Given the definitions of f(x) and g(x) below, find the value of (gof)(3).

f(x) = 2x² - x - 15
g(x) = -5x +9

ANSWER and EXPLANATION

We want to order the functions from widest to narrowest:

To do this, we have to plot the graphs of the functions by using a table of values.

Let us find the values of the functions for values of x = -2, 0, 2

For the first function:

Hence, its table is:

For the second function:

Hence, its table is:

For the third function:

Hence, its table is:

Now, let us plot the graphs of the functions:

Therefore, from the graph, we see that the order of the functions from widest to narrowest is:

The addition of the given two functions  f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

Given f(x)= -4x-2

g(x)=2x²+4x-5

For (f-g)(x) = -4x-2+2x²+4x-5

=2x²-9

(f-g)(x) = 2x²-9

Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9

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The measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.

Triangles:

Triangles are geometric figures of three sides with three internal angles. We can apply different laws and rules to solve different types of triangles. For example, the law of cosines allows us to solve oblique triangles. We can find sides and angles by applying this law. We can use the law of cosines if we have the length of two sides of a triangle and the angle formed by them.

Given that

a = 8

b = 5

c = 42°

To solve the triangle, we are first going to make a diagram with the given information:

We start by applying the law of cosines to find the length of

[tex]c^{2} = a^{2}+ b^{2}-2abcosc[/tex]

Substituting a =8, b = 5 and c = 42°, we have

[tex]c^{2} = 8^{2}+5^{2} -2(8)(5)cos42^{0}[/tex]

[tex]c^{2} = 64+25 - 59.45[/tex]

[tex]\sqrt{c^2} =\sqrt{64-34.45}[/tex]

c = 5.435 = 5.4

Now, we apply the law of cosines to find the measure of angle B

[tex]b^2 = a^2+c^2-2accosB[/tex]

Substituting the lengths a = 8, b = 5, c = 5.4

[tex]5^2 = 8^2+5.4^2- 2(8)(5.4)cosB\\[/tex]

Note: we can substitute the lengths of the sides without the unit. Simplifying, we have:

25 = 64+29.16 - 86.4 cos B

25 = 96.16 - 86.4 cos B

cosB = 0.603

Now, we must apply inverse cosine on both sides of the equation:

[tex]cos^-1(cos B) = cos^-1(0.603)\\\\[/tex]

B = 25.256°

B = 25°

Lastly, we apply summation of internal angles of a triangle to find the angle A:

A + B + C = 180°

we need to isolate angle A:

A + 25°+ 42° = 180°

A + 67° = 180°

A = 113°

Hence the answer is, the measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.

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By using the formula of perimeter of square and triangle, the following results are obtained.

Length of the side of square = 9

length of the side of triangle = 12

Area of square = 81

What is perimeter of square and triangle?

Perimeter of square and triangle is the total space taken by the square and triangle.

If the side of the square is a, then perimeter of square is 4a

If the side of the equilateral triangle is a, then perimeter of square is 3a

Length of the side of square = 4x - 3

Length of the side of triangle = 5x - 3

Perimeter of square = 4(4x - 3) = 16x - 12

Perimeter of triangle = 3(5x - 3) = 15x - 9

By the problem,

[tex]16x - 12 = 15x - 9\\16x - 15x = 12 - 9\\x = 3[/tex]

Length of the side of square = [tex]4 \times 3 - 3 = 9[/tex]

Length of the side of triangle =  [tex]5 \times 3 - 3=12[/tex]

Area of square = [tex]9 \times 9 = 81[/tex]

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The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

Given that,

The library is getting new shelves built.

We have to find how long will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

We know that,

We have to divide

4÷2÷5

2÷5

0.4

In percentage we write as 40%.

Therefore, The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

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The amount Kim and Steve will save is $18.75.

Discount refers to a price decrease on items or services that merchants are willing to sell to customers at a marked-up price. Usually, this portion of the rebate is provided to boost sales or get rid of unsold inventory. The list price, also known as the marked price, is the cost of a product as stated by the manufacturer or the seller, and it does not include any discounts. After any reductions or discounts to the list price, the selling price is the actual price at which an item is sold. Discounts are frequently referred to as "off" or "reductions," among other names. It should be noted that the discounted price is always based on the marked price (also known as the list price or original price) of the product.

Given, the discount they have is of 25%.

Original price of the meal is $75.

Now find the discount on the original price.

Discount = Discount (%) * Original Price

               = [tex]\frac{25}{100} *75[/tex]

               = 0.25*75

               = $18.75

Therefore, they saved an amount of $18.75.

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Answer:

43/80 * 14,200

Step-by-step explanation:

Since 80 random people were sampled its will become our denominator and out of 80 people there were 43 people and that 43 will become our numerator the next step is to mulitply 14,200   (im really bad at explaining stuff hope it helps!)

Answer:

43/80 * 14,200

Step-by-step explanation:

It was right when I answered it.

The correct option is :

A package that weighs 7 pounds will cost $17 for both options.

The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.

The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.

We'll compare the equation as a whole.

In this case,

3 + 2x = 17

Compile similar terms

2x = 17 - 3

2x = 14

x = 14 divided by 2x = 7

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in this problem we have that

Triangle JTN is an isosceels triangle, because the triangle has two equal sides and two equal interior angles

segment TE is the altitude of triangle JTN, its a perpendicular bisector segment JN

that means

JE=NE

we have

JT=NT

mso

triangle TJE and triangle TNE are congruent by SAS

triangles TJE and trTNE are acute triangles

For the negative slope equation y = -x as the value of x increases y decreases.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that the graph of a linear function has a negative slope. Suppose the equation with a negative slope is y = -x.

It would look like y = -m(x) + b.

As an illustration, m is 1 and b is 0. (You can try any random number; however, I looked for the most straightforward one so that we could easily observe it.) It will be written as y = -x. (You can also omit this and use random numbers)

If x = 3, y = -3 ; x = 5, y = -5  (x increases, y decreases)

If x = -1, y = 1 ; x = -5, y = 5 (x decreases, y increases)

Hence the answer is for the negative slope equation y = -x as the value of x increases y decreases.

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Given the following question:

Where the trapezoid is...

6ft by 9ft

Find the area:

Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.

There are two decisions possible regarding the null hypothesis, as follows;

The hypothesis are given as follows:

The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.

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(a) A point-slope form of the line is y - y₁ = m(x - x₁)

(b) The slope of the line is 2.

(c) The point (x₁, y₁) = (-1, -2).

(d) The equation of a line in point-slope form is y + 2 = 2(x + 1).

The formula for a straight line: y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is the coordinates of a specific point on the line

(a) Let the two points are (x₁, y₁) and (x₂, y₂)

Then the slope of the lines is given as

m = (y₂ - y₁)/ (x₂ - x₁)

The point-slope form of the line is given as

(y - y₁) = [(y₂ - y₁)/ (x₂ - x₁)] (x-x₁)

y - y₁ = m(x - x₁)

(b) From the graph, (x₁, y₁) = (-1, -2) and (x₂, y₂) = (1, 2)

So, slope = (2 -(-2))/ (1-(-1))

= (2+2)/ (1+1)

= 4/2

= 2

c) (x₁, y₁) = (-1, -2)

d) The equation of a line in point-slope form is given as

y - (-2) = 2(x- (-1))

y + 2 = 2(x + 1)

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To complete the table of values for y = x² - 4x

The equivalent values to complete the table of values are 5, -1, -4 and 0

Given the function according to the table shown:

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

Now let us insert the values in the above given equation one by one

When we have x = -1

[tex]y = (-1)^{2} -4(-1)[/tex]

y = 1+4

y = 5

When we have x = 1

[tex]y = (1)^{2}-4(1)[/tex]

y = 1-4

y = -3

When we have x = 2

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

y = 4-8

y = -4

when we have x = 4

[tex]y = (4)^{2} -4(4)\\[/tex]

y = 16-16

y = 0

Hence the equivalent values to complete the table of values are 5, -1, -4 and 0

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Okay, here we have this:

Considering the provided function, we are going to calculate the requested roots, so we obtain the following:

Finally we obtain that the roots of the function are x=8 and x=4.

The value of an irrational number  [tex]-16 + \sqrt{40}[/tex]  Is approximate, the nearest tenth is  -9.675.

Irrational numbers include all real numbers that cannot be stated as the ratio of two integers, or p/q, where p and q are both integers.

Given expression:

[tex]-16 + \sqrt{40}[/tex]

Factorize the square part as

[tex]-16 + \sqrt{10\times2^2 }[/tex]

Simplify the above expression as

[tex]-16 + 2\times \sqrt{10}[/tex]

We know that [tex]\sqrt{10} = 3.132[/tex]

Hence, -16 + 2 × 3.132

= -9.675

Therefore, the value of an irrational number  [tex]-16 + \sqrt{40}[/tex]  is approximately the nearest tenth is  -9.675.

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Answer: It is 14,596.

Answer: 10 3\4

Step-by-step explanation:

I did the quiz

Answer:

y = 8*(9/4)^x

Point (1.5, 27)

Step-by-step explanation:

We can solve each unknown in separate steps.  The first step is to take advantage of given point (0,8) to find the value of a.  Since x is zero, b^x will just be 1, regardless of b.  That makes it easy to solve for a, which is found to be 8.      

Once a is known, we can use the next point (1,18) to solve for b.  b is (9/4).  

Once we have a and b, we have the full equation:  y = 8*(9/4)^x

k is found by entering the x value and solving for y (which is k).  k = 27

See attached worksheet

Answer:A

Step-by-step explanation:

we have that

The double angles formula is equal to

and remember that

therefore

substitute in the original expression

therefore

Answer:1/3

Step-by-step explanation:

25/75

25/25=1

75/25=3

Answer is 25/75=1/3

The point slope form is:

where m is the slope and (x0,y0) is a point of the line.

In this case, we know the point (0,-5) and the slope is m=2.

Then, we can write the equation in slope point form as:

Answer: y+5=2x (option b)

Answer:

It's very blurry, try sending one section at a time.

Step-by-step explanation:

The image of the dilation is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5) and the graph is attached

The coordinates of the polygon are given as

P(-1, -1), Q(0, -1), R(2, 1) and S(1, 1)

The transformation is given as

A dilation with a scale factor of 5 about the origin

The dilation has the algebraic rule of

(x, y) ⇒ (5x, 5y)

So, we have

P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)

Hence, the coordinates of the image using the dilation rule is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)

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The total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm.

Radius of 1 sphere = 6.5 cm

We know that the volume of the sphere is given by 4/3 π r³

We will take the radius as 6.5 cm and π as 22/7

Now we will find the volume : 4/3 ×22/7×6.5³ = 1150.81 cubic cm.

Volume of 40 such spheres = 40 × 1150.81 = 46032.38 cubic cm.

The radius of all the spheres are 46032.38 cubic cm.

A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. A sphere is a group of points in three dimensions that are all situated at the same r-distance from one another.

The supplied point is the sphere's center, while the letter r stands for the sphere's radius which is half the diameter. The earliest known allusions to spheres are found in the works of two ancient Greek mathematicians.

Therefore total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm .

Disclaimer: The complete question is : Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.​Find the total volume of water required.

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By forming and solving equations, we know that the speed of the runner is 4 miles per hour.

So, we need to form an equation to get the speed of the runner:

'x' is the speed of the runner. Now, solve for x as follows:

Therefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.

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ANSWER:

2 5/6 cups

STEP-BY-STEP EXPLANATION:

To find the total cups, we must add the number of cups in each case, like this:

For ease, we'll convert each fraction so that they all have the same denominator:

That is to say that in total there are 2 5/6 cups of fruit punch