Find the inverse of “f” algebraically, please!
Answer: [tex]f^{-1}(x) = -\sqrt{36-x^2}[/tex]
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Here are the steps to find the inverse
[tex]f(x) = \sqrt{36-x^2}\\\\y = \sqrt{36-x^2}\\\\x = \sqrt{36-y^2} \ \text{ swap x and y; solve for y}\\\\x^2 = 36-y^2\\\\x^2+y^2 = 36\\\\y^2 = 36-x^2\\\\y = \sqrt{36-x^2}\\\\f^{-1}(x) = \sqrt{36-x^2}\\\\[/tex]
Now this would be the answer if our original domain was [tex]0 \le x \le 6[/tex]
However, that's not the case and instead our domain is [tex]-6 \le x \le 0[/tex]
Reflecting any (x,y) point in this domain restriction, over the the line y = x, will have us land on a point with a negative y value. This is because the inverse will swap the x and y values.
Therefore, the inverse function must ultimately be negative.
Currently [tex]f^{-1}(x) = \sqrt{36-x^2}[/tex] is positive since the result of any square root is never negative.
To fix this, we stick a negative out front to get the final answer being [tex]f^{-1}(x) = -\sqrt{36-x^2}[/tex]
Jason solved the following equation to find the value for x.
-8.5 -3.5x= -78
x = 6.5
Describe how Jason can check his answer.
Answer:
Sample Response: Jason needs to substitute the value he found for x in the original equation. Then he needs to use order of operations to simplify. If the result is a true statement then Jason’s solution is correct.
Step-by-step explanation:
on edge 2021
I need help finding the missing side length with the answer in radicals in the simplest form.
Answer:
C
Step-by-step explanation:
There’s nothing hard with this
You need to know special right triangles
This is a 30,60, 90 triangle
We automatically know becuase theres. Right angle (90) and a 60 degree angle
now the formula is the smallest side is (n) {I’m using N becuase theres already an X) or in this case, 6
The hypotenuse, the one directly above the 2nd biggest side, or the diagnoal side is 2n or (12). Now we know what X is in this situation which is 12. So that narrows it to 2 answers
Now the side on the bottom of the hypotenuse, the second biggest side is used in the formula N[tex]\sqrt{3}[/tex]. So we know what N is in the beginning, 6 so we just plug that in and well get C. Attached is a photo on q 30, 60, 90 special right triangle
There were 3 adults and 9 children on the bus. What was the ratio of children to adults? Enter your answer in reduced form.
Answer:
1/3
Step-by-step explanation:
Answer:
3:1
Step-by-step explanation:
[tex]\frac{9}{3}[/tex] --> [tex]\frac{3}{1}[/tex] or simply 3:1
Given g(x) = -
—x – 2, find g(-3).
Answer:
1
Step-by-step explanation:
negative times negative is positive so that would make it 3-2 which is 1.
I need help determineing the next number.?!
Answer:
The next number is -12 ⇒ B
Step-by-step explanation:
Let us solve the question
∵ The pattern is 2,916, -972, 324, -108, 36, ....
→ All the given numbers are divisible by 3 because the sum of
the digits of each number can divide by 3
2+9+1+6 = 18 → multiple of 39+7+2 = 18 → multiple of 33+2+4 = 9 → multiple of 31+0+8 = 9 → multiple of 33+6 = 9 → multiple of 3∵ The pattern has positive and negative numbers
∴ Each next term = the previous term ÷ -3
→ Let us do that to find the missing number
∵ 2916 ÷ -3 = -972
∵ -972 ÷ -3 = 324
∵ 324 ÷ -3 = -108
∵ -108 ÷ -3 = 36
→ Find the next number by divide 36 by -3
∵ 36 ÷ -3 = -12
∴ The next number is -12
Jakob buys lunch at school on Mondays, Wednesdays, and Thursdays. He spends $3.50 for each lunch. Which equation can be used to find the number of weeks, w, it will take Jakob to spend $84 on lunch? 3.50 w = 84 (3 times 3.50) w = 84 3 w = 84 (3 + 3.50) w = 84
Answer:
The answer is ( 3 * 3.50 )w = 84
Explanation:
You first need to know how much he spends each week, which is 3.50 * 3.
Then, you need to find w in that equation by dividing that result from each side.
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
. Which of the following statements about the graph shown is true?
1 point
Captionless Image
a. The graph represents a function because it has a positive slope.
b. The graph represents a function because it passes the vertical line test.
c. The graph does not represent a function because it does not pass through (0,0).
d. The graph does not represent a function because it does not pass the horizontal line test.
The graph represents a function because it passes the vertical line test thus the best option B.
What is graph?The graph is "pictorial representation or diagram that represents data or value in an organized manner".
What is vertical line test?
If "all vertical line intersect the curve at most once, then the curve represents function" is called vertical line test for function.
According to the question,
In this graph, for one value of x, the graph has one value for y.
Hence, the graph represents a function because it passes the vertical line test thus the best option B.
Learn more about graph here
https://brainly.com/question/12017879
#SPJ2
Give the coordinates and quadrant of Point Z.
Answer:
Z = (9, 10 ) and is in first quadrant
Step-by-step explanation:
The first quadrant is above the x- axis and right of the y- axis
Z is in this quadrant with coordinates Z(9, 10 )
Alicia lives in a town whose streets are on a grid system, with all streets running east- west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia only walks south or east on her way to school,
how many possible routes can she take to school?
Corina read 1/12 of her book in 1/3 of an hour. How much of her book will she have read in 1 hour? A: 1/36 B: 2/3 C: 1/4 D: 1/2. Choose correct answer. Plz and thx.
How many squares can you count?
A) 5
B) 4
C) 8
D) 6
Answer:
Step-by-step explanation:
6
Answer:
6
Step-by-step explanation:
What is the answer to (10y + 6)
Answer:
2 ( 5 + 3 )
Step-by-step explanation:
Common factor
1 0 + 6 10y+6 2 ( 5 + 3 )
Answer:
2 (5y + 3)
Step-by-step explanation:
You can pull out a 2 from both terms to create
2 ( 5y + 3)
it can’t simplify any more
simplify 25+ (15 - 10)
Step-by-step explanation:
25+5
=30
plzzzz if it helps you then plzz give me brainliest
The correct range for the function ƒ(x) = x − 9 if the domain is (3, -3, 0) is:
Answer:
The correct range is thus;
(-6,-12,-9)
Step-by-step explanation:
Here, we want to get the range given the domain
we simply make a substitution of the domain in the equation so as to get the range
So let us substitute the value of the domain one after the other
f(3) is 3-9 = -6
f(-3) = -3-9 = -12
f(0) = 0-9 = -9
4x times4b be fast nowwwwwwwwwwwwwwww pls
Answer:
16xb
Step-by-step explanation:
In algebra the numbers are multiplied with the numbers and the variables are multiplied with the variables.
In this question we would multiply x with b and 4 with 4 .
Multiplying x with b would give xb and 4 with 4 gives 16
So the answer will be 16xb
For example if you have 3x and 10 z the answer would be 30xz
Four different stores are having a sale on the same pair of shoes that cost $325. The signs below show the discounts available at each of the four stores. What is the price of one pair of shoes at each of the stores?
Answer:
I would need to see the signs to show each discount to figure this one out. Can you add it?
Step-by-step explanation:
Simplify the equation: (3√-5+2)(4√-12-1)
Answer: 8/x+5 - 6/x+9
2/x-9 * 5/x-4
Step-by-step explanation: Multiply The numbers 3 * 5 =15 =(15√- +2)(4 * 12√- -1) then multiply the numbers 4 * 12=48 =(15√- +2)(48√- -1) then apply minus -plus rules +(-a)= -a = 15 *48√-√- -15 *1 *√- +2 * 48√- -2 *1 then simplify =81√- -722
The Viking football team won 4 out of every 5 of their football games. If they played 20 games, how many games did they lose? help me plzz i give you brianlist
Answer: The Viking football team lost 4 games.
Step-by-step explanation: Since the Vikings WON 4/5 of their 20 games, you need to find the other 1/5. That means you need to find 1/5 of 20. Divide 20 and 5. The final answer is 4.
Kayla invests $8,213 in a savings account with a fixed annual interest rate of 6% compounded continuously. What will the account balance be after 12 years?
can someone plz help me with this
i give u a brainllest
Answer:
it is a and b because you have to do step by step
Jason and Abby finished a meal at a fancy restaurant and their bill was $136.89. They wanted to give the waiter a 20% tip. How much is the tip? _____ (remember to round to the nearest hundredth.) How much is their total bill, including the tip? _____
A pencil costs $0.25 more than an eraser. If the cost of eight pencils is $6.80, what is the cost of one eraser?
Answer:
A single pencil costs $0.85 and a single eraser costs $0.60
Answer: The cost of one eraser is $0.6
Step-by-step explanation:
When solving this problem, it's best to set up a system of equations. Let pencil = p and eraser = e.
p = $0.25 + e
8p = $6.80
Now, we can use the second equation to solve for p by dividing both sides by 8. 6.8/8 = 0.85. Therefore, p = $0.85.
Then, use the value of p to find e by plugging the value of p we just found back into the first equation we wrote. Doing so, we get $0.85 = $0.25 + e. To solve for e, we must subtract 0.25 from both sides, giving use 0.85-0.25 = 0.6
Therefore e = $0.6, so the cost of one eraser is $0.6 or 60 cents.
Bart needs 18 pieces of string 35 inch in length. He cut a 825inch piece of string into pieces that are 35 of an inch long. How many more pieces of string does he need? Show your work.
Answer:
He needs 4 more pieces
Step-by-step explanation:
Here, we want to know the number of more string pieces that are needed
Firstly, we need to the number of string pieces obtained from the 8 2/5 inch piece
we divide 8 2/5 by 3/5
That will be;
42/5 * 5/3 = 14
So what he will get is 14 pieces from the 8 2/5 inch
The number of pieces needed is thus;
18-14 = 4
Ben's earnings for work he did from Monday through Saturday were: $78, $94, $115, $108, $67, $78. What was his average daily pay for the days he worked?
Answer:
His average daily pay was $90.
Step-by-step explanation:
78+94+115+108+67+78=540
540/6= 90.
What number makes this equation true?
4×3,270=(4×3,200)+(4×□)
Find the area of the equilateral triangle whose side length is a. Please help, 10 points.
Answer:
see explanation
Step-by-step explanation:
The area (A) of an equilateral triangle with side a is calculated as
A = [tex]\frac{a^2\sqrt{3} }{4}[/tex]
Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and y represents the total cost. The total cost for 35 brochures is $41.45. The total cost for 65 brochures is $55.55.
Step 1: Write the ordered pairs (35, 41.45) and (65, 55.55).
Step 2: Find the slope. m = StartFraction 55.55 minus 41.45 Over 65 minus 35 EndFraction = 0.47
Step 3: Find the y-intercept to write the equation in slope intercept form. y minus 55.55 = 0.47 (x minus 35). Y minus 55.55 = 0.47 x minus 16.45. y = 0.47 x + 39.1.
Which explains the error that Lila made?
A. Lila made in error in Step 1 by reversing the ordered pairs.
b.Lila made an error in Step 2 by not using the slope formula.
c.Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.
d.Lila made an error in Step 3 when she did not use the distributive property correctly when multiplying.
since its hard first answer = brainliest
Answer:
c
Step-by-step explanation:
Please see the attached picture for the full solution.
Answer:
C.
Step-by-step explanation:
Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1,670 km per hour. What is the circumference of Earth's equator?
Answer:
Solution in photo
Step-by-step explanation:
Help pls and thank you :)
Answer:
[tex]\displaystyle m=7[/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 (0, 0)
Point (1, 7)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]\displaystyle m=\frac{7-0}{1-0}[/tex]Subtract: [tex]\displaystyle m=\frac{7}{1}[/tex]Divide: [tex]\displaystyle m=7[/tex]