Use the elimination method. When setting the equations up, you can see that the y values already cancel out. This makes it easy to find the x value.  

3x+4y=4                  3x+4y=4  

2x-4y=6     ----->  (-) 2x-4y=6

For the x value, you would get 2. 5x=10 therefore x=2.

Now that you have your x value, choose one of the original equations(either works). I chose 3x+4y=4. Now, substitute 2 into the x value then solve your equation for the y-value.

3x+4y=4   --->  3(2)+4y=4

3(2)+4y=4 then becomes 4y=-2 and when you isolate the variable, you get -1/2.

Answer:

D. 3/2

Step-by-step explanation:

You can see the graph is going up, so that eliminates A. and C. as they are both negative. Next, you can see that according to the graph, the line goes up 6 for every 4 to the right, so the equation is 6/4 which simplifies to 3/2.

Answer:

The Answer is D 3/2

Step-by-step explanation:

Hope this Helps!!!

Riley needs 18 rooms for 72 puppies.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

Riley works for puppy shelter moving to a new building.

The rooms in the new building are built to hold 4 puppies each.

Now, There are 1 room for 4 puppies.

Number of room for 4 puppies = 1

Hence, Number of room's for 72 puppies = 1/4 × 72

                                                                 = 72/4

                                                                 = 18

So, Riley needs 18 rooms for 72 puppies.

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Based on the exterior angle theorem, an expression that can be used to find the measure of angle 4 is:

m∠1 + m∠2 = m∠4.

The exterior angle theorem is a theorem that states that the sum of the measures of two opposite interior angles is equal to the measure of an exterior angle of the triangle.

For example, if c is an exterior angle of a triangle, and a and b are the two interior angles that are opposite to c, the exterior angle theorem states that: a + b = c.

Angle 1 and angle 2 are interior angles of the triangle in the diagram which are opposite to angle 4.

Therefore, based on the exterior angle theorem, an expression that can be used to find the measure of angle 4 is:

m∠1 + m∠2 = m∠4.

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The area of a rectangular flower garden is 25/16

the area of the rectangular garden is =length x width

 given,

length=5/8

width=2 1/2

area = l x b

       =5/8 x 2 1/2

        = 25/16

To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.

Area is the amount of space that a flat, 2D object takes up. Area is measured in square units, like square feet or square meters.

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The area of a rectangular flower garden is 25/16 .

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

To find the area of a rectangle, multiply its height by its width.

The area of the rectangular garden is =length x width

Given that: length=5/8

width=2 1/2

Area = l x b

        =5/8 x 2 1/2

        = 25/16

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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.

Answer:

yessssssssssss

Step-by-step explanation:

omg this is so easy why would u even feel the need to ask such simple question just use ur caluculator

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

Answer:

They are conguent.

Step-by-step explanation:

Based on the advertisement seen by Dazuri, the cost of each soccer ball is $22.50

The advertisement says that the original cost of the ball is $30 but there is a 25% discount.

The price of each soccer ball is therefore reduced by the 25% discount on the ball.

The amount that each soccer ball costs is therefore:
= 30 - ( 30 x 25%)

= 30 - 7.5

= $22.50

Rest of the question is:
Soccer balls on sale at a 25% discount. Prices go back to $30 in a week. Don't miss out.

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the real roots are

y=0

x=3

x=4

therefore two rational roots (A)

Answer: 27

Step-by-step explanation:

[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:

4953

Step-by-step explanation:

- - =+

771+4182=4953

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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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:

y=2x+25

Step-by-step explanation:

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