Answer:
[tex]\huge\boxed{f^{-1}(x)=4x+48}[/tex]
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a couple of steps.
Step 1: Write the function as [tex]y=mx+b[/tex] Step 2: Swap all x and y values Step 3: Solve for y Step 4: Replace y with [tex]f^{-1}(x)[/tex]We can follow these steps to find the inverse of this function.
Step 1: We can just replace the f(x) with y, making our function [tex]y=\frac{1}{4}x-12[/tex].
Step 2: We can swap where the x and y values are, making our equation
[tex]x = \frac{1}{4}y-12[/tex]
Step 3: We can now solve for y.
[tex]x = \frac{1}{4}y-12[/tex] [tex]x + 12 = \frac{1}{4}x[/tex] [tex]4x+48 =y[/tex]We now have the function as [tex]y = 4x+48[/tex].
Step 4: We can now replace the y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) =4x+48[/tex]
Therefore the inverse of [tex]f(x) = \frac{1}{4}x-12[/tex] is [tex]f^{-1}(x) =4x+48[/tex].
Hope this helped!
Which of the expressions below has the value found farthest to the left on a
number line?
A. 7-10
B. -7 - 10
C. 10 - (-7)
D. 10 - 7
Answer:
-7 - 10
Step-by-step explanation:
The values found farthest to the left of a numbwr line are negative values, with positive values located to the right and 0 being the midpoint.
Thus positive values increase towards the right of the number line while negative values on the other hand reduces as we move farther to the left of the number line.
Hence , from the options given, - 7 - 10 gives a total of - 17 is the lowest negative value given in the option.
what is the equation of the line passing through the points 2/5 19/20 and 1/3 and 11/12 is a slope intercept form
Answer:
y= (1/2)x+(3/4)
Step-by-step explanation:
Find the least common multiple of: 6, 3, 2
least common multiple of 6,3,2 is 6.
- 6 is the smallest number that is divisible by all three.
Answer:
.5
Step-by-step explanation:
2. Carlos and Seth are catching bugs. The picture shows the number of bugs that Carlos has and the number of bugs that Seth has.
Which expression is equivalent to (4g3h2k4)3
Answer:
d) [tex]8g^{6}h^{4} k^{12} - (h^{25} k^{15} )[/tex]
[tex]\frac{(4g^{3} h^{2}k^{4} )^{3} }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}[/tex] [tex]= 8g^{6}h^{4} k^{12} - (h^{25} k^{15} )[/tex]
Step-by-step explanation:
Explanation
Given expression
= [tex]\frac{(4g^{3} h^{2}k^{4} )^{3} }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}[/tex]
By using
(ab)ⁿ = aⁿbⁿ
[tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]
= [tex]\frac{(4)^{3} g^{9} h^{6}k^{12} ) }{8g^{3}h^{2} } - (h^{5} k^{3} )^{5}[/tex]
After simplification , we get
[tex]= 8g^{9}g^{-3} h^{6} h^{-2} k^{12} - (h^{5} k^{3} )^{5}[/tex]
[tex]= 8g^{9-3}h^{6-2} k^{12} - (h^{5} k^{3} )^{5}[/tex]
[tex]= 8g^{6}h^{4} k^{12} - (h^{25} k^{15} )[/tex]
Math problem please help
Answer:
[tex]\displaystyle -2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Average Rate of Change: [tex]\displaystyle \frac{f(b) - f(a)}{b - a}[/tex]Step-by-step explanation:
Step 1: Define
a = 4
b = 8
f(4) = -1
f(8) = -9
Step 2: Find Average Rate
Substitute [ARC]: [tex]\displaystyle \frac{f(8) - f(4)}{8 - 4}[/tex]Substitute: [tex]\displaystyle \frac{-9 + 1}{8 - 4}[/tex][Frac] Add/Subtract: [tex]\displaystyle \frac{-8}{4}[/tex][Frac] Divide: [tex]\displaystyle -2[/tex]3y−3x= 21 standard to slope intercept form
Answer:
y=x+7
Step-by-step explanation:
As part of a survey of college students a researcher is interested is the variable, class standing. She records a '1' if the student is a freshman, a '2' if the students is a sophomore, a '3' if the student is a junior, and a '4' if the student is a senior. The variable, class standing is:________.
a. both categorical and quantitative
b. quantitative
c. categorical
d. none of the above
Answer:
c. categorical
Step-by-step explanation:
Categories of the record
1 2 3 4
Freshman Sophomore Junior Senior
This is simply a categorical arrangement of students in the college by the researcher who is interested in the variable, class standing. So option C is correct
HELP ASAP PLS THANKS SO MUCH
Answer:
(-4,1)
Step-by-step explanation:
Multiply first equation by 2
4x+6y=-10
Then subtract with second equation you get:
y=1
So put the value in first equation you get :
2x+3=-5
x=-4
A bear has a mass of
126 kg. It is up in a
tree that is 2 m high.
How much potential
energy does the
bear have?
Answer:
2469.6 Joules
Step-by-step explanation:
simplify 5a+3a ???????
Answer:
8a
Step-by-step explanation:
group all similar terms
3a + 5a = 8a
Thirty years ago Mike McNamara cycled 445.0km in 12 hours – a new British men’s record at that time. In the same time trial Beryl Burton (who died last year) completed 446.2km.
How much faster was Beryl Burton’s average speed than Mike McNamara’s (in metres per hour)?
Answer:
1000m/h
Step-by-step explanation:
You figure out both of the cyclists km/h times but converting their distance in the 12 hours into a rate
Mike McNamara:
[tex]\frac{445}{12}[/tex]
Beryl Burton:
[tex]\frac{446.2}{12}[/tex]
You then divide the denominator (12) by itself so that it becomes 1
Mike McNamara:
[tex]\frac{445}{12}[/tex] = [tex]\frac{445/12}{1}[/tex]
Beryl Burton:
[tex]\frac{446.2}{12}[/tex] = [tex]\frac{446.2/12}{1}[/tex]
You then divide the numerators by what you divided the denominator by (12) to get the km/h
Mike McNamara:
[tex]\frac{445}{12}[/tex] = 37.08km/h (rounded to two decimal places)
Beryl Burton:
[tex]\frac{446.2}{12}[/tex] = 37.18km/h (rounded to two decimal places)
You them have to convert km/h to m/h by multiplying the numerators (37.08 & 37.18) by 1000 to get the distance in metres
Mike McNamara:
37.08 x 1000
= 37080m
=37080m/h
Beryl Burton
31.18 x 1000
= 37180m
= 37080m/h
Therefore Beryl Burton's average speed was faster than Mike McNamara's by 1000m/h
What is the slope of the line that passes through the points (-5,8) and (-11,8)?
Write your answer in simplest form.
Answer:
[tex]\displaystyle m=0[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-5, 8)
Point (-11, 8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [SF]: [tex]\displaystyle m=\frac{8-8}{-11+ 5}[/tex][Fraction] Subtract/Add: [tex]\displaystyle m=\frac{0}{-6}[/tex][Fraction] Divide/Simplify: [tex]\displaystyle m=0[/tex]Find the unit rate.
180 miles in 3 hours
Answer:
60 miles per hour
Step-by-step explanation:
First, put the equation in a fraction.
You would put 180 up top because people always say miles per hour not the other way around.
You can see the dividing line as your "per" and your "hour" would be the bottom number.
To find the unit rate, you will divide the numerator (180) and the denominator (3).
Your final answer should be 60 miles per hour.
[tex]\frac{180}{3} = \frac{60}{1}= 60[/tex]
one number is three times of the other and their arithmetic mean is 10 find them
Step-by-step explanation:
data
let the unknown numbers = x and y respectively
y is 3 × greater than x so, y = 3x
x+y/ 2 = 10
solution:
x + 3x= 10
4x=10
divide both sides by 4
x=4/10 or 2 1/2Ben deposited $650 from his pressure washing business into a savings account. The simple interest rate paid by the bank is 3.5%. If Ben makes no deposits or withdrawals, how much interest will he earn in 4 years?
Answer:
Simple interest of Ben :
[tex] \frac{\$650 \times 3.5\% \times 4years}{100} = \frac{9100}{100} = \$91 \\ [/tex]
Ben earn $91 in 4 years.
Find cos θ for θ = 60°
Question
Find cos θ for θ = 60°
Which inequalaty Is shown in this grap
Answer:
C. y ≤ -2x - 2Step-by-step explanation:
Lets analyze the graph:
1. It is decreasing function as line goes down as x-value increases. It means the slope is negative. We have two same negatives: -22. Line is solid, so the inequality sign is either ≤ or ≥3. Shaded region is 'under' the line, it means the sign is ≤Based on above observations and the fact that all have same y-intercept of -2, we can say required inequality is:
y ≤ -2x - 2Correct option is C
5. (06.01)
Evaluate the expression 5^3 - (13 – 8) x 2. (4 points)

Answer:
=21.2
Step-by-step explanation:
53/(13-8)*2
=53/5*2
=10.6*2
=21.2
Answer:
21.2 i got this correct on my test
Step-by-step explanation:
PLEASE HELP, TIME SENSITIVE
A rectangular paperboard measuring 35in long and 26in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for π(pi), and do not round your answer. Be sure to include the correct unit in your answer
Answer:
644.67 in^2 remaining
Step-by-step explanation:
So first find the area of this rectangle
rectangle area formula= A=LW
35*26=910
Now we have to find the semi circle value
so we know the diameter is 26 becuase the 2 sides (26 in) are equal and if you fill in the circle the diameter is still 26
A circle formula is
A= π*radius^2
So to find radius divide the diameter by 2
26/2=13
now 13^2=169
Now 169 *3.14 since asked that pi is 3.14
169*3.14=530.66
But Thats the whole circle
The circle that seems to be cut off is half of the original Circle so we half the original circle
530.66/2=265.33
Now we subtract that from the original
910-265.33=644.67
So
644.67 In^2
A ball is projected vertically upward from the surface of the earth with an initial speed of 49 meters per second. The ball reaches its maximum height in 5.0s. What is the vertical velocity of the ball when it strikes the ground
A. 0 m/s
B. -9.8m/s
C. 49m/s
D.-49m/s
PLEASE ANSWER QUICK! WILL MARK BRAINLIEST!
Answer:
Step-by-step explanation:
AB=99
ABC=1391
BAC=992
ACB=3301
Which is more, 5 meters or 4,996 millimeters?
Answer:
5 meters in milli is 5,000. 5,000 is more than 4996
Step-by-step explanation:
Answer:
5 meters
Step-by-step explanation:
one meter equals 1000 millimeters so obv 5 meters is bigger
halloween hut ordered 80 boxes with 20 costumes in each box. they also ordered 12 boxes with 90 masks in each box. how many more costumes than masks did they order?
Find the x - intercept and
y - intercept of the graph of the
equation 4x + 7y = 6
Step-by-step explanation:
Step-by-step explanation:
x- intercept is the x coordinate when y is 0
4x + 7(0) = 6
4x = 6
x = 1.5
(1.5, 0)
y- intercept is when x is 0
4(0) + 7y = 6
7y = 6
y = 6/7
( 0, 6/7)
I hope this helps!!!
True or False: The following table is proportional
Answer:
True
Step-by-Step
When the x was 2, the y was 11.
When the x was 4, the y was 19.
So for every two on the x side, the y side adds 8.
So yes, there's a pattern AKA, this a proportional table.
Hope this helped! :)
Anyone know how to solve these
Answer:
1: 64π
2: 49π and 153.86
Step-by-step explanation:
For the first one we know that it has a diameter of 16 which means it has a radius of 8 (half the diameter)
To find the area of a circle use the following formula
π*r² where r is the radius
This means that the first answer is π*8^2
which is 64π
For the second one it's the same deal but the radius is 7
so the answer is 49π
PLZZZ HELP ME ITS DUE TODAY AT 11:59, HELPPPP
1: In one year, Jerry lost $1,620 in the stock market. What was the average change in his stocks each months.
2: Devon lost 3 pounds each month for 7 months. What was the net change in Devons weight after the 7 months.
3: In a game, your score starts at 0. You lose four points three times in a row. You then gain two points. What is your score after those four turns?
Answer:
1) . Divide that number by 12 months
1620/12 = 135
2) 3 x 7 = 21
21 pounds lost
3) 0 - 4 - 4 - 4 + 2 = -10 points
hope this helps :)
Step-by-step explanation:
Answer:
1. 135
2. 21
3.-10
Step-by-step explanation:
Which measurements could NOT represent the side lengths of a right triangle?
O 8 cm, 15 cm, 17 cm
O 20 cm, 21 cm, 29 cm
O 36 cm, 77 cm, 85 cm
O 7 cm, 28 cm, 32 cm
Step-by-step explanation:
A. 8 cm, 15 cm, 17 cm => This is a right triangle.
B. 20 cm, 21 cm, 29 cm => This is a right triangle.
C. 36 cm, 77 cm, 85 cm => This is a right triangle.
D. 7 cm, 28 cm, 32 cm => This is not a right triangle.
answer questions 15 and 16.
Answer:
Step-by-step explanation:
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