The function pairs are inverses as f(x) = 2x-3 and g(x)=(x+3)/2. The correct answer would be an option (D).
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function. To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
As per the options, we have
f(g(x))=x is expressing f is the inverse of g.
f(g(x))=x is expressing f is the inverse of g but g is not the inverse of f, g(f(x))≠x.
f(g(x))= g(f(x)) is expressing the composition of functions f(g(x)) is equal to the composition of functions g(f(x)), but not necessarily inverses. It doesn't define each equal x.
f(g(x))=x and g(f(x)) =x is expressing f is the inverse of g and g is the inverse of f.
Thus, the function pairs are inverses as f(x) = 2x-3 and g(x)=(x+3)/2.
Hence, the correct answer would be an option (D).
Learn more about inverse functions here:
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Which equation represents a line parallel to the line shown on the graph. I need this for a test so pls be quick. Last answer choice is y=-1/3x+12
Determine the domain and range for this relationship.
f(x)=72-12x
Domain:
Range:
Answer:
see below
Step-by-step explanation:
f(x)=72-12x
Domain:
Is the possible values that x can take
This is a line and x can take all values
(-∞,∞) or all real numbers
Range:
Is the possible values the output can take
This is a line and y can take all values
(-∞,∞) or all real numbers
Answer: The domain is 6, and range is 72 I believe.
Step-by-step explanation:
I really hope it helps :0
If BD and EG are parallel lines and mDCA = 127°, what is mDCF?
Answer:
In the diagram above, AB is parallel to EH, and BD is parallel to FH. Also, AB = BC, and EF = FH. If ∠EGC = 70°, then ∠D =
(A) 65°
Step-by-step explanation:
∠IHJ and ∠FEH are the corresponding angles in the given figure.
What are Angles?an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line
CJ is the transversal to DF and GI.
From the given options Angle IHJ and angle FEH are corresponding angles.
Hence, ∠IHJ and ∠FEH are the corresponding angles in the given figure.
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Use the graph to determine the domain and range of the relation, and whether the relation is a function.
a. Domain: {x| -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}
Range: {y| -6, -5, -1, 1, 3, 4, 5, 7, 8, 10}
Yes, the relation is a function.
b. Domain: {x| -10 ≤ x ≤ 10}
Range: {y| -6 ≤ y ≤ 10}
Yes, the relation is a function.
c. Domain: {x| -10 ≤ x ≤ 10}
Range: {y| -6 ≤ y ≤ 10}
No, one y-value is shared by two x-values.
d. Domain: {x| -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}
Range: {y| -6, -5, -1, 1, 3, 4, 5, 7, 8, 10}
No, one y-value is shared by two x-values.
Answer: A.
Step-by-step explanation:
just answered on edge2020
The functions below represent the amounts of water released from two reservoirs over x weeks: Reservoir A f(x) = x2 – 7x + 5 Reservoir B g(x) = 3x2 – 6x + 2 The function h(x) = f(x) – g(x) represents the difference in the amounts of water released. Determine which statements about h(x) and about the reservoirs are true. Check all that apply.
Answer:
Step-by-step explanation:
Find the option below:
h(x) = –2x2 – 13x + 6
h(x) = –2x2 – x + 3
Reservoir A releases less water than Reservoir B over 1 week.
Reservoir A releases the same amount of water as Reservoir B over 1 week.
Reservoir A releases more water than Reservoir B over 1 week.
Given the expressions
Reservoir A f(x) = x^2 – 7x + 5
Reservoir B g(x) = 3x^2 – 6x+2
We are to find the f=difference between the functions h(x) = f(x)-g(x)
Substitute
h(x) = x^2 – 7x + 5 -(3x^2 – 6x+2)
h(x) = x^2 – 7x + 5 -3x^2 +6x-2
collect like terms
h(x) = x^2 -3x^2 +6x– 7x+ 5-2
h(x)= -2x^2-x+3
Next is to know the amount of water released by Reservoir A after 1 week. To do that we will substitute x = 1 into h(x)
h(x)= -2x^2-x+3
h(1)= -2(1)^2-1+3
h(1)= -2-1+3
h(x)= -3+3
h(x)= 0
This shows that Reservoir A releases the same amount of water as Reservoir B over 1 week
Answer:
a,c,b
Step-by-step explanation:
i took the test
plz help me!! Polynomial Long Division (Level 1)
Answer:
x² + x + 1
Step-by-step explanation:
F(x)=e*1/x
Calculate f'(x)
Answer:
[tex]\huge\boxed{f'(x)=-\dfrac{e^\frac{1}{x}}{x^2}}[/tex]
Step-by-step explanation:
[tex](e^x)'=e^x\\\\\bigg[f\bigg(g(x)\bigg)\bigg]'=f'\bigg(g(x)\bigg)\cdot g'(x)\\\\\left(\dfrac{1}{x}\right)'=-\dfrac{1}{x^2}\\\\====================[/tex]
[tex]f(x)=e^\frac{1}{x}=\left(e^\frac{1}{x}\right)'\cdot\left(\dfrac{1}{x}\right)'=e^\frac{1}{x}\cdot\left(-\dfrac{1}{x^2}\right)=-\dfrac{e^\frac{1}{x}}{x^2}[/tex]
Please help me with this problem
Answer: D) [tex]m \angle 2 = m\angle 5[/tex]
================================================
Explanation:
Let's go through the answer choices to see what's true and what's false.
A) This is true because they are corresponding angles. Corresponding angles are congruent when we have parallel lines.B) This is true as well. The reasoning is the same as choice A.C) These angles are vertical, so they are congruent angles. This is true.D) This is false. The angles are supplementary. They would only be congruent if both angles were 90 degrees; otherwise, they aren't congruent.What is the solution to the following system of equations?
y = 6x - 11
-2x - 3y = -7
A. -13/10, -94/5
B. -1/2, -14
C. (1, –5)
D. (2, 1)
Answer:
D.(2,1)
Step-by-step explanation:
All I did was solve by substitution.
Answer:
D
Step-by-step explanation:
Given the 2 equations
y = 6x - 11 → (1)
- 2x - 3y = - 7 → (2)
Substitute y = 6x - 11 into (2)
- 2x - 3(6x - 11) = - 7 ← distribute and simplify left side
- 2x - 18x + 33 = - 7
- 20x + 33 = - 7 ( subtract 33 from both sides )
- 20x = - 40 ( divide both sides by - 20 )
x = 2
Substitute x = 2 into (1) for corresponding value of y
y = 6(2) - 11 = 12 - 11 = 1
solution is (2, 1 ) → D
A circular dining room table top has a radius of 22 inches. What is the
diameter of the table top?
What is the circumference of the table top? Write your answer using m.
Show your work.
I need help Type fast
show work .-12.4+9.2
Answer: -12.4 + 9.2 = -3.2
4-2=2
9-12=3
Step-by-step explanation: An easy way that I've found is to just subtract the smaller digits (9.2) from the larger digits (12.4) and make the answer a negative.
Answer:
-3.2
Step-by-step explanation:
This is the longer explanation.
-12.4+9.2 let's start with the tenth values.
On a number line, when you're adding a positive number to a negative number you go up. -.4+.2 would be -.2, but if that's too difficult imagine if it was tens place meaning -4+2 which would equal 2 but the difference is you have to add the decimal in this problem. So the answer is -.2.
Now, we are adding 9 to -12. On a number line, think of it as being positioned at -12 and having to go up 9 times because remember when you're adding a positive number to a negative number you go up. When you go up the number line 9 times you stop at -3. When you go back down subtracting 9, you'll be placed at -12. So our answer is -3.
-3.0+-.2= -3.2. When you add -.2 to -3 you end up with -3.2. Line it up as a typical addition problem if you need to.
In 2019-2020, North Carolina spent $10,632 per student. The per-pupil spending has decreased at 6% per year. If this continues, what will be the per-pupil spending in 4 years?
Answer:
The per-pupil spending will be approximate $8,300 in 4 years
Step-by-step explanation:
Exponential Model
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the current quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The statistics of the years 2019-2020 at North Carolina indicate initial spending of Co=10,632 per student. The decaying rate is r=6% = 0.06 per year, thus the exponential model is:
[tex]C(t)=10,632\cdot(1-0.06)^t[/tex]
[tex]C(t)=10,632\cdot(0.94)^t[/tex]
where t is expressed in years.
We are required to know the expected spending for t= 4 years. Substitute t=4:
[tex]C(t)=10,632\cdot(0.94)^4\approx 8,300[/tex]
The per-pupil spending will be approximate $8,300 in 4 years
Jordan get a $10 allowance and works a job that pays $7.00 per hour. Alex gets a $20 allowance and works a job that pays $6.50 per hour. If they both work the same number of hours each week, how many hours would they need to work to have the same amount of money for the week?
Answer:
20 hours
Step-by-step explanation:
Let x = number of hours
Jordan
Allowance = $10
Pay per hour = $7
Total = 10 + 7x
Alex
Allowance = $20
Pay per hour = $6.50
Total = 20 + 6.50x
Equate total of Jordan and Alex earnings
10 + 7x = 20 + 6.50x
Collect like terms
10 - 20 = 6.50x - 7x
-10 = - 0.5x
Divide both sides by - 0.5
x = -10 / -0.5
= 20
x = 20 hours
Jordan and Alex will both work for 20 hours to have the same amount of money in a week
HELP!!! Please I need this soooooooooooo much
Answer:
I think the answer is A,C, and D. Sorry if I'm wrong, but if it's right pls mark brainliest.
PLEASE HELP ME ASAP! I WILL DO AND GET YOU ANYTHING YOU WANT! PLEASE! THANKS!
Answer:
18 square units how to solve this is there are four square units and four sides that’s 16 plus the top one and bottom one. That makes 18
Step-by-step explanation:
Lily loves horses. Recently, a hurricane traveled through an area of Texas were there is a dense population of horses. Lily can get food for the horses for $0.30 per pound and medical supplies for $.40 per pound. An anonymous donor pledged $8,000 to the effort and has offered to send his plane which can hold 20,000 pounds of cargo to transport the food to the relief effort location. Let x = Number of pounds of Horse Food Let y = Number of pounds of Medical Supplies
Step-by-step explanation:
Let x = Number of pounds of Horse Food
Let y = Number of pounds of Medical Supplies
so
0.3x+0.4y=8000----1
x+y=20000-----------2
multiply eqn 2 by 0.3 to eliminate x we have
0.3x+0.4y=8000
0.3x+0.3y=6000
-0+0.1y=2000
0.1y=2000
y=2000/0.1
y= 20000
put y=2000 in eqn 2
x+20000=20000
x=20000-20000
x=0
its quite unfortunate that for her to maximize the opportunity and the money she has to carry 20,000 pounds of only Medical Supplies
HELP please ASAP Hw for math class
2x^4–5x^3+x^2+3x+2=?
X=5
Answer:
[tex]2x^4–5x^3+x^2+3x+2=[/tex]
[tex]2 \times 5^4–5 \times 5^3+5^2+3 \times 5+2[/tex]
= 2 × 625 – 5 × 125 + 25 + 3 × 5 + 2
=1250 – 625 + 25 + 15 +2
= 1292 – 625
= 667
tia has 53 balloons equally among 4 kids how many balloons will be left over
Answer:
There will be 1 balloon left over.
Step-by-step explanation:
Each kid will be able to get 13 balloons, and 4 times 13 is 52, so 1 balloon will be left.
Answer:
1Step-by-step explanation:
Because 4 times 13 = 52
4 times 13.25 = 53
Each kid will get 13, but
in return, you will get 1 of your balloon's left.
Hope this helps! <3
need help with solving equations
Answer:
1) -2
2) 6
3) -9
Step-by-step explanation:
1)2/5(x+7)=2(x+3)
2/5x+2.8=2x+6
2/5x=2x+3.2
-1.6x=3.2
x=-2
2)2x+6=2/3x+14
2x=2/3x+8
1 1/3x=8
x=6
3)40+2x=6-8x-56
40+2x=-8x-50
90+2x=-8x
90=-10x
x=-9
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION RQ!!!!!!
Answer: 6 i thank
Step-by-step explanation:
So three quarters is 1/3. So 1/3 of 18 is 6.
And the average size of an Gecko is 18in
And a Iguanas is 1/3 that of an Gecko
Hopefully that helps
20 POINTS AND BRAINLIEST
This table shows the cost (y) for mailing a package. The customer is charged an
initial fee for mailing the package. An extra charge is added based on the weight of
the package (x).
Package Weight
1.3 lb
1.5 lb
2.0 lb
3.0 lb
5.0 lb
Cost
$3.70
$4.00
$4.75
$6.25
$9.25
What does the value of the y-intercept represent when the data in the table are
modeled using a linear function?
the package weight
the total mailing cost
the cost per pound
the initial fee
The initial fee.
Hope this helps ;)
Answer:
initial feee
Step-by-step explanation:
Question 16 (1 point)
(02.06)
Simplify (3 + 2i )(7 - 5i). (1 point)
1) 21 - 10i²
2) 11-i
3) 21 - i - 10i²
4) 31-i
Answer:
31-i
Step-by-step explanation:
I just took the test and I got it right.
How do you calculate (2x-5)^2
WILL GIVE BRAINLST FOR WHOEVER ANSWERS FIRST Which of the following equations is equivalent to 6(3p – 2) = 20?
Group of answer choices
9p – 4 = 20
9p – 8 = 20
18p – 12 = 20
18p – 2 = 20
a rectangular sheet of paper is 5 2/3cm long and 3 1/5cm wide. find its perimeter
Answer:
85/15+48/15=133/15 ×2=266/15 cm
=17 11/15 cm
Step-by-step explanation:
The graph shows the cost of purchasing T-shirts. Find the constant rate of change for the graph. Then explain what points (0,0) and (1,9) represent
Answer:
See below
Step-by-step explanation:
As per the attached graph we observe that the constant rate of change is 9 as each step of horizontal change corresponds to 9 steps of vertical change
It is found as the division below:
(9-0)/(1-0) = 9/1 = 9Point (0, 0) indicates the start point
Point (1, 9) indicates the cost of 1 t-shirt
As to the attachment graph ;
we observed that the constant rate is 9each step of horizontal change correspond to 9 steps of vertical changeNow,
according to the question
it is found as the division below ;
(9-0)/(1-0)=9/1 = 9the point which is indicating the starting point ;
(0,0)the point which indicate the cost of one t-shirt ;
(1,9)A square on a coordinate plane has the points A(0, 0), B(0, 5), C(5, 5) and D(5, 0). If Square ABCD is rotated about the origin 180 degrees clockwise to form Square A'B'C'D', what would be the length of one of the sides? A. 0 units B. 5 units C. 10 units D. 20 units
Answer:
B. 5 units
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, dilation, rotation or translation.
If a point X(x,y) is rotated about the origin 180 degrees clockwise the new point is at X'(-x, -y).
If the square with vertices at A(0, 0), B(0, 5), C(5, 5) and D(5, 0) is rotated about the origin 180 degrees clockwise the new points are at A'(0, 0), B'(0, -5), C'(-5, -5), D'(-5, 0)
A square has four equal sides. The distance between two points [tex]X(x_1,y_1)\ and\ Y(x_2,y_2)[/tex] is:
[tex]|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence:
[tex]|A'B'|=\sqrt{(0-0)^2+(-5-0)^2} =5[/tex]
What expressions are equivalent to 10^-5x10^2
Answer:
Answer= D and E
Step-by-step explanation:
(for two powers multiplied together we add them)
[tex]10^{-5}[/tex]×[tex]10^{2}[/tex]
=[tex]10^{-5+2}[/tex]
=[tex]10^{-3}[/tex]
this is the same as:
=[tex]\frac{1}{10^{3} } =\frac{1}{1000}[/tex] (as [tex]x^{-y}[/tex] is the same as [tex]\frac{1}{x^{y} }[/tex])
or
[tex](\frac{1}{10})^{3}[/tex] (as this is the same as [tex]\frac{1}{10}[/tex]×[tex]\frac{1}{10}[/tex]×[tex]\frac{1}{10}[/tex] which is equal to [tex]\frac{1}{1000}[/tex] the answer for the question)