II. Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following:
9. H(g(x)) and h(g(f(x)))
Answer:
[tex]h(g(x))=x^2+x-2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
Step-by-step explanation:
Composite Function
Suppose f(x) and g(x) are real functions, the composite function named [tex](f\circ g)(x)[/tex] is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]
The composite function can be found by substituting g into f.
We are given these functions:
[tex]f(x)=9-x[/tex]
[tex]g(x)=x^2+x[/tex]
[tex]h(x)=x-2[/tex]
Find:
a) h(g(x))
Substituting g into h:
[tex]h(g(x))=x^2+x-2[/tex]
b) h(g(f(x))
First we find g(f(x)):
[tex]g(f(x))=(9-x)^2+(9-x)[/tex]
Operating:
[tex]g(f(x))=81-18x+x^2+9-x[/tex]
Simplifying:
[tex]g(f(x))=90-19x+x^2[/tex]
Now find h(g(f(x)) replacing the above equation into h:
[tex]h(g(f(x))= 90-19x+x^2-2[/tex]
Simplifying and rearranging:
[tex]h(g(f(x))= 88-19x+x^2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
1
Amber ran 1
miles over a period of
1
of an hour. How fast in miles per hour is Amber running?
Answer: 1mph
Step-by-step explanation:
She s running 1 mile per hour because that's what it says in the problem.
please i need help!!! Beth enlarged the triangle below by a scale of 5.
A triangle with a base of 4 centimeters and height of 3.5 centimeters.
She found the area of the enlarged triangle. Her work is shown below.
One-half (4) (3.5) (5) = 35 centimeters squared
Answer:
Your answer is: There is a mistake in Beth's answer the mistake was that she multiplied the area of the original triangle by the scale factor.
Step-by-step explanation:
Hope this helped : )
Which is the simplified form of r Superscript negative 7 Baseline + s Superscript negative 12?
Answer:1/r7+1 over 8 and 12
Step-by-step explanation:
The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
r Superscript negative 7 Baseline + s Superscript negative 12
⇒ r ⁻⁷ + s ⁻¹²
Now, We can simplify the expression as;
⇒ r ⁻⁷ + s ⁻¹²
⇒ 1 / r⁷ + 1 / s ¹²
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
Thus, The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,
⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]
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What value of x is in the solution set of 3(x-4) 5x + 2?
1) -10
2) 5
3) 5
4) 10
Answer:
the answers is -10. I hope this helps you out
The solution to the inequality 3(x-4) ≥ 5x + 2 is when x = -10
Therefore, the correct answer is Option A. -10
Given data:
The inequality relation is represented as 3(x-4) ≥ 5x + 2
On simplifying the equation:
From the distributive property:
3x - 12 ≥ 5x + 2
Adding 12 on both sides:
3x ≥ 14 + 5x
Subtracting 5x on both sides:
-2x ≥ 14
Divide by -2 on both sides:
x ≤ -7
The inequality relation changes when the operand is -1.
So, the values of x should be less than -7
Hence, the solution is when x = -10, the inequality satisfies.
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The complete question is attached below:
What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?
–10
–5
5
10
The original amount borrowed is called the
A.principal
B.Time
C.interest
D.rate
What is the image of (8,-5) after a reflection over the line y = -x?
Answer:
(8,−5)
Step-by-step explanation:
My brother is 6ft tall. How tall is he in centimeters? (1 inch = 2.54cm)
Answer:
182.88cm
Step-by-step explanation:
multiply the length value by 30.48
The masses of two objects are compared during Mrs. Mobley’s Science experiment. It is determined that object A has a mass of 3 × 10^−2 grams and object B has a mass of 2 × 10^−3 grams. Mrs. Mobley offers extra credit to the first team that can determine how many times larger is the mass of object A than the mass of object B?
Answer:
15 times larger than b
Step-by-step explanation:
=3×10^-2/2×10^-3
=15×10^-1×10^+1
=15
Given the speeds of each runner below, determine who runs the fastest. Emily runs 15 feet per second. Noah runs 358 feet in 36 seconds. Liz runs 1 mile in 405 seconds. Zach runs 768 feet in 1 minute.
The graph of the linear equation 3x + 5y
= 15 cuts the x-axis at the point ________.
Answer:
(0,5)
Step-by-step explanation:
3x-5y=15
Plug in 0 for y, because we are trying to find the value of x, when y is 0
so, 3x-5(0)=15
3x=15 Divide both sides by 3
x=5
so the answer in coordinate form is (0,5)
Aubrey is looking to purchase sons for her phone. Plan A will cost $2.00 per song. Plan B will require a $15 joining fee and $1.49 per song. When will Plan A be a less expensive option for Aubrey? When will Plan B be a less expensive option for Aubrey? (SHOW ALL WORK BY TYPING HERE). * 3 points
Given :
Plan A will cost $2.00 per song. Plan B will require a $15 joining fee and $1.49 per song.
To Find :
When will Plan A be a less expensive option for Aubrey? When will Plan B be a less expensive option for Aubrey?
Solution :
Let, after x songs Plan A will be less expensive.
So,
2x < 15 + 1.49x
0.01x < 15
x < 29.41 i.e x < 30
Before, 30 songs Plan A will be less expensive.
After, 30 songs Plan B will be less expensive.
Hence, this is the required solution.
Are the triangles similar?
Work out the size of angle x
Answer:
angle X will be 180-47=133---------------------------------------------
Your answer would be 133.
does anyone know it i think ik it but im not sure so i need help
Answer:
The "if" part is the hypothesis.
The "then" part is the conclusion.
Hypothesis: an animal is a poodle
Conclusion: it is a dog
I need help (please explain the answer and how you got it)
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Ok! So you want to find slope! First, you will need two points which you already have. Next, you will want to plot those two points on a graph. Once, you have that you can draw a straight line between the two points and until the end of the graph. After that, you want to find the rise/run or rise over run. Rise meaning up or down and run meaning left or right. Sometimes your problem will want you to keep the rise/run format and sometimes your problem will ask for a who number in which case you will divide your rise/run (rise ÷ run). How to find the rise over run you ask, simple! Draw a line-up or down from your first (or second) point whichever works, until you reach the y-value of your second (or first) point one your two points are connected, count the rise (up or down) and then the run (left or right). If your run goes left its a negative, right a positive. If your rise goes up its a positive, down a negative.
Boom! You know how to find slope!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Which one of these show the multiplication property of equality? I know what is it I just don’t see it on here, 5 and 9 both look like the substitution property but I don’t know.
Answer:
5 is c 9 is f
Nadya has 19 1/4 yards of ribbbon she cuts ribbon into peices that measure 1 3/4 how many pieces of ribbon doe Nadya have?
Answer:
11
Step-by-step explanation:
Well basically i took 19 1/4 and divided it by 1 3/4 and there for i got 11. YOUR WELCOME.
There are 11 pieces of ribbon doe Nadya have.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Nadya has 19 1/4 yards of ribbon she cuts ribbon into pieces that measure 1 3/4.
Now, We can find the number of pieces as;
⇒ 19 1/4 ÷ 1 3/4
⇒ 77/4 ÷ 7/4
⇒ 77/4 × 4/7
⇒ 77/7
⇒ 11
Therefore, There are 11 pieces of ribbon doe Nadya have.
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use the slope to determine if lines AB and CD are parallel, perpendicular, or neither. (please help asap!!)
Answer:
It’s perpendicular
Step-by-step explanation:
If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
lines AB and CD are perpendicular to each other
This is all about getting the slope of a line between two coordinates.
The formula for the slope in this case is;
m = (y2 - y1)/(x2 - x1)
We are given coordinates of A and B as;
A(9, 2) and B(-1, 8)
Thus;
m = (8 - 2)/(-1 - 9)
m = 6/-10
m_ab = -6/10 = -3/5
For coordinates of C and D, we have;
C(-5, 16) and D(-8, 11)
Thus;
m_cd = (11 - 16)/(-8 - (-5))
m_cd = -5/-3 = 5/3
For the slopes to be parallel, they have to be equal but for the slopes to be perpendicular, one of them would have to be negative inverse of the other.
We see that; m_cd = 5/3 is same as -1/(m_ab) = -1/(-3/5) = 5/3
Thus, lines AB and CD are perpendicular to each other.
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solve the system of equations by the addition method
5x + 2y = 6
4x - 3y = 14
Answer: x=2, y=-2
Step-by-step explanation:
1) I will find x first, so make the amount of Ys same
3(5x+2y=6)
2(4x-3y=14)
2) 15x+6y=18
8x-6y=28
3) combine them together so Ys are all cancelled and 23x=46
4) x=2
5) for solving y, you can just plug in the x to any of that 2 equations, then 4(2)-3y=14
6) 8-3y=14
7) -3y=6
8) y=-2
(w-2) (w+5)
I need help I don't understand ...
===============================================
Work Shown:
Let x = w-2
This will allow us to replace the (w-2) with x to get...
(w-2)(w+5)
x(w+5)
x*w + x*5 ... distribute
w(x) + 5(x)
Now replace x with w-2 and distribute again
w(x) + 5(x)
w(w-2) + 5(w-2)
w*w + w*(-2) + 5*w + 5*(-2)
w^2 - 2w + 5w - 10
w^2 + 3w - 10
Kk someone explain this i feel so dumb thanks
Answer:
Yes
Step-by-step explanation:
The reason is all u do is 12 +1=13 aka 1pm then 30 +50=80 making the time 2:20
Record the length of this line shown in centimeters.
Answer:
12
Step-by-step explanation:
the ruler measured 12
Translate (-2, -3) up 2 units.
Then reflect the result over the x-axis.
What are the coordinates of the final point?
Answer:
0,1
Step-by-step explanation:
i believe that’s the answer sorry if it’s incorrect
Mike had some candy to give to his four
children. He first took two pieces for
himself and then evenly divided the rest
among his children. Each child received
two pieces. With how many pieces did he
start?
PLEASE HELP ME ASAP!
Divide.
(2x^3 - 5x^2 + 7) divided by (x - 2)
Answer:
2x^2 -x - 2 + (3/x-2)
Step-by-step explanation:
I’m doing a review but I forgot how to do this can someone help?
Answer:
-3x+10=5x-8
so basically its like grouping.
so answer is
8x=18?
Step-by-step explanation:
sorry if incorrect
Answer:
x=2.25
Step-by-step explanation:
three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8
which makes
-3x+10=5x-8
just solve
18=8x
2.25=x
Help me solve this problem please
Answer:
h(3) = 2
Step-by-step explanation:
The absolute value function always gives a positive value, that is
| - a | = | a | = a
To find h(3) substitute x = 3 into h(x), that is
h(3) = | 5(3) - 17 | = | 15 - 17 | = | - 2 | = 2
How many times greater is 5.6 x 10^6 than 1.4 x 10^2
Answer:
b
Step-by-step explanation:
Paul's car is 16 feet long. He is making a model of his car that is 1/8 the actual size. What is the length of the model?
The length of the model car is 2 feet
Paul's car is 16 feet long. To create a model of his car that is 1/8 the actual size, we need to determine the length of the scaled-down model.
To find the length of the model, we multiply the length of the actual car by the scaling factor of 1/8.
Length of the model = Length of the actual car * Scaling factor
Length of the model = 16 feet * (1/8)
Length of the model = 16 feet * 1/8
Length of the model = 16/8 feet
Length of the model = 2 feet
Therefore, the length of the model car is 2 feet. The model car is 1/8 the size of the actual car, so it measures 2 feet in length.
This scaled-down model allows Paul to create a representation of his car that is much smaller and more manageable while maintaining the same proportions as the original car.
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