For
f(x) = (x − 1)3
and
g(x) = 1 − 6x,
find the following.
(a)
(f ∘ g)(x)
(b)
(g ∘ f)(x)
(c)
f(f(x))
(d)
f 2(x) = (f · f)(x)

The system of inequalities is:

y < -4*x + 1

y ≥ (1/2)*x + 1

Here we can see two lines, one dashed that passes through (0, 1) and (-1, 5), then the slope is:

s = (5 - 1)/(-1 - 0) = -4

And the y-intercept is 1, then the inequality is:

y < -4*x + 1

The other line is solid, and the shaded region is above the line.

This line passes through (0, -1) and (2, 0), then the slope is:

s = (0  + 1)/(2 - 0) = 1/2

So the inequality is:

y ≥ (1/2)*x + 1

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From the following figures, we have that:

a) The sequence of transformations that maps triangle ABC to triangle A''B''C'' is given by:

b) The rules are given as follows:

The transformations used in this problem are as follows:

For this problem, the orientation of the triangle changed, with the C at the bottom of the triangle being transformed into C'' at the top of the transformed triangle, hence the figure was reflected over the x-axis, and the rule is:

(x,y) -> (x, -y).

After the reflection, the coordinates of C' are given as follows:

C' (-4, -1).

The final coordinates of C'' are given as follows:

C'' (7, 0).

Meaning that it was translated 11 units right and 1 unit up, and the rule is given by:

(x,y) -> (x + 11, y + 1).

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Answer:

slope :

Correct option - F

....................... .x=3

a. Solving for 'd' as the subject of formula gives d = P/64

b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

Given the function as;

P = 64d

Where;

Now, let's make the variable 'd' the subject of formula

Divide both sides of the equation with the coefficient of the variable 'd' which is 64. This is done so that the variable stands alone.

We have;

P/64 = 64d/64

d = P/ 64

If the pressure, P equals  672 pounds per square foot

Substitute the value of the variable into the formula, we have;

d = P/64

Then,

d = 672/64

Find the quotient

d = 10. 5 feet.

Thus, the value is 10. 5 feet

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Answer:

63

Step-by-step explanation:

23 + 94  = 117

180 degrees ( sum of all angles in a triangle)

180 - 117 = 63

Answer:

Step-by-step explanation:

divide 7.2 by 2 so you have an hourly rate. Then you have 3.6, multiply that by 7 to get 25.2. Assuming its not in km cause that wouldn't make sense you would just have to convert it into whichever unit it would take

Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope formula is the quotient of the difference in y-values and the difference in x-values.

Yes, This situation represent a function.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The cost of each car = $40

The cost of each person = $8.50

Let the number of car = x

The number of persons in a car = z

Then, Total cost of car = $40x

Total cost of persons in car = $8.50z

So, Total cost (y) = $40x + $8.50z

Thus, The function for this situation is;

y = $40x $8.50z

Clearly, This is a linear function with three variable.

Thus, This situation represent a function.

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Answer:

16000

Step-by-step explanation:

Answer:

u - 6 + 13/u+3

Step-by-step explanation:

Have a good day :)

The time taken for the bomb to fall to the ground is 2.5 sec.

Given:

Height (h) = 50 m

Horizontal velocity(u) = 20 m/s

Time (t) =?

We use, h = ut to determine the time

50 = 20 × t

Divide both sides by 20,

t = 50 / 20

t = 5/2 s ≅ 2.5 sec

Thus, the bomb will take 2.5 sec to land on the ground.

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The complete question is: "A bomb is projected horizontally downward from a height of 50m with a velocity of 20m/s. Calculate the time taken for the bomb to fall to the ground."

The angles congruent to ∠5 are as follows:

According to the diagram, line l, m and n are parallel lines.

Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.

Hence, the angles that are congruent to ∠5 can be solved as follows:

∠5 ≅ ∠8 (vertically opposite angles)

Vertically opposite angles are congruent.

∠5 ≅ ∠1 (corresponding angles)

Corresponding angles are congruent.

∠5 ≅ ∠4 (alternate angles)

Alternate angles are congruent.

∠5 ≅ ∠9 (corresponding angles)

∠5 ≅ ∠12 (alternate exterior angles)

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Answer:

Perpendicular

Step-by-step explanation:

It js seems right. i did one very similar and the awnser was Perpendicular

Answer:

3.204

Step-by-step explanation:

3 + 0.2 +  0.004

Answer:  there 3,000 total milliliters accourding to my calculation

there for your looking for 60% so your answer should be 1800 since 60% of 3,000 is 1800

1800 ML = 60%

Step-by-step explanation:

the math is above

we have

10x + 8 y = 20 ------> equation A

10 x + 2 y = -10 ​------> equation B

Multiply equation A by -1 both sides

so

-10x-8y=-20 -----> new equation A

Adds new equation A and equation B

\

--------------------

-8y+2y=-20-10

-6y=-30

y=5

Find the value of x

substitute the value of y in equation A or equation B or new equation A

10x + 8(5) = 20

10x+40=20

10x=20-40

10x=-20

x=-2

therefore

Answer:

Step-by-step explanation:

To find the median of a stem and leaf plot, use the equation:

Therefore, for the given plot, there are 16 elements.

When there are two middle values, the median is the mean of these two values:

The provided translated function, f(x), shifts left by two units on the horizontal axis.

One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.

The given graph equation for the translation, as per the query, is g(x) = (x + 2)²

The translation of the given quadratic function is: y = g(x) = (x + 2)²

Consequently, the parent function is written as y = g(x) = x2.

Additionally, the vertex should be known when graphing the translated function:

a(x - h)2 + k = y = g(x);

where the parent function is (0, 0) and the vertex values are (h, k).

(h, k) = is the vertex for the function that is provided (-2, 0)

This information causes the translation function to move the graph two units to the left.

Horizontal translation is the name given to the translation.

As a result, the given function, f(x), shifts horizontally, or left, by 2 units.

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After 10 years, the money dis she earn is $800 with the interest of 6%.

Interest:

Interest is the amount for a particular principal amount of money at some rate of interest.

Given,

Jackie deposited $500 in an account for 10 years at 6% interest.

Here we need to find the money did she earned.

We know that, the interest for the amount is 6%.

So, the amount after 10 years is,

=> 500 x (6/100) x 10

=> 30 x 10

=> 300

Therefore, the interest amount is 300.

So, the total amount she will receive after 10 years is,

=> 500 + 300

=> 800

Therefore, she will earn $800 after 10 years.

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substitute the given values in the formula of (BAC) we have

Remember

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

so

step 1

solve the multiplication

48*3.2=153.6

substitute

step 2

Solve the division

153.6/160=0.96

substitute

step 3

solve the multiplication

3*0.015=0.045

substitute

step 4

solve the subtraction

0.96-0.045=0.915

Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.

In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:

In conclusion, we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.

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Answer:

x = 8

y = 8

Step-by-step explanation:

The two equations are:

x + y = 16    (1)

x = y           (2)

Since x = y substitute for y in terms of x in (1):
x + x = 16

2x = 16

2x/2 = 16/2

x = 8

y = 8

The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)

An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.

The initial constant, “a,” cannot be 0, and this is an unbreakable rule.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.

Thereafter draw a sloping triangle connecting the two spots you find on the line.

If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:

-2 = a(0+3)(0+1)

-2 = 4a

a = -1/2

So the equation can be written as y = -1/2 (x+3)(x+1)

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The required rational number is 7/11.

let the denominator be x.      

and since we are given that the numerator of a rational number is 4 less than its denominator, the numerator will be x-4.

working on the given condition, i.e. If I is added to both its numerator and denominator, it becomes 2/3

(x-4+1)/(x+1) = 2/3

further solving it by cross multiplication we get,

3(x-4+1)=2(x+1)

=> 3(x-3)=2x+2

=> 3x-9=2x+2

=> 3x-2x=9+2

=> x=11

=> x= 11 (denominator)

we know the numerator is 4 less than the denominator i.e.

11-4=7

thus the required fraction will be 7/11.

What are rational numbers?

A rational number is-" one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero".

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Answer:

Step-by-step explanation:

Given that:-

Since, Serving of 1 pancakes takes 2/3 cups of milk

Hence, serving of 24 pancakes takes (2/3)*24

                                                    =48/3

                                                   =16

So that; 16 cups of milk are required for serving of 24 pancakes.

Answer:

16 cups of milk

Step-by-step explanation:

Make a proportion

[tex]\frac{serrvings}{cups of milk}[/tex] = [tex]\frac{servings }{cups of milk}[/tex]

[tex]\frac{1}{\frac{2}{3} }[/tex] = [tex]\frac{24}{x}[/tex]  cross multiply and solve

1x = [tex]\frac{2}{3}[/tex][tex](\frac{24}{1})[/tex]       1x is the same a x.  24 is the same as [tex]\frac{24}{1}[/tex]

x = [tex]\frac{48}{3}[/tex]

x = 16

By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.

Here we have the functions:

f(x) = -2x +4

g(x) = 2x - 8

We want to find the value of x such that:

f(x) = g(x).

If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.

The graph can be seen in the image below.

There we can see that the graphs intercept at (3, -2), meaning that the solution of:

f(x) = g(x) is x = 3.

Which is the same thing that if we write:

f(x) = g(x)

-2x + 4 = 2x - 8

4x = 12

x = 12/4 = 3

x = 3

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The median of a set of numbers is the number that appears in the middle after arranging the set of numbers in ascending or descending order

Step 1:Arrange the given values in ascending order.

Step 2. Find the number of observations in the given set of data. It is denoted by n.

Step 3. If n is odd, the median equals the [(n+1)/2]th observation.

The set of numbers given in the question are

By rearranging the numbers in ascending order, we will have

The numbers are 7 in number that is

Since the value of N is an odd number, then the median will be calculated using the formula below

The 4th number after arranging the set of numbers is

Hence,

The median of the set of numbers in the question = 11

Answer:

Step-by-step explanation:

The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data using 7 classes. Limits Boundaries 27-33 26.5-33.5 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 34-40 33.5-40.5 14 41-47 40.5-47.5 15 48-54 11 47.5-54.5 54.5-61.5 55-61 3 62-68 61.5-68.5 3 69-75 68.5-75.5 55