Answer:
[tex]f^{-1}[/tex](x) = 9x + 18
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x
Multiply through by 9 to clear the fraction
9y + 18 = x
Change y back into terms of x
[tex]f^{-1}[/tex] (x) = 9x + 18
The inverse of the function is 9y+18
What is inverse of function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
Given:
f f (x) = one-ninth x minus 2
f(x)= 1/9 x - 2
let f(x)=y
Now, solve for x
y = 1/9x -2
y+2 = 1/9x
9y+18 = x
Hence, the inverse of the function is 9x+18.
Learn more about inverse function here:
https://brainly.com/question/2541698
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What type of transformation?
(X,y) (x + 7, -y -6)
Answer:
Translate right 7 units (x+7)
Reflect over x-axis (-y) and translate down 6 units (-y - 6)
If Jeff washes his car in 6 minutes and bob washes the same car in 8 minutes. How long does it take both of them to wash the same car?
Answer:
3 3/7 or 24/7 mins
Step-by-step explanation:
Let total job = X
Jeff's rate = X/6
Bob's rate = X/8
Combined rate = X/6 + X/8
(4X × 3X)/24 = 7X/24
7X/24 = X/T
T = X ÷ (7X/24)
T = X × (24/7X)
T = 24/7 mins
Shortcut:
T = product of individual times/sum of individual times
T = (6×8)/(6+8)
T = 48/14
T = 24/7
T = 3 3/7 mins
Answer:
3 3/7 minutes or 3.4mins
Step-by-step explanation:
If Jeff washed husband car in 6 minutes and Bob washed the same car in 8 minutes , the time taken by both of them in washing the car ?
If Jeff washed the car in 6 minutes , in one minute, Jeff’s work = 1/6
If bob washed in 8mins, in one minute, bob’s work = 1/8
Add both together
1/6 + 1/8
Lcm of 6 and 8 Is 24
Divide the Lcm by the denominators and multiply the results by the numerator
We have 4+3 /24
7/24
Therefore time taken by both of them in Washing is 24/7
= 3 3/7 minutes 0r 3.4mins
Using the formula V=lwh, find w when l=10, h=20 and v=2000
Answer:
w = 10
Step-by-step explanation:
Given
V = lwh ← substitute the given values
2000 = 10 × w × 20, that is
2000 = 200w ( divide both sides by 200 )
10 = w
Please help. I’ll mark you as brainliest if correct
Answer:
527, no mistakes this time
Step-by-step explanation:
???????????anybody helppp
Answer:
B) 24 p-35
Step-by-step explanation:
Step :1
Apply distributive property a.(b+c) = a.b+a.c
Given data 1+4(6 p-9)
= 1+4.6 p - 4.9
multiply
= 1+ 24 p - 36
subtracting
= 24 p - 35
Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions. Choose 2 answers: Choose 2 answers:
Answer:
18(p-2) and 2(9-18)
Step-by-step explanation:
The circumference of a circle is 12 what is the radius
Answer:
6
Step-by-step explanation:
12/2=6
What is the value of d + e + fwhen d = 20, e = -4 and f = -2?
0-26
O 14
0-22
18
The value of d + e + f is 14
Solution:
Given that,
d = 20
e = -4
f = -2
We have to find the value of d + e + f
Substitute d = 20 and e = -4 and f = -2
Thus we get,
d + e + f = 20 + (-4) + (-2)
Remove the parenthesis
We know that, when we multiply negative sign with positive sign, we get negative sign as result
d + e + f = 20 - 4 - 2
d + e + f = 20 - 6
d + e + f = 14
Thus value of d + e + f is 14
converting to standard form y=3x-8
Standard form for a linear equation is Ax+By=C.
Problem: Write #y=3x-8 in standard form.
Subtract 3x from both sides of the equation.
−3x+y=−8
Multiply both sides by −1.
answer ==> 3x−y=8
If f(x) = 2x^2+x find f(x+1)
Answer:
f(x+ 1) = 2x^2 + 5x + 3.
Step-by-step explanation:
We replace the x in the expression for f(x) by x+1:
f(x+1) = 2(x + 1)^2 + x + 1
= 2(x^2 + 2x + 1) + x + 1
= 2x^2 + 4x + 2 + x + 1
= 2x^2 + 5x + 3.
why did the donkey get q passport
Answer:
because it can go overseas
The perimeter of a rhombus is 84 inches. What is the length of each side of the rhombus? Explain
Answer:
Each side of the rhombus is 21 inches
Step-by-step explanation:
A rhombus has 4 equal sides: So all sides are the same
So you take the total perimeter and divide it by 4
84/4=21
Final answer:
The length of each side of a rhombus with a perimeter of 84 inches is 21 inches, calculated by dividing the total perimeter by the number of sides, which is four.
Explanation:
The question asks for the length of each side of a rhombus given its perimeter. The perimeter of a rhombus (or any polygon) is the total distance around the figure, and since all sides of a rhombus are equal in length, we can determine the length of one side by dividing the perimeter by the number of sides. A rhombus has four sides, so if the perimeter is 84 inches, the length of each side is the perimeter divided by four.
Here is the calculation for the length of each side:
Divide the perimeter (84 inches) by the number of sides (4).This gives us 84 inches / 4 = 21 inches.Therefore, the length of each side of the rhombus is 21 inches.
Which one of these graphs matches the function below?
Answer:
The lower right graph.
Step-by-step explanation:
Solve 3^n=5. How to solve n?
Answer:
[tex]\huge\boxed{n=\log_35}[/tex]
Step-by-step explanation:
[tex]3^n=5\Rightarrow\log_33^n=\log_35\qquad\text{use}\ \log_ab^n=n\log_ab\\\\n\log_33=\log_35\qquad\text{use}\ \log_aa=1\\\\\boxed{n=\log_35}[/tex]
NEED HELP ON THIS QUESTION ASAP PLEASE
Answer:
the last one
Step-by-step explanation:
The fact family model represents 3 + 14 = 17.
A triangle. 17 is in the top corner. 3 is in the bottom left corner. 14 is in the bottom right corner.
How does 17 compare to 3?
14 is 17 less than 3.
3 is 14 less than 17.
3 is 17 greater than 14.
3 is 14 greater than 17. ANSWER PLEASE 100 POINS
Answer:
3 is 14 less than 17
Step-by-step explanation:
17-3=14
Answer:
the answer is B 3 is 14 less than 17
hope it helps!
Mr. Markowski drives to his office one morning. After he leaves his house, he drives
at a constant speed until he reaches his office. After work, he drives home at a
constant speed until he reaches a stop light. He waits at the stop light and then
continues at the same speed as before until he gets home.
Which is the graph of Mr. Markowski's distance from his office?
Distance
from office
An
rawr raw
Step-by-step explanation:
Please help! I can't figure this out!
Answer:
1 & -1
Step-by-step explanation:
f(x) = g(x)
Find the inputs for which outputs are equal
Both outputs are 1 when x = -1
Both outputs are -7 when x = 1
What is the answer for the question
r = 16/2 = 8 cm
C = 2π·r = 2×3.14×8 = 50.24 cm
Angel and Jayden were at track practice. The track is 2/5 kilometers around.
•angel ran 1 lap in 2 minutes
•Jayden ran 3 laps in 5 minutes
How far does angel run in one minute
Answer: 66
Step-by-step explanation:
6 laps
Is x^2+y^2= 100 a function
Answer:
No
Step-by-step explanation:
Two angles are supplementary.The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle
Step-by-step explanation:
Let the smaller angle = x and
The larger angle = 10x + 15°
To find, the measure of each angle = ?
We know that,
The sum of two supplementary anges = 180°
∴ x + (10x + 15°) = 180°
⇒ x + 10x + 15° = 180°
⇒ 11x = 180° - 15°
⇒ 11x = 165°
Dividing both sides by 11, we get
[tex]\dfrac{11x}{11} =\dfrac{165}{11}[/tex]
⇒ x = 15°
∴ The smaller angle = 15° and
The larger angle = 10(15° ) + 15° = 165°
Jamison graphs the function ƒ(x) = x4 − x3 − 19x2 − x − 20 and sees two zeros: −4 and 5. Since this is a polynomial of degree 4 and he only sees two zeros, he determines that the Fundamental Theorem of Algebra does not apply to this equation. Is Jamison correct? Why or why not?
Answer:
Jamison is not correct
Step-by-step explanation:
According to the Fundamental Theorem of Algebra, an nth degree polynomial has n roots.
These roots comprises of real roots and imaginary roots.
The given function is
[tex]f(x) = {x}^{4} - {x}^{3} - 19 {x}^{2} - x - 20 [/tex]
Based on the Fundamental Theorem of Algebra, this function should have four roots.
The graph of the function only reveals real zeros and not the imaginary zeros.
So aside −4 and 5, there are two complex zeros
Jamison is incorrect; according to the Fundamental Theorem of Algebra, a fourth-degree polynomial will have four roots, which could include complex numbers. The zeros he observed are real, but the polynomial may also have complex zeros.
Explanation:Jamison is not correct because the Fundamental Theorem of Algebra states that every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots in the complex number system. The function ƒ(x) = x4 − x3 − 19x2 − x − 20 is a fourth-degree polynomial, therefore it will have four roots, not necessarily all distinct. Jamison has found two real zeros at −4 and 5. There could be additional complex zeros that were not visible on the graph. The theorem does not specify that all zeros must be real, only that there will be n zeros when including complex numbers.
Polynomials of the second order always have two roots in the complex number system, which explains why real polynomials without real roots (like x2 + 1) have complex roots i and −i. A polynomial of degree four such as the one Jamison is working with can be factored completely into four linear factors in the complex number system, leading to four complex roots. Therefore, it is possible that the remaining two roots of Jamison's polynomial are complex, which is consistent with the Fundamental Theorem of Algebra.
Polygon JKLMNO and polygon PQRSTU are similar. The area of polygon
PQRSTU is 75. What is the area of JKLMNO?
Answer:
The area of polygon JKLMNO is 48 square units
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the scale factor
we know that
If two figures are similar, the the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z ----> the scale factor
The scale factor of the dilation of polygon PQRSTU to polygon JKLMNO is
[tex]z=\frac{KJ}{QP}[/tex]
substitute the given values
[tex]z=\frac{4}{5}[/tex]
step 2
Find the area of polygon JKLMNO
we know that
If two figures are similar, the the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> area of polygon JKLMNO
y ----> area of polygon PQRSTU
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{5}[/tex]
[tex]y=75\ units^2[/tex]
substitute
[tex](\frac{4}{5})^{2}=\frac{x}{75}[/tex]
solve for x
[tex]x=(\frac{16}{25})75=48\ units^2[/tex]
therefore
The area of polygon JKLMNO is 48 square units
Answer:48units
Step-by-step explanation: I know
It takes time 42 minutes to ride his bike 7 miles. How many minutes does it take him to ride 1 mile? Find a unit rate for using what you know about raIt takes time 42 minutes to ride his bike 7 miles. How many minutes does it take him to raid 1 mile?
Answer:
Step-by-step explanation:
42/7
= 8
y × 6 for y = 2/3. what is the y? please help.
Answer:
The answer is Y = 4. Hope this helps.
Answer: y is 2/3, or the answer to the equation is 4
Step-by-step explanation:
it tells you what y is with y=2/3, so you need to plug that into the equation nto get 4, or just use 2/3 as your answer
(56 x10°)-4,000,000 =
Answer:
-3999944
Step-by-step explanation:
There is another option that got cut off, it is
D: -1;the amount of water decreases by 1 gallon per minute
PLEASE ANSWER
Answer:
answer is b
Step-by-step explanation:
look at the picture
129 original price with a 30% discount
Answer:
i think it is $38.70
Step-by-step explanation:
The wolverines scored 42 points in a football game they scored 2 more field goals (3 points each) than touchdowns 6 points each how many field goals and touchdowns did they score
Answer:
6 touchdowns
Step-by-step explanation:
You just subtract the (2*3) from the 42 and get 36 than you divide by 6.