The inverse of the function y = (x - 5)² + 10 is given by f⁻¹(x) = ±√(x - 10) + 5.
What is the inverse of the function?An inverse function is simply a function which can reverse into another function.
Given the function in the question:
y = ( x - 5 )² + 10
To find the inverse of the function y = ( x - 5 )² + 10,
Swap or interchange the variables x and y
y = ( x - 5 )² + 10
x = ( y - 5 )² + 10
Next, solve for y in terms of x:
Subtract 10 from both sides
x - 10 = ( y - 5 )² + 10 - 10
x - 10 = ( y - 5 )²
( y - 5 )² = x - 10
Take the sqaure roots
y - 5 = ±√(x - 10)
Add 5 to both sides
y - 5 + 5 = ±√(x - 10) + 5
y = ±√(x - 10) + 5
Replace y with f⁻¹(x)
f⁻¹(x) = ±√(x - 10) + 5
Therefore, the inverse function is f⁻¹(x) = ±√(x - 10) + 5.
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Kevin is sowing seeds in the flower beds of his garden. He sowed 30% of the flower beds in 15 minutes. How much longer will it take him to sow the rest of the field?
Jay makes $9 an hour plus a 12.5% commission selling jewelry how much does she earn on an 8-hour shift and what she sells $380 worth of jewelry
Answer:
117.6
Step-by-step explanation:
Please help:))))) AsAP
Answer:
10b-2b-8x+14
(the last one)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
6x + 8b = x + 5x + 8b
help its pre-pre
a triangle has two angles that measure 18.6 degrees and 113.4 degrees respectively. what is the measure of the third angle?
Sum of all angles of a triangle = 180°
Let the third angle be x.
So, 18.6° + 113.4° + x = 180°
=> 132° + x = 180°
=> x = 180° - 132°
=> x = 48°
So, the third angle is 48°.
Step-by-step explanation:
sum of all Δangle of a triangle = 180°so, let 3rd angle be x18.6° + 113.4° + x = 180°132° + x = 180°x = 180° - 132°x = 48°MARK ME AS BRAINLISTSolve the following system of equations
3x-3y=4
-3x+3y=3
Answer:
Step-by-step explanation:
1. Elimination
2. zero solutions
0 ≠ 7
Gabby makes banana bread at her bakery every Monday and Wednesday,
Her banana bread calls for the ratio of ingredients shown
5 cups of sugar for every 50 tablespoons of butter
80 tablespoons of butter for every 32 bananas
Complete that table to show the ratio of ingredients Gabby used to make her
banana bread.
Answer:
Monday:
Cups of Sugar: 3
Tablespoon of Butter: 30
No. of Bananas: 75
Wednesday
Cups of Sugar: 1.12
Tablespoons of Butter: 11.2
No. of Bananas: 28
What is the equation of the line that passes through (0, -2) and has a slope of 0?
y = -2
y = 2
x = 2
Answer:
y = - 2
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (0, - 2) with y- coordinate - 2 , then
y = - 2 ← equation of line
x^2 + 5x + 13 pls help
Answer:
Not factorable
Step-by-step explanation:
We are given a polynomial and are asked to solve or factor it I am assuming.
To solve this, there is a certain rule I like to follow, which is for b (in this case 5), you have to find two numbers that multiply to it, and for c (in this case 13), you have to find two numbers that add to it.
Since no two numbers multiply to 5 and add to 13, therefore this polynomial is not factorable.
triangle ABC is isosceles with AB=AC and angle A=50°. the bisector of angle B and angle C meet at D. find the measure of BDC
Answer:
115 degrees
Step-by-step explanation:
From what I'm visualizing, D is a point of another isosceles triangle within ABC, so to find the measure of angle BDC, we have to find the other angles first.
First, we have to find angle B and C. since this is an isosceles triangle and AB=AC, these two angles are equal and we find their angle measure by subtracting the known angle A, from the total measure of all angles in a triangle, 180
180 - 50 = 130
then divide that by two to get the two equal angles
130/2 - 65
angle bisector divides the angles in half so the measures of CBD and BCD are 65/2
that leaves the last remaining angle BDC. Again, we take the known angles and subtract them from 180
180 - 65/2 -65/2 = 115
$2500 at 5% for 60 months
What's the answer ?
Quick!
Answer:
0.04%
Step-by-step explanation:
The pool is partially filled with water. The volume of the water in the pool is 45 ft3. How deep is the
water?
A.)0.5 ft
B.)1.5 ft
C.)2.5 ft
D.)3.5 ft
C.)2.5 ft
it's just a guess
Find the area of the similar
figure.
20cm
25cm
Area = 320cm2 Area = [?]cm2
Given:
Base of smaller figure = 20 cm
Area of smaller figure = 320 cm²
Base of the larger figure = 25 cm
To find:
The area of the larger figure.
Solution:
We know that the areas of the similar figure are proportional to the square of corresponding sides of them.
Let A be the area of the larger figure.
[tex]\dfrac{\text{Area of the larger figure}}{\text{Area of the smaller figure}}=\dfrac{(\text{Base of the larger figure})^2}{(\text{Base of the smaller figure})^2}[/tex]
[tex]\dfrac{A}{320}=\dfrac{(25)^2}{(20)^2}[/tex]
[tex]\dfrac{A}{320}=\dfrac{625}{400}[/tex]
[tex]\dfrac{A}{320}=\dfrac{25}{16}[/tex]
Multiply both sides by 320.
[tex]A=\dfrac{25}{16}\times 320[/tex]
[tex]A=500[/tex]
Therefore, the area of the larger figure is 500 cm².
A wire attached to the top of a building makes a 15° angle with the ground. If the building is 25 feet high, how
long is the wire?
Answer:
96.6feet
Step-by-step explanation:
,
From the attachment, we can see that a triangle is formed.
From trigonometry,
Sin(X)= opposite/hypothesis
Where Opposite sides=25feet
Hypotenuse sides= X feet
Sin(15)= 25/X
Cross multiply
Sin(15)= 0.2588
0.2588=25/X
X= 25/0.2588
X=96.6feet
Hence, the wire is 96.6 feet high
CHECK THE ATTACHMENT FOR THE FIQURE.
Find the missing length indicated.
Help pls
2. none of the answers are correct
Answer:
400
Step-by-step explanation:
Use the right triangle altitude theorem.
All three triangles are similar, so we can write a proportion of corresponding side lengths.
Let y = x - 144
192/144 = y/192
144y = 192 * 192
144y = 36,864
y = 256
x = y + 144 = 256 + 144
x = 400
Choose all the ways the ratio of five girls to 9 boys can be written. the options are
9:5
9 to 5
5:9
5 to 9
5/9
9/5 i need helppp im so confused.
Answer:
5/9
5 to 9
5:9
hope this helps <3
Answer:
5/9,
5:9,
and 5 to 9
The equation y = 700x + 800 models the typical annual cost, y, in dollars, of medical expenses x years after a person’s 20th birthday. What does 800 represent?
Answer:the annual medical expenses for a typical 20 yr old
Step-by-step explanation:
The cost of a car rental is $30 per day plus 23 cents per mile. you are on a daily budget of $76 . You can drive at most how many miles per day
Answer:
200 miles
Step-by-step explanation:
y=0.23x+30
76=0.23x+30
46=0.23x
x=200
The moving of the orientation or position of an angle changes the measurement of the angle. True or false
Answer:
the correct answer is true
Answer:
I believe this is true!
Hope that helps!
My brain isn't working today, help me out pls :)
Complete the equation of the line whose slope is −2 y-intercept is (0,3)
Answer:
y=-2x+3
Step-by-step explanation:
hope this helps
Answer:
y = -2x + 3
Step-by-step explanation:
So you want to put it in the form y = mx + b where m is the slope and b is the y-intercept (an example of an equation in this form is y = 2x + 1).
It tells you that the slope is -2 and the y-intercept is at y = 3, so the equation would be:
y = -2x + 3
Mason’s mom bought g games online. The games cost $12 each plus a $7 shipping fee.write an equation.
Answer:
f(x) = 12x + 7
Step-by-step explanation:
easy
Answer:
12g + 7 = total price
Step-by-step explanation:
Find the missing exponent.
?
916 x 918
x 918 = 9
Answer:
um i think its 6
Step-by-step explanation:sorry if im wrong
2(2b+2cd)
(2+b) (2a+7)
Step-by-step explanation:
The answer to the first one is: 4cd+4b.
The answer to the second one is: 2ab+4a+7b+14
(I'm assuming that you want to simplify)
help me pleaseeeeeeeee
Answer:
15m squared
Step-by-step explanation:
1 + 3+ 1 + 3 + 1 + 5 + 1 = 15
Answer:
D
Step-by-step explanation:
We know that the length of the middle rectangle is 1 + 3 + 1 + 3 = 8 and that the width is 5 so 8 x 5 = 40. We have two rectangle with a width of 1 and a length of 3 so 2 x 1 x 3 = 6. 40 + 6 = 46.
Carla has 10 fewer books than Dominic.
Create an expression to represent the number of books that Carla has, wher
x is the number of books Dominic has. 4.9
Answer:
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Step-by-step explanation:
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.25 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Assumed 20% tip is on the discounted meal.
The cost of the meal is $78.65 .
The cost of the meal after discount (15%) is
78.65⋅(1−0.15)≈$66.85
Tip (20%) is : 66.85⋅0.2≈$13.37
Total cost of the meal is 66.85+13.37≈$8
What is x ?? - 2/5x- 4 = 4
Answer:
-0.05 (-1/20)
Step-by-step explanation:
Answer:
x= -20
Step-by-step explanation:
+4 on both sides
-2/5x=8
(5) on both sides
-2x= 40
/-2 on both sides
x= -20
Can someone please help me I’m stuck
9514 1404 393
Answer:
x = 22
Step-by-step explanation:
When lines l and m are parallel, the marked angles are supplementary.
(2x -3)° +(6x +7)° = 180°
8x +4 = 180 . . . . . . . . . . . divide by °, collect terms
8x = 176 . . . . . . . . . . subtract 4
x = 22 . . . . . . . . divide by 8
Murray’s father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account?
x + y = 6,000. 0.025 x + 0.015 y = 110.
x + y = 6,000. 0.25 x + 0.15 y = 110.
x + y = 6,000. 0.025 x minus 0.015 y = 110.
x + y = 6,000. 2.5 x minus 1.5 y = 110.
Answer:
6000
Step-by-step explanation:
Answer:x+y = 6,000
0.025x-0.015y
Step-by-step explanation: did it on edge
She measured the circumference of the globe along the equator to be 12π centimeters. Which of the following measures is closest to the volume of Tiffany’s globe?
Answer:
117 i think not sure
Step-by-step explanation:
help me
for question 6, write the equation in standard form ax by=c (show your work). from: y=m b to Ax By=c
Since you have the slope m = -3 and the point (-9, -2) you can use the Slope Intercept Form to find b
y = mx + b
-2 = -3(-9) + b
-2 = 27 + b
Subtract 27 from both sides of the equation to get b
-2 - 27 = b
-29 =b
And the Slope Intercept Form
y = -3x -29
Now you can rearrange the Slope Intercept Form to give the Standard Form by adding 3x to both sides of the equation.
y + 3x = -29
I hope you find this useful and if you have any questions please send me a message.