The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
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If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
Danielle needs to walk 3 miles. If she wants to reach her destination in 45
minutes ( hour), how fast does she need to walk?
A. 135 miles
per hour
B. 2.25 miles per hour
C. 15 miles per hour
D. 4 miles per hour
Answer:
4 miles per hour
Step-by-step explanation:
3 miles
Change the 45 minutes to hours
45 minutes * 1 hour/60 minutes = 3/4 hour
3 miles ÷ 3/4 hour
Copy dot flip
3 * 4/3
4 miles per hour
It's camping season! Ernie and Bert set up their tents 15 m from
each other. Ernie has Tent 1 and Bert has Tent 2. The angle
between the line of sight from Bert's tent to the shower and the
line of sight from Bert's tent to Ernie's tent is 78 degrees. If
Ernie's tent is 19m away from the shower, is Bert 's tent closer or
further away from the shower and by how much? In your
calculations, round your angles to the nearest whole degree and
side measurements to the nearest tenth of a metre.
1
2
Answer:
The answer is "21.6".
Step-by-step explanation:
Let A stand for tent 1
Let B stand for tent 2
Let C be a shower
Using cosine formula:
[tex]c= \sqrt{b^2 +a^2 - 2ab\cdot \cos(C)}\\\\[/tex]
[tex]= \sqrt{(19)^2 + (15)^2 - 2\cdot 19 \cdot 15 \cdot \cos(78^{\circ})}\\\\= \sqrt{361 + 225 - 570\cdot \cos(78^{\circ})}\\\\ = \sqrt{586- 570\cdot \cos(78^{\circ})}\\\\= 21.6\\\\[/tex]
Therefore, you need to reduce the similarity from B to C which is the length from tent 2 to shower:
Tent 2 Distance to Dusk = 21.6m
Bert's tent is 21.6m away from the shower
PLZZZZZZ HELP WILL GIVE BRAIN THING AND EXTRA POINTS !What is the least common denominator of the rational expressions below?
Answer:
D is the least common denominator
Which expressions are equivalent to -7+3(-4e-3)
Choose all answers that apply:
A. -4(3e+4)
B. 12e
C. None of the above
Answer: A
-4(3e+4)=
-12e-16
Step-by-step explanation:
-7+3(-4e-3)=
-7-12e-9=
-12e-16
1. One half of a number added to a second
number equals 4. One half of the first
number decreased by the second number
equals zero. Find the two numbers.
Answer:
(4, 2)
Step-by-step explanation:
½x + y = 4
y = 4 - ½x
½x - y = 0
½x - (4 - ½x) = 0
½x - 4 + ½x = 0
x = 4
y = 4 - ½(4)
y = 2
Javier jogs 3/4 of a mile in 8/1/2 minutes.
If he keeps the same pace, how many minutes will it take him to jog 1 mile?
Answer:
11 1/3 minutes per mile.
Step-by-step explanation:
3/4 miles jogged in 8 1/2 minutes.
So 1 mile jogged in: 8 1/2 divided by 3/4 = 8 1/2 x 4/3 = (17 x 4) / (2 x 3) = 11 1/3 minutes per mile
Answer:
x = 11 1/3 minutes
Step-by-step explanation:
We can write a ratio to solve
3/4 mile 1 mile
----------------- = --------------
8 1/2 minutes x minutes
Using cross products
3/4 *x = 8 1/2
Multiply each side by 4/3
4/3 * 3/4x = 8 1/2 * 4/3
x = 17/2 * 4/3
x = 34/3
x = 11 1/3
The side length of an equilateral triangle is x + 3. Write an expression for the perimeter of the triangle. *
Answer:
Perimeter = (x+3) * 3 = 3x+9
Step-by-step explanation:
(x+3) would be multiplied by 3 in order to account for each of the three sides of the equilateral triangle-
The expression for the perimeter of the triangle is 3x+9.To find the expression for the perimeter of the triangle.
What is the perimeter?Perimeter is the distance around the edge of a shape. The continuous line forms the boundary of a closed geometrical figure.In an equilateral triangle, all 3 sides are the same length, so the equation would look something like this:
P=the perimeter of the triangle
(x+3)=length of each side
P=3(x+3)
To simplify further, distribute the 3 to both the x and the 3 inside of the parentheses, getting
P=3x+9.
So, the expression for the perimeter of the triangle is 3x+9.
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Given the function, calculate the following values:
Answer:
Step-by-step explanation:
The figure below consists of a rectangle and a
semicircle. Find the perimeter of the figure. Use π =
3.14.
Step 1: Find the perimeter of the rectangle
The rectangle has two lengths and one width that we need to add together. The width of the rectangle is equal to 2 times the radius (or the diameter) of the circle, which is 16.
25 + 25 + 16 = 66
Step 2: Find the perimeter of the semicircle
The perimeter of a semicircle is equal to half of the circumference.
C = pi x diameter
1/2 (3.14) x (16) = 25.12
Step 3: Find the perimeter of the figure
All that's left to do is add the two perimeters together.
66 + 25.12 = 91.12 m
Hope this helps!
find all the missing measurement
Answer:
find all the missing measurementPLEASE HELP ME IM HAVING TROUBLE WITH IT
Answer:
True
False
Step-by-step explanation:
BC are on the same line so, the new [tex]B^{1}[/tex][tex]C^{1}[/tex] will also be on the same. Just a different line than the original. The both move the same distance when dilated.
CD and the new [tex]C^{1}[/tex][tex]D^{1}[/tex] cannot be the same length. The dilation will increase their length by 1[tex]\frac{2}{3}[/tex]
Please help!
Solve for x
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The product of lengths to the two circle intercepts are the same for each secant.
7(7+9) = (8x)(8x+6x)
112 = 112x² . . . simplify
1 = x² . . . . . . divide by 112
x = 1 . . . . . . . take the square root (segment lengths are positive)
In a sample of 56 bags of fertilizer, the average weight was found to be 17.2lb with a standard deviation of 0.7. Give a point estimate for the population standard deviation of the weight of the bags of fertilizer.
Answer:
???????????????????????
MFP15017010 2021 Question 2 2.1 Calculate the following 2- and 3-digit numbers using strategic doubling: 34 2.1.2 340 2.13 277 214 00 (10) 2.15 500
Answer:
plz check ur school solution down.
Step-by-step explanation:
A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.
Answer:
At most 3 calls: 64.7%
At least 3 calls: 57.7%
5 or more calls: 18.5%
Step-by-step explanation:
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
Convert the following fraction to a decimal.
1/3
A. 0.3
B. 0.03
C. 0.303
D. 3.9
Answer:
Option A, 0.3
Step-by-step explanation:
Step 1: Convert the fraction into a decimal
Technically, 1/3 is an irrational number meaning that it never ends. However, if we round it, it would round to 0.3 since 1/3 = 0.3333333.....
Answer: Option A, 0.3
Catriona spotted a major problem having to do with patient billing. A number of people may have received the wrong bills. When should she have told her boss? O a) When she was evaluating how to alert the patients O b) After she sent patient notices out c) When she first noticed the problem O d) After she decided on a communication plan
Answer:
C
Step-by-step explanation:
When she first noticed the problem
FIND THE LENGTH OF MP
Answer:
D.21
Step-by-step explanation:
MP=MV - PV= 67 -46 = 21
fill in each blank with a true statement
Answer:
See below.
Step-by-step explanation:
7.)
Supplementary angles add up to 180°. ∠B's supplement is 22°. This means ∠B is 158°. Since ∠A ≅ ∠B, the m∠A = 158°.
8.)
Again, supplementary angles add up to 180°. ∠P is a right angle meaning it is 90°. Therefore, the m∠Q is 90° as well.
9.)
Complementary angles add up to 90°. In order for ∠S and ∠T to be complementary, they both need to angle measurements less than 90° meaning they both need to be acute angles.
Now that we know that ∠T is acute, the only way ∠U can be its supplement is if it has an angle measure greater than 90°. Therefore, ∠U is an obtuse angle.
10.)
Similar to question 9, if an angle is obtuse, its supplement must be an acute angle.
What is a40
a
40
of the arithmetic sequence for which a8=60
a
8
=
60
and a12=48
a
12
=
48
?
9514 1404 393
Answer:
-36
Step-by-step explanation:
Using the expression for the general term, you can fill in the known values and solve for the parameters of the sequence.
an = a1 +d(n -1)
a8 = a1 + d(8 -1) = 60
a12 = a1 + d(12 -1) = 48
The difference of these equations is ...
(a1 +7d) -(a1 +11d) = (60) -(48)
-4d = 12
d = -3
Substituting into the first equation, we have ...
a1 +7(-3) = 60
a1 = 81 . . . . . . . . . add 21
Then the 40th term is ...
a40 = 81 -3(40 -1) = 81 -117
a40 = -36
determine a simplified expression
Answer:
For Task B: [tex]3x^4 - 2x^3[/tex]
Step-by-step explanation:
Given that Volume = l*w*h, we can plug in the values on the diagram, so we get the equation (3x-2)([tex]\frac{1}{2}x[/tex])([tex]2x^2[/tex]) = [tex](\frac{3}{2} x^2 - x)(2x^2) = 3x^4-2x^3[/tex]. Hope this helps!!!
expand and simplify √3(√3-1)
Answer:
[tex]3 - \sqrt{3} [/tex]Step-by-step explanation:
[tex] \sqrt{3} ( \sqrt{3} - 1)[/tex]
[tex] = \sqrt{3} \times \sqrt{3} - \sqrt{3} \times 1[/tex]
[tex] = 3 - \sqrt{3} (ans)[/tex]
A cube has an edge of 8cm. Calculate its Volume.
Answer:
512cm³
Step-by-step explanation:
to get the volume the formula is Base area x height
BA X H
=8x8x8 because all sides of a cube are equal
=512cm³
Question 4 4 pts Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: 5 years? 10 years? 486 months?
Answer:
Step-by-step explanation:
5 years
[tex]1500(1+\frac{.06}{12})^{12*5}=2023.275229[/tex]
10 years
[tex]1500(1+\frac{.06}{12})^{10*12}=2729.095101[/tex]
486 months:
[tex]1500(1+\frac{.06}{12})^{486}=16935.47074[/tex]
round those as you please
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
Answer:
y+1 = 2(x-1)
Step-by-step explanation:
Point slope form for a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
We are given the point(1,-1)
y --1 = 2(x-1)
y+1 = 2(x-1)
PLEASE HEP ME
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
9514 1404 393
Answer:
TrueTrueStep-by-step explanation:
The center of dilation (point D) is a point that doesn't move. Any line not through that point will be moved to a parallel location when a dilation factor is applied.
Any line through the center of dilation will still go through the center of dilation. Its slope does not change, so the line will appear to be the same.
AB ║ A'B' — True
AD ≅ A'D' — True
_____
You can see these relationships in the attached figure.
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T
Answer: x³+y³=180
Step-by-step explain: let's remember the formula x³+y³=(x+y)(x²-xy+y²) and also x³+y³=(x+y)³-3xy(x+y) then [tex]\displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180[/tex]
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
