Given the functions:
f(x) = 6x + 11 and g(x) = x + 6,

which of the following represents f[g(x)] correctly?

A. F[g(x)] = 6x + 47
B. F[g(x)] = 6x + 17
C. F[g(x)] = 6x^2 +47
D. F[g(x)] = 6x^2 + 17

Answer:

Gradient: 5

y-intercept: (0, 15)

Step-by-step explanation:

The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.

Use a³+b³ +c³ - 3abc

Here a = 2a²

b= -a

And c = 1

Answer:

Step-by-step explanation:

The proof to show that at least 80% of students who study both art and science, also study math is illustrated below.

From the information given, it was stated that at least 80% of students study both math and art and that at least 80% of students study both math and science.

Therefore, about (100 - 80) 20% doesn't study the combination of both subjects.

Here, those students who study both art and science, and also study math will be:

= 100% - 20%

= 80%

Therefore, at least 80% study the subjects.

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money paid by employer to Alan is $ 155.09

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

money paid for dinner by employer=$20.20

money paid for lunch by employer =$10.70

money paid for breakfast by employer =$6.93

according to question,

in this problem we will simply multiply quantity of dinners with amount

to get our answer.

so as given in problem  Alan scheduled 4 dinners , 5 lunches and 3 breakfast

(4×$20.20)+(5×$10.70)+(3×$6.93)

80.8+53.5+20.79

=$ 155.09

hence money paid by employer to Alan is $ 155.09

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The slope of the line is - 3 / 2 .

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, using (0, 6)(4, 0)

Hence,

m = slope = y₂ - y₁ / x₂ - x₁

slope = 0 - 6 / 4 - 0

slope = -6 / 4

slope = - 3 / 2

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The Surface Area of the sphere is 1017.16 unit^2.

what is the surface area of the sphere?

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

            =4*3.14*9^2

            =4*3.14*81

            =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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The Surface Area of the sphere is 1017.16 unit^2.

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

           =4*3.14*9^2

           =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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Answer:

6

Step-by-step explanation:

[tex]\frac{y}{2} =x^{2} -7[/tex]

[tex]\frac{a}{2} =2^{2} -7[/tex]

[tex]\frac{a}{2} =-3[/tex]

[tex]a=-6[/tex]

[tex]\frac{b}{2} =1^{2} -7[/tex]

[tex]\frac{b}{2} =-6[/tex]

[tex]b=-12[/tex]

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

[tex]-6=2m+b[/tex]        

[tex]-12=m+b[/tex]

[tex]-24=2m+2b[/tex]

[tex]18=-b[/tex]

[tex]b=-18[/tex]

[tex]-12=m-18[/tex]

[tex]m=6[/tex]

Therefore, the slope of line l is 6.

Answer:

slope = 6

Step-by-step explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6

The volume of the box without the lid is 500 cubic inches.

The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

Another way to think of volume is as the amount of space a three-dimensional object takes up.

Calculation for the volume of the box-

The volume of a box without a lid is given by the formula v = 4x(10-x)².

Where,

'x' is a length in inches, and

'v' is the volume in cubic inches.

The volume when x = 5 inches.

Substitute the value of 'x' in the formula of volume;

v = 4×5(10-5)²

  = 20×5²

v  = 500

Therefore, the volume of a box without a lid is 500 cubic inches.

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Answer: A. (4, 4) and (4, 5)

Step-by-step explanation:

The same x value maps onto more than one y value.

it is a relatively easy way to draw a sample while ensuring randomness is the answer.

Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.

These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.

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TRUE

The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.

An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.

Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.

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Answer: 18

Step-by-step explanation:

There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.

I hope this helps!

There are [tex]\frac{30!}{(3!)^{10} }[/tex] ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.

A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.

A whole number's "n" factororial is the sum of that number and each whole number up to one.

When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.

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The transformation that produces same image are:

The transformation that produces different image are:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation, reflection and rotation are rigid transformation which produces same image while dilation produces similar shapes.

The transformation that produces same image are:

The transformation that produces different image are:

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Answer:

f(g(2)) = 50

Step-by-step explanation:

evaluate g(2) then substitute the result obtained into f(x)

g(2) = 3(2) - 2 = 6 - 2 = 4 , then

f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50

Answer:

f[g(2)] = 50

Step-by-step explanation:

Given functions:

[tex]f(x)=2(x+1)^2[/tex]

[tex]g(x)=3x-2[/tex]

We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.

Step 1: Find the value of g(2) by substituting 2 for x in function g(x).

[tex]\implies g(2)=3(2)-2[/tex]

[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]

Step 2: Substitute the found value into the composite function.

[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]

[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]

Hence, the value of the composite function f[g(2)] is 50.

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Answer:

7/100000000

Step-by-step explanation:

to find this out we can start by saying that 0.7 is 7/10

every 0 in front of 7 after that is adding another 0 to 10

so

0.07 is 7/100

0.00000007 is 7/100000000

The second bus is traveling at a speed of 33.3 miles per hour.

Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.

We are required to find the speed of second car which is heading towards south.

If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.

We have been given that the distance between both the cars after 8 hours is 700 miles,So,

Distance of second car after 8 hours=700-480=220 miles.

We know that the speed is equal to distance divided by time.

We know that we have calculated distance after 8 hours so the speed of second car will be =20/6

=33.3 miles per hour

Hence the speed of second car which is heading towards south is 33.3 miles per hour.

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Answer:

probability of choosing two women over people in a community=⅔

The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, angle of depression from the helicopter can be found as follows:

tan x = opposite / adjacent

where

x = angle of depression

Hence,

tan x = 660 / 280

tan x = 2.35714285714

x = tan⁻¹ 2.35714285714

x = 67.1231281953

x = 67°

Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

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Answer:

D = 67

Step-by-step explanation:

Answer:

No, they can't

Step-by-step explanation:

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.

2+4= 6<7

As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.

2+7=9>4

4+7=11>2

Answer:

Option (4)

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

32 = 2 : 5

32/7 = 4

2 x 4 : 4 x 5

8 : 20

Based on the graph of the function (F(x) = log6x), the following facts are true:

A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).

This ultimately implies that, the following facts are true:

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Complete Question:

Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x

A. It is increasing.

B. The range is y > 0.

C. The x-intercept is (1, 0).

D. It is decreasing.

E. The y-intercept is (0, 6).

F. The domain is x > 6.

Answer:

see explanation

Step-by-step explanation:

to find the zeros let f(x) = 0

1

f(x) = 0 , that is

x(x + 10) = 0

equate each factor to zero and solve for x

x = 0

x + 10 = 0 ⇒ x = - 10

2

f(x) = 0 , that is

x(x - 3) - 4(x - 3) = 0 ← factor out (x - 3) from each term on the left side

(x - 3)(x - 4) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

Answer:

1) x₁ = 0, x₂ = -10

2) x₁ = 3, x₂ = 4

Step-by-step explanation:

Given functions:

[tex]1)\ f(x)=x(x+10)[/tex]

[tex]2)\ f(x)=x(x-3)-4(x-3)[/tex]

.................................................................................................................................................

Zero Product Property: If m • n = 0, then m = 0 or n = 0.

Distributive Property: a(b + c) = ab + ac.

Standard Form of a Quadratic: ax² + bx + c = 0.

.................................................................................................................................................

The Zero Product Property

1) f(x) = x(x + 10)

Step 1: Set the function to zero.

[tex]\implies 0=x(x+10)[/tex]

Step 2: Apply the Zero Product Property.

[tex]\boxed{x_1=0}[/tex]

[tex]x+10=0\implies \boxed{x_2=-10}[/tex]

The solutions to this quadratic are: [tex]x_1=0,\ x_2=-10[/tex].

.................................................................................................................................................

The Zero Product Property

2. f(x) = x(x - 3) - 4(x - 3)

Step 1: Set the function to zero.

[tex]\implies 0 = x(x - 3) - 4(x - 3)[/tex]

Step 2: Factor out [tex]x- 3[/tex].

[tex]\implies 0 = (x - 3)(x - 4)[/tex]

Step 3: Apply the Zero Product Property.

[tex]x-3=0\implies \boxed{x_1=3}[/tex]

[tex]x-4=0 \implies \boxed{x_2=4}[/tex]

The solutions to this quadratic are: [tex]x_1=3,\ x_2=4[/tex].

.................................................................................................................................................

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Answer: A

Step-by-step explanation:

Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.

In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A

The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.

Based on the definition of the circumcenter, and Y is the circumcenter, therefore:

YE = FY

Plug in the values

5x - 3 = 3x + 7

5x - 3x = 3 + 7

2x = 10

x = 5

FY = 3x + 7 = 3(5) + 7

FY = 22 units.

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Answer:

D

Step-by-step explanation:

Answer:

D. y =  √(x - 12)

Step-by-step explanation:

x  = y² + 12

y² = x - 12

y = √(x - 12)

Answer: (-4,2)

Step-by-step explanation:

To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint

So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)

To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B

A possible critical point of the function f(x) is given by: (0,-2)

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

At these points, the function can change from decreasing to increasing, or vice-versa.

For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).

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