Simplify the expression.

The function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

The given parameters are:

f(x) = 3x - 6; g(x) = 8x +4

The composite function is calculated as:

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (3x - 6) * (8x + 4)

Expand

(f.g)(x) = 24x^2 + 12x - 48x - 24

Evaluate the difference

(f.g)(x) = 24x^2 - 36x - 24

The above function is a quadratic function;

Quadratic functions have a domain of all set of real numbers

Hence, the function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers

Read more about composite functions at:

https://brainly.com/question/10687170

#SPJ1

The range for the following inequality rounded to nearest hundredth is 46.57≤x≤52.45

In mathematics, an inequality is a relation that holds between two values when they are different. The notation a ≠ b means that a is not equal to b. It does not say that one is greater than the other, or even that they can be compared in size . Inequality are the sign which assign the great and less of amount between to numbers,`<. .>

Let's solve your inequality step-by-step.

16≤1.02x−31.5≤22

Add 31.5 to all parts:

16+31.5≤1.02x−31.5+31.5≤22+31.5

Adding we get:

47.5≤1.02x≤53.5

Divide all parts by 1.02:

47.5/1.02≤1.02x/1.02≤53.5/1.02

Dividing we get:

46.568627≤x≤52.45098

Rounding it to nearest hundredth we get

46.57≤x≤52.45

LEARN MORE ABOUT INEQUALITIES FROM:

https://brainly.com/question/11613554

#SPJ10

Answer:

Step-by-step explanation:(-4, -1) --> (4, -1). Translating two units to the right means adding two units to the x-coordinate: (4, -1) --> (6, -1). This is our final point

Answer:

3.) b) The straight line that divides the parabola into half.

4.) b) 1/11^4

Explanation:

3. The axis of the symmetry is the straight line that divides the parabola into half.

Note down: the image below which shows a parabola (red line) and axis of symmetry (blue line).

4. Formula's: [tex]a^{-1} = \dfrac{1}{a}[/tex] , same with [tex]a^{-4 } = \dfrac{1}{a^4}[/tex]

So here: [tex]11^{-4}[/tex] is equivalent to [tex]\dfrac{1}{11^4}[/tex] which later equals to [tex]\dfrac{1}{14641}[/tex]

The amount of money​ you'll have at the end of 10 years is $3900.

Given that, P=$3000, R=3% and T=10 years.

The formula to find the simple interest is [tex]Interest=\frac{P \times T \times R}{100}[/tex].

Now, simple interest [tex]=\frac{3000 \times 10 \times 3}{100}=\$900[/tex].

Amount=Simple Interest+Principal

=900+3000=$3900

Therefore, the amount of money​ you'll have at the end of 10 years is $3900.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

#SPJ1

The solution to When asked to find the sum of two mixed numbers with different denominators, you should before you add, find a common denominator.

For instance,

4 1/3 + 3 2/5

= 13/3 + 17/5

find common denominator

= (65+51) / 15

= 116/15

= 7 11/15

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

The attached graph represents a histogram that has a range of 55

The range is given as:

Range = 55

The range is calculated as:

Range = Maximum - Minimum

So, we have:

Maximum - Minimum = 55

Rewrite as:

Maximum = Minimum + 55

Let the minimum be 10.

So, we have:

Maximum = 10 + 55

Evaluate

Maximum = 65

The following dataset can be used to create the histogram

Score   Frequency

10           2

15            5

45          3

65         1

This is so because it has a range of 55

See attachment for the histogram

Read more about histogram at:

https://brainly.com/question/14421716

#SPJ1

Using the Pythagorean Theorem, the altitude to side c has a length of 11.3 inches.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

To find the altitude relative to side c, we bisect this side, which cuts it's length into half(now of 4 inches), forming a right triangle in which:

Hence:

[tex]x^2 + 4^2 = 12^2[/tex]

[tex]x = \sqrt{12^2 - 4^2}[/tex]

x = 11.3 inches.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

#SPJ1

Answer:

The 1st one is 540π

The 2nd one is 1696.46

Step-by-step explanation:

To find the volume of a cylinder, you do the following:

[tex](r)^2\pi \times h[/tex]

Where r represents the radius of the circle and h represents the height. Because it's multiplication, we can change it to:

[tex]r^2\times h \times \pi[/tex]

So since the radius is 6, 6^2 is 36. Then we multiply by 15, to get 540. Then now since we don't need to multiply the pi, you just leave it as 540π.

For the second one, multiply 540 by pi to get the answer, then round it to the nearest hudredth to get 1696.46.

I don't know please help me

Answer:

c

Step-by-step explanation:

y=[tex]\sqrt{x+7}[/tex]

Answer:

(c - 2d) (3a - 2b)

Step-by-step explanation:

if you need the steps just ask me in the comments and I’ll type them lol

Answer: Addition Rule

Step-by-step explanation:This is the probability that either one or both events occur. a. If two events, say A and B, are mutually exclusive - that is A and B have no outcomes

The expression that can be used to find the area of the tiled floor is 4w² + 200w

Length = 70 Meters

Width = 30 meters

Area = length × width

= 70 × 30

= 2100

Length = 70 + 2w meters

Width = 30 + 2w meters

Area = length × width

= (70+2w) (30+2w)

= 2100 + 140w + 60w + 4w²

= 4w² + 200w + 2100

Area of the tiled floor = Area of new rectangle - area of old rectangle

= (4w² + 200w + 2100) - 2100

= 4w² + 200w + 2100 - 2100

= 4w² + 200w

Learn more about area of rectangle:

https://brainly.com/question/13048427

#SPJ1

The answer to this question is choice C

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

the sides of a 30 60 90 triangle are x, 2x, and [tex]x\sqrt{3}[/tex], with [tex]x\sqrt{3}[/tex] being opposite to the 60 degree angle, and x being adjacent to the 60 degree angle. If [tex]x\sqrt{3}[/tex] = 15 (as given from the image), you can calculate x to be [tex]5\sqrt{3}[/tex].

Answer:

72

Step-by-step explanation:

Answer:

0.8 hrs it take to drive 80 km at 100 km an hour

Step-by-step explanation:

Hello,

Answer:

48 min

Step-by-step explanation:

Cross product :

80 km   ⇒  x h

100 km  ⇒ 1 h

x = (1 × 80)/100 = 8/10 = 0,8 h    

                                   = 0,8 × 60 min

                                  = 48 min

Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

From the graph;

Using midpoint formula;

[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We substitute in our values

[tex]( \frac{0+2}{2},\frac{4+(-2)}{2}) \\\\( \frac{2}{2},\frac{4-2)}{2}) \\\\( \frac{2}{2},\frac{2}{2}) \\\\( 1, 1 )[/tex]

Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).

Learn more about midpoints here: https://brainly.com/question/4747771

#SPJ1

The first thing we need to do is evaluate the function at its endpoints.

[tex]f(-2)=-1\\\\f(5)=-183[/tex]

Then, we need to find the critical points to find if the stationary points give the absolute min/max values.

[tex]f'(x)=12x^2 - 36x-48=0\\\\x^2 - 3x-4=0\\\\(x-4)(x+1)=0\\ \\ x=-1, 4[/tex]

[tex]f(-1)=33\\\\f(4)=-217[/tex]

So, the absolute maximum is 33 and the absolute minimum is -217

Answer:

A. there is exactly one solution. the solution set is {(2, 0)}.

Step-by-step explanation:

3x + 8y = 6

3x - 8y = 6

when we add these 2 equations, we get

6x + 0 = 12

6x = 12

x = 2

now we use one of the original equations to get y :

3×2 + 8y = 6

6 + 8y = 6

8y = 0

y = 0

The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of individual songs and y represent the number of albums, hence:

x + 8y ≤ 50   (1)

x ≤ 30    (2)

y > 2   (3)

The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for each course, the parameters are given as follows:

[tex]n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3[/tex].

Hence the number of ways is given by:

N = 5 x 4 x 4 x 3 = 240.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

Answer:

20

Step-by-step explanation:

-3(-6+4)+2y(-6+-4)

18 - 12 - 12y - 8y

6 +-20y

This exercise is about Linear Functions. From the values given, we can state that:

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

(-12, 17)

(-10, 19)

To determine the slope between (-12, 17) and (-10, 19), we need to use the formula:

Slope = (y2-y1)/(x2 - x1)

Recall that:

(x1, y1) = (-12, 17); and

(x2, y2) = (-10, 19)

m = 19 -17/-10 -17

m = 1

Leveraging the point-slope to create the linear equation, we have:

y-y1 = m(x-x1)

where m is the slope of the line and (x₁, y₁) is the point substituting the values m = 1 and the point (-12, 17). Hence, we have:

y-y1 = m(x-x1)

→ y-17 = 1 (x-(-12))

→ y - 17 = x +12

y = x + 12 + 17

y = x + 29 ..................................Linear Equation

Next, we substitute x = -8 into the Linear Equation

y = (-8) + 29
y = 21

Hence, the missing y = 21; and

The missing x = -8

If we substitute y = 23 into the equation, we have:

y = x + 29
23 = x + 29
x = 29 - 23

x = 6

Thus, when the value of y = 23, the missing x is = 6

Conclusively,

The value of missing x = 6

The value of missing y = 21

Full Question

Determine any data values that are missing from the table, assuming that the data represent a linear function.

X Ix ly |-12 17 -10 19 -8 23

a. Missing x:-6 Missing y:22

b. Missing x:-7 Missing y:22

c. Missing x:-7 Missing y:20

d. Missing x:-6 Missing y:21

Please select the best answer from the choices provided.

Learn more about Linear Function at:
https://brainly.com/question/4025726
#SPJ1

Answer:

Step-by-step explanation:

For all rectangles, the area is the length multiplied by the height. For squares (a special type of rectangle), the length and height are the same, so you just use [tex]s^2[/tex], where [tex]s[/tex] is the side length.

[tex]A=s^2=16^2=\boxed{256}[/tex]

The formula for the area of the circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is pi, a constant, and [tex]r[/tex] is the radius of the circle, or the length from the center point to the edge.

We're given the side length of the square, which is the same as the diameter of the circle (length from edge to edge going through the center point). Divide the diameter by [tex]2[/tex] to get the radius of [tex]8[/tex] kilometers.

[tex]A=\pi r^2=\pi8^2=\boxed{64\pi}\approx201.1[/tex]

The area of the blue section is simply the area of the square minus the area of the circle since we just want what's left over.

[tex]A=\boxed{256-64\pi}\approx54.9[/tex]

You can keep the answer exact (the boxed expression) or use the approximate value of 54.9, depending on the instructions for the assignment.

[tex] \frac{2}{5} \: \: and \: \: \frac{3}{2} [/tex]

L.C.M. of 5 and 2 = 10

[tex] \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \\ \\ \frac{3 \times 5}{2 \times 5} = \frac{15}{10} [/tex]

[tex] \frac{5}{10} , \frac{6}{10} , \frac{7}{10} , \frac{8}{10} , \frac{9}{10}, \frac{10}{10} , \frac{11}{10} , \frac{12}{10} , \frac{13}{10} , \frac{14}{10} [/tex]

The 10 rationals numbers are :

[tex] \frac{1}{2} , \frac{3}{5} , \frac{7}{10} , \frac{4}{5} , \frac{9}{10} , \frac{1}{1}, \frac{11}{10} , \frac{6}{5} , \frac{13}{10} , \frac{7}{5} .[/tex]

Answer:

Step-by-step explanation:

Formula

c^2 = a^2 + b^2

Givens

Solution

c^2 = 3^2 + 8^2                 Substitute givens

c^2 = 9 + 64                       Combine

c^2 = 73                             Take the square root of both sides

√c^2 = √73  

c = √73                        \

Exact answer

c = √73                                73 is prime. It will break down no further

Approximate answer

c = 8.54400                         Both zeros must be entered

To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.

Since we have given that,

A total number of sales = 35

According to the question, his goal is to make add-on sales during 85% of sales.

So, His added sales would be 85% of sales,

A percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.

85  percent of 35

[tex]=(\frac{85}{100}) \times 35\\[/tex]

=29.75

To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.

To learn more about the percentage of sales visits:

https://brainly.com/question/1579410

#SPJ1