Consider these functions: f(x)= -2x - 1 g(x)= -1/2x + 1/2 Which statements, if any, are true about these functions? I. The function f(g(x)) = x for all real x. II. The function g(f(x)) = x for all real x. III. Functions f and g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.
Answer:
A. I only
Step-by-step explanation:
Given the functions
h(x)= -2x - 1 g(x)= -1/2x + 1/2
h(g(x) =h( -1/2x + 1/2)
=f((-x+1)/2)
We are to replace x in h(x) with -x+1/2
h((-x+1)/2) = -2(-x+1)/2 + 1
h((-x+1)/2) = -(-x+1)+1
h((-x+1)/2)= x-1+1
h((-x+1)/2) = x
h(g(x) = x
Also for g(h(x))
g(h(x)) = g(-2x-1)
Since g(x) = -x+1/2
g(-2x-1) = -(-2x-1)+1/2
g(-2x-1) =2x+1+1/2
g(-2x-1) = 2x+2/2
g(-2x-1) = 2(x+1)/2
g(-2x-1) = x+1
Sine g(h(x)) ≠ h(g(x)), hence both functions are not inverses of each other
Hence I. The function h(g(x)) = x is the only correct option. Option A is correct
The correct option is: A. I only
We have functions:
[tex]h(x)= -2x - 1 \\g(x)= -\frac{1}{2} x +\frac{1}{2} \\h(g(x)) =h(-\frac{1}{2} x +\frac{1}{2}) \\h(g(x))=f(\frac{-x+1}{2} )[/tex]
Now, replace x in h(x) by [tex]\frac{-x+1}{2}[/tex]
So,
[tex]h(\frac{-x+1}{2} ) = -2(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} ) = -(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} )= x-1+1\\h(\frac{-x+1}{2} )=x\\h(g(x)) = x[/tex]
Now, g(h(x))
g(h(x)) = g(-2x-1)
Since [tex]g(x) = \frac{-x+1}{2}[/tex]
[tex]g(-2x-1) = \frac{-(-2x-1)+1}{2} \\g(-2x-1) =\frac{2x+1+1}{2}\\g(-2x-1) =\frac{2x+2}{2}\\g(-2x-1) = x+1[/tex]
As g(h(x)) ≠ h(g(x)),
Therefore, both functions are not inverses of each other.
Hence A. I only
The function h(g(x)) = x is the only correct option.
So, option A is correct.
Learn more:https://brainly.com/question/10572318
Find the rate of change from the given table.
Answer the answer is 2:)
Step-by-step explanation:
Answer:
D. 8
Step-by-step explanation:
To find rate of change
m=y2-y1
------
x2-x1
I'm gonna use coordinates (7,56) and (9,72)
m= 72-56
---------
9-7
m= 16
---
2
m=8
will mark BRAINLIEST
Answer:
(2, - 1 )
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
The lines intersect at (2, - 1 ) ← solution
Answer:
the answer is C
Step-by-step explanation:
I think pls dont come at me if i am wrong
At attorney charges, a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that. Find the slope and y-intercept for the data.
slope:
y-intercepy:
Answer:
slope: 150
y-intercept: 250
y= 150x+250
Step-by-step explanation:
8. What's the GCF of *
(1 Point)
4x2 - 6x + 8
Answer:2
Step-by-step explanation:
When converting rational exponents to radical notation, which of the following are correct? Choose all that apply:
1. Numerator of the rational exponent becomes index of the radical notation
2. Negative exponent of the rational exponent makes the radical notation a negative value
3. Denominator of the radical exponent becomes the power of the radicand in the radical notation
4. Denominator of the rational exponent becomes the index of the radical notation
5. Numerator of the rational exponent becomes power of the radicand in the radical notation
Given:
Converting rational exponents to radical notation.
To find:
The correct statements.
Solution:
According to the property of exponents, conversion of rational exponents to radical notation is
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]
In [tex]x^\frac{a}{b},[/tex] x is base, a is numerator of the rational exponent and b is denominator of the rational exponent.
In [tex]\sqrt[b]{x^a}[/tex], x is radicand, a is power of radicand and b is index of radical notation.
Denominator of the rational exponent becomes the index of the radical notation.
Numerator of the rational exponent becomes power of the radicand in the radical notation.
Therefore, the correct options are 4 and 5.
Using the conversion of rational exponents to radical notation, it is found that the correct options are:
4. Denominator of the rational exponent becomes the index of the radical notation
5. Numerator of the rational exponent becomes power of the radicand in the radical notation
The conversion of rational exponents to radical notation is modeled by:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
That is:
The numerator becomes the power of the radicand, hence item 5 is correct.The denominator becomes the index of the radical notation, hence item 4 is correct.A negative exponent just is represented by a fraction, as [tex]a^{-\frac{n}{m}} = \frac{1}{a^{\frac{n}{m}}}[/tex], hence the radical is not negative, and item 2 is incorrect.
A similar problem is given at https://brainly.com/question/13133871
Solving each system elimination.
(Help I’ll mark you brainly)
Answer:
1) x=6, y=-6 which is (6,-6) as an ordered pair
3) x=10, y=-1 which is (10,-1) as an ordered pair
Step-by-step explanation:
Question 1:
Solve them like an addition problem:
-4x-2y=-12
4x+8y=-24
________
(-4x+4x)+(-2y+8y)=(-12+-24)
0x+6y=-36
6y=-36
y=-6
Plug value of y into one of the original equations:
4x+8(-6)=-24
4x-48=-24
4x=24
x=6
Question 3:
Solve them like an addition problem:
x-y=11
2x+y=19
_______
(x+2x)+(-y+y)=11+19
3x+0y=30
3x=30
x=10
Plug value of x into one of the original equations:
10-y=11
-y=1
y=-1
5 · 6 – 33 ÷ 3 + (5 · 2) what is the awnser
Answer:
29
Step-by-step explanation:
A store pays $840 for an oil painting. The store marks up the price by 46%. What is the amount of the mark-up? please help!!!! IXL is driving me crazy
Answer:
A store pays $840 for an oil painting. The store marks up the price by 46%. What is the amount of the mark-up?
=
$386.40
WILL GIVE BRAINLEST! Is this relationship proportional why or why not?
Yes it is because it passes the line and made at exact point on 12. :)) ^^ give them brainly though
jamie reads 15 pages in 25 minutes and wants to know how many pages she can read in 65 minutes
Answer:
39
Step-by-step explanation:
15/25 = 0.6 - She can read 0.6 pages in 1 minute.
0.6 X 65 = 39
There are 39 pages she can read in 65 minutes.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Jamie reads 15 pages in 25 minutes
And, wants to know how many pages she can read in 65 minutes
Now, Let number of pages read in 65 minutes = x
Hence, We can formulate;
x / 65 = 15 / 25
x = 15 x 65 / 25
x = 39
Thus, There are 39 pages she can read in 65 minutes.
Learn more about the proportion visit:
https://brainly.com/question/1496357
#SPJ2
The graph shows the first quadrant portion of four exponential functions. Which equation could generate the BLUE curve? Assume a > 0 for all functions.
A) y = a-x
B) y = a-x + 1
C) y = a-x + 2
D) y = a-x + 3
Answer:a
Step-by-step explanation:
The solution is:
The initial value of the function is 2
The base of the function is 3
The function shows exponential growth
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
f(x) = 2(3^x)
Exponential functions are those with the following equation:
y = a*b^x
where a ≠ 0, b > 0 and b ≠ 1 and x is a real number.
a is the y-intercept and b is the base.
The initial value of the function is the same as the y-intercept
If a is positive, the function growth. If a is negative, the function decay
Hence, The initial value of the function is 2
The base of the function is 3
The function shows exponential growth
To learn more on function click:
brainly.com/question/21145944
#SPJ3
complete question:
Consider the exponential function f(x) = 2(3x) and its graph.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. The equation of the function is y = f (x). The function crosses the y-axis at (0, 2).
The initial value of the function is.
The base of the function is.
The function shows exponential
How do I solve this equation?
Answer:
x = 132
Step-by-step explanation:
Solve by raising both sides to the multiplicative inverse of the exponent.
[tex]((x-7)^{\frac{2}{3} } )^{\frac{3}{2} } =25^{\frac{3}{2} }[/tex]
x - 7 = 125
x = 132
What is the Least Common Multiple (LCM) of 3 and 6?
Answer:
6
Step-by-step explanation:
Both numbers can evenly go into 6: 3 can go into 6 two times, and 6 can go into 6 one time.I hope this helps!
The LCM of 3 and 6 is 6, which is the smallest positive integer that is a multiple of both numbers.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
We can use the prime factorization method to find the LCM. We can write each number as a product of its prime factors:
3 = 3
6 = 2 x 3
The LCM is the product of the highest powers of all the prime factors.
Here, the highest power of 2 is 2, and the highest power of 3 is 3. So, the LCM is:
LCM(3, 6) = 2 x 3 = 6
Thus, the LCM of 3 and 6 is 6, which is the smallest positive integer that is a multiple of both numbers.
To learn more about the Least Common Multiple(LCM) here :
https://brainly.com/question/17256135
#SPJ2
For question 2, find the x- and y-intercept of the line.
5x + 4y = 80
O A. x-intercept is 4; y-intercept is 5.
O B. x-intercept is 20; y-intercept
16.
O C. x-intercept is 5; y-intercept is 4.
O D. x-intercept is 16; y-intercept is 20.
pls help i need help quickly
Answer: 5/6?
Step-by-step explanation:
5th grade math. Correct answer will be marked brainliest. What goes in the blank box?
Answer:
The answer is 1.97 meters per second
Step-by-step explanation:
Plz give brainliest thanks :) Let me explain you how you do this Housefly is 1.967
The 7 is the tenth and the 6 is the hunderth
1.967 round to 1.96 from the hunderths because the last number is greater than 5 so you round up!
Answer:
1.97
Step-by-step explanation:
REMEMBER: 5 or higher, round up, 4 or lower, round down
Since 7 is above 5, we round it up, turning 1.967 to 1.97
whats 10 plus 10 ..........................
Answer:
20!!!!!!!!!
Step-by-step explanation:
The numbers in this number set are _______ their absolute values. Answer choices: Smaller than, the same, and larger than. Numbers larger than 1: Zero: Negative Numbers: Positive Proper fractions Non- negative numbers:
Answer:
Smaller than
Positive numbers
Step-by-step explanation:
The absolute value of a number is the distance from the zero. This can be positive or negative forming the absolute number. The distance is negative when the number is positive. The absolute numbers are used in the equations for the solutions. The numbers greater than zero are positive numbers.
Select the number line model that matches the expression 4 - 1
Answer:
c. None of the above
Step-by-step explanation:
Given the expression, |4 - 1|, the value of the expression would give us 3. Meaning that the distance between coordinate 4 and 1 is 3 units.
None of the graphs given models the expression, |4 - 1|.
Option A, would match |-4 -1| = 5 units
Option B, would match |-1 - 4| = 5 units.
Therefore, the answer is c. None of the above
please help! all answers are appreciated
I think it would be 1,200ml or 800 try 1,200ml first
Answer:
Its A. 600 ml.
Step-by-step explanation:
1st. Find the ml of milk for one pancake. So 400 divided by 10, it equals 40ml. So to find how many ml for 15 pancakes...you multiply 15 and 40 ml, and that will give you 600ml needed.
Answer quick please!!
Answer:
8
Step-by-step explanation:
Simplify the expression 288 · 1318 − 288 · 1316.
Answer:
576
Step-by-step explanation:
x/4 + 5 = 8
PLEASE HELP ME
Answer:
hiii...hopefully this is correct x=12
Name the property. 7xy = 7yx
URGENT.
The ice cream shop sells sundaes for $2 each and banana splits for $3 each. One day, the shop sold 8 more sundaes than banana splits and also made a total of $156. Which system of equations represents the situation?
Answer:
156=2s+3b s-8=b
Step-by-step explanation:
s=sundaes
b=banana splits
Cows and horses cost $250 each and sheep and goats each cost $200 at the county fair. Chickens sell for $50. How much could McDonald make by selling all his animals except the dogs and cats?
Answer:
the total amount of animals in McDonald's farm is missing, so I looked for a similar question and found the attached image:
McDonald can earn:
15 cows x $250 = $3,750
2 horses x $250 = $500
20 sheep x $200 = $4,000
25 goats x $200 = $5,000
17 chickens x $50 = $850
total = $14,100
Brandi earned $140 from a summer job to buy new clothes for school. She found several items she would like to buy, but is trying to decide if she has enough money to buy all the items she likes. She found two pairs of shorts for $25 each and four shirts with an average cost of $19 per shirt. She will have to pay 7.5% sales tax.
Answer:
She will pay a tax of $9.45
Step-by-step explanation:
The question doesn't seem complete, but since we are given her tax rate, then they would surely ask for the amount of tax she paid. So let's work on this.
We are told that she bought two pairs of shorts and one short goes for $25 each, this implies that she will get the two for:
= $25 × 2
= $50
We are also told that she got four shirts that have an average cost of $19 per shirt. This implies that she will get the four shirt for:
= $19 × 4
= $76
Since she will have to pay a tax of 7.5%, then we will calculate it as:
= 7.5% × ($50 + $76)
= 0.075 × $126
= $9.45
Answer:
A. $9.45
B. Total cost = $135.45
Step-by-step explanation:
PART A: If she buys all of the items, how much sales tax will she have to pay?
The sales tax for Brandi's purchase will be $(insert answer here)
PART B: What is the total cost of her purchase including sales tax?
Brandi will spend $(insert answer here) on her purchases, including sales tax.
A.
Total amount earned = $140
Two pairs of shorts = $25 each
Total cost of 2 shorts = 2 shorts × $25 each
= $50
Four shirts = $19 each
Total cost of 4 shirts = 4 × $19
= $76
Amount of Sales tax = 7.5% of Total cost of 2 shorts + Total cost of 4 shirts
= 7.5% ($50 + $76)
= 0.075 × 126
= $9.45
Total cost = Total cost of 2 shorts + Total cost of 4 shirts + Amount of Sales tax
= $50 + $76 + $9.45
= $135.45
Therefore, she has enough money to buy all the items she likes
What is the main idea of the White House
Answer:
The White House is the solemn residence and the workplace of the President in the United States Of America. The president can also have his family there.
Step-by-step explanation:
The main motto or goal of the white house is to give and protect the fundamental rights of United States citizens
Jylene and her brother had a total of $35.19 to buy school supplies. Jylene’s school supplies cost $12.78
Answer:
whats the question
Step-by-step explanation:
Answer:
What is the question???
Step-by-step explanation: