Answer:
The inverse function of f(x)=2.5*x+150 is f⁻¹(x)=[tex]\frac{2}{5}x-60[/tex]
Step-by-step explanation:
An inverse or reciprocal function of f (x) is called another function f ⁻¹(x) that fulfills that:
If f(a)=b then f⁻¹(b)=a
That is, inverse functions are functions that do the "opposite" of each other. For example, if the function f (x) converts a to b, then the inverse must convert b to a.
To construct or calculate the inverse function of any function, you must follow the steps below:
Since f (x) or y is a function that depends on x, the variable x is solved as a function of the variable y. And since inverse functions swap the input and output values (that is, if f (x) = y then f⁻¹(y) = x), then the variables are swapped and write the inverse as a function.
You know that he function f(x) = 2.5*x + 150 or y=2.5*x +150
Solving for x:
2.5*x +150=y
2.5*x= y-150
[tex]x=\frac{y-150}{2.5}[/tex]
[tex]x=\frac{y}{2.5}-\frac{150}{2.5}[/tex]
[tex]x=0.4y-60=\frac{2}{5}y-60[/tex]
Exchanging the variable, you obtain that the inverse function of f(x)=2.5*x+150 is f⁻¹(x)=[tex]\frac{2}{5}x-60[/tex]
ok there’s the science slides , and i think they are quite easy i just need some help bc im lazy . ik this is the math thing but
Answer:
just look up the answers on google
Step-by-step explanation:
The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t) =???
MARK AS BRAINLIST
Step-by-step explanation:
L = 6t+5
H = √t
A = L*H
= (6t+5) *√t = 6t√t + 5√t
A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t
= 6t/2√t + 6√t + 5/2√t
Expression for the rate of change of the area with respect to time will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second
It's given in the question,
Length of a rectangle is given by the expression(6t + 5) cm
Width or height of the rectangle is given by the expression,[tex]\sqrt{t}[/tex] cm
Area of the rectangle is given by,
Area = Length × Height
A = (6t + 5)(√t)
A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]
Now find the derivative of area (A) with respect to time (t).
[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]
A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Therefore, expression for the rate of change of the area will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Learn more,
https://brainly.com/question/12596049?
What is 125 x 64 in expanded form
Solve for b : 1/2b+G=D
Answer:
I believe the answer is b=1/2(d-g)
Step-by-step explanation:
multiply to remove the variable from the denominator.
26 beats in 1/6 minute
Answer:
If you wanna know how many beats are in a full minute, the answer is 156 beats
Step-by-step explanation:
1/6*6=1
26*6=156
Find the angle BCD.PLZ!!!!!!!
Answer:
19
Step-by-step explanation:
Firstly find BCE then divide by 2.
Select the correct answer. The equation of a line in the point-slope form is show below. y - 9 = ls 1/5(x - 2) What is the slope of this line?
Answer Choices:
A. 2
B. 1/9
C. 5
D. 1/5
Answer:1/5
Step-by-step explanation:
f(x) = 4x – 1
g(x) = x2 - 3x + 5
5914 1404 393
Answer:
f(1) = g(1) = 3
f(6) = g(6) = 23
Step-by-step explanation:
Perhaps you want to know the solutions to ...
f(x) = g(x)
Substituting the function definitions, this is ...
4x -1 = x^2 -3x +5
0 = x^2 -7x +6 . . . subtract 4x-1
0 = (x -6)(x -1) . . . factor the equation
Solutions are x = 1 and x = 6, the values that make the factors zero.
The corresponding function values are ...
f(1) = 4(1) -1 = 3
f(6) = 4(6) -1 = 23
Solutions for y = f(x) = g(x) are (x, y) = (1, 3) and (6, 23).
Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year. How much money did she put in each account? Use the general formula, I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.
Answer:
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
Step-by-step explanation:
Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year.
I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.
Step 1
We have to calculate the total interest earn on the initial capital
P = $2,560
R = 7.25% = 0.0725
T = 1
I = $2,560 × 0.0725 × 1
I = $185.60
Let the amount Invested in the account that paid 6% interest = x
Let the amount Invested in the account that paid 8% interest = y
Hence:
$185.60 = x × 6% + y × 8%
$185.60 = 0.06x + 0.08y......Equation 1
$2560 = x + y........ Equation.2
x = $2560 - y
$185.60 = 0.06x + 0.08y......Equation 1
185.60 = 0.06(2560 - y) + 0.08y
185.60 = 153.6 - 0.06y + 0.08y
185.60 - 153.60 = 0.02y
y = 32/0.02
y = $1600
x = $2560 - y
x = $2560 - $1600
x = $960
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
I need help answer this Question!
-6+3(-4-2x)>=-16-6x
There is no solution for that problem....
help me!!!!!!! I need help
Answer:
the answer is 8
Step-by-step explanation:
BC
Answer:
8
Step-by-step explanation:
18-inches is 1.5 feet.
is this a function or not?
Answer: yes
Step-by-step explanation:
The x value does not repeat itself
Which of the following numbers would be an outlier if added to the data set below?
234, 187, 201, 199, 217, 200, 201, 193
A: 111
B: 201
C: 235
D: 204
Answer:
111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
The regular price of a baseball hat is $15.65. If Julio buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?
Picture provided
Please solve.
Step-by-step explanation:
hope this helps, good night!!!!
999÷128= plz help mee
Answer:
The answer is (7.8046875)
Step-by-step explanation:
Hope this helped
Mr. Cooper is baking chocolate chip cookies using his grandma's recipe. The number of cups of chocolate chips needed to the number of dozens of cookies made can be represented by the ratio 4 : 5. Using the same recipe, what is the amount of chocolate chips needed for 1 dozen?
Answer:
0.8 cups
Step-by-step explanation:
Given that:
Numbe of cups of chocolate chips needed to the Number of dozens of cookies made can be represented using the ratio 4:5
Hence,
The proportion of cups of chocolate chips to the number of dozens of cookies = 4 / 5
4 cups of chocolate chips to 5 dozens of cookies ;
For 1 dozen of cookies, number of chocolate chips will be (x)
4 / 5 = x / 1
Cross multiply
4 * 1 = 5 * x
4 = 5x
x = 4/5 = 0.8
Hence, for 1 dozen of cookies, 0.8 cups of chocolate chips is required
A polar bear was sitting on the top of an ice float that was 2.5 meters above the surface of the water. The polar bear dove 6.5 meters from the top of the float into the water to catch a seal. Relative to the surface of the water, which equation best represents how far below the surface the polar bear dove?
Answer:
Step-by-step explanation:
Let the surface of the water be at 0m
If a polar bear was sitting on the top of an ice float that was 2.5 meters above the surface of the water, the distance between the ice float and the surface of the water will be:
= 2.5 - 0
= 2.5m
If the polar bear dove 6.5 meters from the top of the float into the water to catch a seal, to get the distance between the bear under the water to the sea level, we will use the expression:
2.5 + x = 6.5
Subtract 2.5 from both sides
2.5+x -2.5 = 6.5-2.5
x = 4.0m
Hence the equation that best represents how far below the surface the polar bear dove is 2.5 + x = 6.5 where x is the distance between the polar bear below and the surface of the water
8. A sequence can be generated by using 2n - 11. What are the first four terms in
the sequence?
Answer:
[tex]\bold{a_1=-9\,,\quad a_2=-7\,,\quad a_2=-5\,,\quad a_4=-3}[/tex]
Step-by-step explanation:
[tex]a_n=2n-11\\\\a_1=2(1)-11=2-11=-9\\\\a_2=2(2)-11=4-11=-7\\\\a_3=2(3)-11=6-11=-5\\\\a_4=2(4)-11=8-11=-3[/tex]
A dock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes? O 14 O 21 O 35 O 42
Answer: 42
Step-by-step explanation:
Did the test
Paul's mom sent him to the grocery store with $10 to buy bread and cheese for sandwiches. Paul picked out a loaf of bread that costs $3.25, and a deli cheese that costs $5.99 a pound. He would like to buy as much cheese as possible, so he asks the deli worker to see how much each slice weighs. Each slice weighs 0.04 pounds. Which inequality can be solved to find x, the number of slices that Paul can afford to buy?
Given:
Total amount = $10
Cost of loaf of bread = $3.25
Cost of cheese = $5.99 per pound
Each slice weights = 0.04 pounds.
To find:
The inequality for the number of slices that Paul can afford to buy.
Solution:
Let x be the number of slices that Paul can afford to buy.
Weight of on slice is 0.04 pounds. So, weight of x slices is 0.04x pound.
Cost of cheese = $5.99 per pound
So, total cost of cheese for x slices = $5.99 × 0.04x
Now, Paul has $10 to buy bread and cheese for sandwiches. Cost of loaf of bread is $3.25.
[tex]3.25+(5.99\times 0.04x)\leq 10[/tex]
[tex]0.2396x\leq 10-3.25[/tex]
[tex]0.2396x\leq 6.75[/tex]
Divide both sides by 0.2396.
[tex]x\leq \dfrac{6.75}{0.2396}[/tex]
[tex]x\leq 28.172[/tex]
The maximum integer value of x is 28.
Therefore, the required inequity is [tex]3.25+(5.99\times 0.04x)\leq 10[/tex] and 28 number of slices Paul can afford to buy.
Write in slope-intercept form with the given information. Show all work. Passes through (-8,3) with a slope of -2
Answer:
y=-2x-13
Step-by-step explanation:
y=mx+b
3=-2(-8)+b
3=16+b
3-16=b
-13=b
The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, squared, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=
Answer:
(x-2)(x+3)(x+6)
Step-by-step explanation:
Given the polynomial function p(x)=x^3+7x^2-36
We are to write it as a product of its linear factor
Assuming the value of x that will make the polynomial p(x) to be zero
Let x = 2
P(2) = 2³+7(2)²-36
P(2) = 8+7(4)-36
P(2) = 8+28-36
P(2) = 0
Since p(2) = 0 hence x-2 is one of the linear factors
Also assume x = -3
P(-3) = (-3)³+7(-3)²-36
P(-3) = -27+7(9)-36
P(-3) = -27+63-36
P(-3) = 36-36
P(-3) = 0
Since p(-3) = 0, hence x+3 is also a factor
The two linear pair are (x-2)(x+3)
(x-2)(x+3) = x²+3x-2x-6
(x-2)(x+3) = x²+x-6
To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.
x^3+7x^2-36/x²+x-6 = x+6
Hence the third linear factor is x+6
x^3+7x^2-36 = (x-2)(x+3)(x+6)
Answer:
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Step-by-step explanation:
Here we want to rewrite the polynomial
P(x) = x^3 + 7x^2 - 36
As a product of linear factors given that we have one of the roots already as (x + 3)
What we shall do here is to divide the polynomial by x + 3
Please check attachment for long polynomial division
From the division, the other factor is x^2 + 4x -12
So we can rewrite the polynomial as;
x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)
So let’s now write x^2 + 4x -12 as a product of its linear factors
x^2 + 4x -12 = x^2 + 6x -2x -12
= x(x + 6)-2(x + 6)
so we have;
(x -2)(x + 6)
Therefore;
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
question attached through picture
Step-by-step explanation:
(1/n)^-2/3
= n^2/3
= 3 root of n^2
solution is 3)
Multiply. Write each product in simplest form, 1 4/5 x 1/2
8/9
9/8
1 1/8
1/8
9/10 or 0.9
mark me brainliest if you feel like mine was helpful!! I hope that helped!
Algebra Test Question! Please answer correctly!! :)
Please answer the following questions with this format
A:
B:
C:
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation that represents your distance from home ( y ) after ( x ) hours
b. find the y-intercept of the graph
c. find the x- intercept of the graph
Answer:
A: y=9-6x
B: y=6x+9
C: y=9-6x
Step-by-step explanation:
a) y=9-6x, standard form is ax+by=c so add 6x to both sides
b) from the first, we had it in slope intercept form, mx+b where b is the y-intercept. y=-6x+9
c) The x intercept occurs when y=0 so: y=9-6x
x=1.5
Arron can join a gym for $19.99 per month plus an annual fee of $12.80 or he can pay $21.59 per month. He thinks the second option is better because he plans to use the gym for 10 months. Is Aaron correct ? Set up an equation (with variables on both sides) to describe the situation.
Answer: Aaron is wrong. The first option is better as it costs less than the second option.
Step-by-step explanation:
Arron can join a gym for $19.99 per month plus an annual fee of $12.80.
Since Aaron wants to spend 10 months at the gym, this will cost him:
= $12.80 + ($19.99 × 10)
= $12.80 + $199.9
= $212.7
Paying $21.59 for 10 months will be:
= $21.59 × 10
= $215.9
The first option is better as it costs less than the second option.
Find the Value of 2a2+5b2
Answer:
I get 92 but not really sire
Is 9 4/9 greater than less than or equal to ✓144
Answer: less than
Step-by-step explanation:
Because the square root of 144 is 12 it would be greater than 9 4/9. So 9 4/9 is less than 12
Which of the following numbers is written
in CORRECT scientific notation?
3.41 · 104
34.1 : 105
3.41 + 104
0.341 · 106
HELPP PLZZ