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
how to solve
[tex] \frac{a(a - 5)}{6} - 1 = 0[/tex]
Answer:
a = -1 and 6
Step-by-step explanation:
[tex] \frac{a(a - 5)}{6} = 1[/tex]
[tex]a(a - 5) = 6[/tex]
[tex] {a}^{2} - 5a = 6[/tex]
[tex] {a}^{2} - 5a - 6 = 0[/tex]
[tex](a + 1)( a- 6)[/tex]
a = -1 and a = 6
An art museum opens at 9 a.M. And closes at 5 p.M. The function V gives the number of visitors in a museum h hours after it opens. Explain what this statement tells us about the situation: V(1.25)=28
Answer:
What the equation is telling us is that after opening for 1 hour 15 minutes, there were 28 visitors
Step-by-step explanation:
The function we are given is ;
V(1.25) = 28
what this mean is that the number of visitors in the museum after 1.25 hours of opening is 28
1.25 hours is same as 1 hour (0.25 * 60) minutes
What is in the bracket is trying to convert the 0.25 hours to minutes
Since 1 hour is 60 minutes, 0.25 will be (0.25 * 70)
Which is 1 hour 15 minutes
So after opening for 1 hour 15 minutes, the museum had 28 visitors
A statement is convert into the equation by keeping the conditions equal in the form of expressions.
The given function tells that, in 1 hour, 15 minutes of the number of visitors, visit the museum is 28.
To identify the statement in the form of equation we need to know about the equation of statement.
How to make equation using statement?A statement is convert into the equation by keeping the conditions equal in the form of expressions.
Given information-
The art museum opens at 9 A.M.
The art museum closes at 5 P.M.
The function [tex]V[/tex] gives the number of visitors in a museum [tex]h[/tex] hours after it opens.
The statement in the form of equation given in the problem is,
[tex]V(1.25)=28[/tex]
As the above equation is the function of visitors visit the museum in to the number of hours.
Here bracket value (1.25) of function [tex]V[/tex] tells the number of hours in which 28 visitors visit the museum.
Convert 1.25 hours is the 1 hour and 0.25 hours.
AS one hour equal to 60 minutes thus, the number of minutes in 0.25 hours,
[tex]=0.25\times60\\=15[/tex]
Hence the given function tells that, in 1 hour, 15 minutes of the number of visitors, visit the museum is 28.
Learn more about the equation made by statement here;
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Simplify
8x - (4x – 3x)
Answer:
8x - 1x
Step-by-step explanation:
Just do the stuff in the ()'s first, for this it's is 4x - 3x, then rewrite the problem and it is simplified
Express 28% as a
(a)
fraction in its lowest terins,
A cube-shaped box has a volume of 1 cubic meter. What is the area of one in f it’s faces?
Answer: 1 meter squared
Step-by-step explanation: 1 meter by one meter is one meter squared
Find the area of the rhombus.
7.5 yd
13 yd
13 yd
7.5 yd
[ ? ] yd2
Answer:
195
Step-by-step explanation:
Find the solution of the system of equations.
3x+2y=-16
-3x-8y=46
Answer:
(-2,-5)
Step-by-step explanation:
(-2,-5)
Meg is recording all her expense (using negative numbers)and allowances.At the end of the month,she added her total allowances to her total expenses and got zero.Which statement must be correct?
Answer:
Expenses= AllowanceStep-by-step explanation:
The statements are not provided in the question, however, we can deduce from the information given.
in the information provided, expenses are -ve(negative)
and allowances are +ve (positive)
if at the end of the month she balances are account and the total is zero
We can conclude that:
1. Her total expenses is equal to her allowance for the month
2. Meg spent all her allowances for the month
Hi. I need help with these questions.
See image for question.
No jokes
Step-by-step explanation:
Given
P(x) = 6x³ + 4x² - x + 5Divide by the following:
(a) 3x² + 2x + 1
6x³ + 4x² - x + 5 = 2x(3x²) + 2x(2x) + 2x - 3x + 5 =2x(3x² + 2x + 1) + (-3x + 5)Quotient = 2x, remainder = -3x + 5
(b) x³ - 3x + 2
6x³ + 4x² - x + 5 =6(x³) - 6(3x) + 6(2) + 4x² + 22x - 76( x³ - 3x + 2) + (4x² + 22x - 7)Quotient = 6, remainder = 4x² + 22x - 7
(c) 6x² + x - 2
6x³ + 4x² - x + 5 =x(6x²) + x(x) - x(2) + 3x² + x + 5 =x(6x² + x - 2) + (3x² + x + 5)Quotient = x, remainder = 3x² + x + 5
Calculate the slope of a line that passes through the points (6, -12) and (15, -3).
A.0
B.1
C.53
D.9
Answer:
B. 1
Step-by-step explanation:
The slope is calculated by taking the difference in the y-coordinates of two points and dividing that by the difference in the x-coordinates of those two points.
Here, we have (6, -12) and (15, -3).
The difference in the y-coordinates is:
15 - 6 = 9
The difference in the x-coordinates is:
-3 - (-12) = -3 + 12 = 9
Divide 9 by 9:
9/9 = 1
The slope is thus 1, and the answer is B.
5)
A grocery store sells oranges by the crate. An empty crate weighs 1,000 grams. Each orange weighs at least 300
grams. Which inequality best describes the total weight in grams, w, of the crate of oranges in terms of, g, the
number of oranges in the crate?
A) w 300g + 1,000
B) w 2 300g - 1,000
C) w S 300g - 1,000
D) W S 300g + 1,000
Answer:
A.
[tex] w \ge 300g + 1000 [/tex]
Step-by-step explanation:
weight of empty crate = 1000 grams
weight of an orange = at least 300 grams
That means that the weight of an orange is equal to or greater than 300 grams.
Weight of g oranges = at least 300g
Total weight of crate and oranges = w
[tex] w \ge 300g + 1000 [/tex]
х = 3y — 1
3х – бу = 12
Answer:
1000000
Step-by-step explanation:
29292929292
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Question 5 of 5
Steven plays piano for 30 minutes a day, every day. How many hours
does he play in 2 weeks?
Answer: 7 Hours
Step-by-step explanation: 30 x 14(days)=420(mintue)/60( 1 hour)=7
what makes two angles exterior versus interior ?
Answer:
Any angle that is on the inside of a shape is called an interior angle.
Step-by-step explanation:
Any angle that is on the outside of a shape is called an exterior angle. An exterior angle is made by extending one of the lines of the shape beyond the intersection point. ... Notice that the two angles make a straight line.
$d/20 hrs $180 for 12 hrs (answer is $300)
true or false help meh
Answer:
false
Step-by-step explanation:
What is the value of (5.3 times 10.4
If LaTeX: P\left(6,-2\right),\:Q\left(-2,\:8\right),\:R\left(-4,\:3\right),\:P ( 6 , − 2 ) , Q ( − 2 , 8 ) , R ( − 4 , 3 ) ,and LaTeX: S\left(-9,\:y\right)\:S ( − 9 , y )find the value of LaTeX: yy so that LaTeX: PQ\bot RS.
Answer:
y = -1Step-by-step explanation:
First let us get the slope of the line PQ and RS
For PQ;
Given P(6, -2) and Q(-2,8)
slope m = 8-(-2)/-2-6
slope of pQ = 10/-8
slope of PQ = -5/4
For RS
R ( − 4 , 3 ) and S(-9, y)
slope of RS = y-3/-9+4
slope of RS = y-3/-5
For PQ to be perpendicular to RS, the product of their slope must be -1
Hence -5/4 (y-3/-5) = -1
y-3/4 = -1
cross multiply
y-3 = -4
y = -4+3
y = -1
Hence the value of y for PQ to be perpendicular to RS is -1
MULTIPLE CHOICE:
A Rhombus is labeled ABCD, which line segment could be a diagonal:
a) AB
b) BC
c) AC
d) CD
6x-3-11-8x=2 please show work
Answer: is x = -8
this is how i got it ______
6 x - 3 - 11 - 8 x = 2
(simplify both sides and combine like terms)
(6x + -8x ) + ( -3 + -11) = 2
- 2x + -14 = 2
-2x - 14 = 2
( then you add 14 to both sides)
- 2x - 14 = 2
+14 +14
-2x = 16
( then you divide both sides by -2)
-2x / -2 = 16/ -2
x = -8
ta da!! happy to help!
it made it here. this is for the second one.
( first, we subtract 8n from both sides)
13n + 26 = 8n - 29
-8n -8n
5n + 26 = -29
( then we subtract 26 from both sides)
5n + 26 = -29
- 26 -26
5n = - 55
(after that we divide both sides by 5, we do this to make n alone )
5n/ 5 = -55/ 5
n = -11
Add. (2n+4)+(4a+2) (2n+4)+(4a+2)
Answer: 8an + 20a + 6n + 14
Step-by-step explanation:
True or False?
The equation ?
15 has two solutions,
Answer:false
Step-by-step explanation:
what's the approximate value of x
Answer:
I think it's c. dndndbxbxhebd
I’ll give brainless!!! Pls helpp
Four of the interior angles of a pentagon are congruent and the fifth angle is five times as large as the measure of the other four angles. What is the measure of each of the smaller angles?
A. 60
B. 72
C. 90
D. 108
E. 120
Answer: its 60 i just did this test
Step-by-step explanation:
yolo Tallahassee Florida Free the North Side.
The measure of each of the smaller angles is 60 degrees. The correct answer would be an option (A).
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
Let's represent the measure of each of the four congruent interior angles of the pentagon "x". Then the fifth angle would have a measure of 5x.
The sum of the interior angles of a pentagon is equal to 180(n-2) degrees, where n is the number of sides of the polygon. In this case, n = 5, so the sum of the interior angles is equal to 180(5-2) = 540 degrees.
Therefore, the equation for the measures of the interior angles of the pentagon is:
x + x + x + x + 5x = 540
Simplifying the equation, we get:
9x = 540
Dividing both sides by 9, we find:
x = 60
So, each of the smaller angles has a measure of 60 degrees, and the larger angle has a measure of 5x = 5 × 60 = 300 degrees.
Learn more about the polygons here:
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Find the composite function (please help) :)
Hi there!
[tex]\large\boxed{g(f(x)) = 108x^{2} - 156x + 46}[/tex]
f(x) = 6x - 4
g(x) = 3x² - 2x - 10
To find (g(f(x)), substitute in the equation of f(x) as 'x' in g(x):
g(f(x)) = 3(6x - 4)² - 2(6x - 4) - 10
Simplify:
= 3(36x² - 48x + 16) - 2(6x - 4) - 10
= 108x² - 144x + 48 - 12x + 8 - 10
= 108x² - 156x + 46
Simplify the following expression, then evaluate when x=1:
-8x + 5 - 2x - 4 + 5x
Eric spends 45 minutes getting to work and 45 minutes returning
home. What percent of the day does Eric spend commuting?
plz help and if you know the awnser pleasee tell me how to get thereee
Answer:
6.25% of the day commuting
Step-by-step explanation:
45+45=1 hour 30 minutes
1.5/24
0.0625
6.25%
Answer:
6.25% of the day is spent commuting
Step-by-step explanation:
45+45=90 minutes
turn this into hour form because you want to make it easier to find out how much of a 24-hour day is spent commuting so 90 minutes = 1.5 hours
then you use 24 hours as the denominator since that is how many hours are in the day so 1.5/24=0.0625
to get this into a percentage, you multiply by 100 so 0.0625*100=6.25%
you can also solve this using solely minutes but converting to hours makes it easier in my opinion
у = 3х – 5
2х + 4 = 8
What is an equation of the line that passes through the points (3, 4) and (4,6)? Put
your answer in fully reduced form.
At a zoo, 3 pandas eat a total of 181 1 2pounds of bamboo shoots each day. The male panda eats 3 times as much as the baby. The female eats twice as much as the baby. How many pounds of bamboo shoots does the female panda eat?
Answer:
6037.2 pounds of bamboo shoots does the female panda eat.
Step-by-step explanation:
Total pandas = 3
Total bamboo shoots eaten = 18112 pounds
Let baby panda eats bamboo = x
Male panda eats bamboo= 3x
Female panda eats bamboo = 2x
So, the equation will become
[tex]x+3x+2x=18112[/tex]
Now solving the equation to find value of x
[tex]x+3x+2x=18112\\6x=18112\\x=\frac{18112}{6}\\x=3018.6[/tex]
The value of x we get : x=3018.6
So, baby panda eats bamboo shoots = 3018.6 pounds
Male panda eats bamboo shoots = 3x = 3(3018.6) = 9055.8 pounds
Female panda eats bamboo shoots = 2x = 2(3018.6)= 6037.2 pounds
So, 6037.2 pounds of bamboo shoots does the female panda eat.