Find the inverse of “f” algebraically, please!
Answer: [tex]f^{-1}(x) = -\sqrt{36-x^2}[/tex]
====================================================
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]
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
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:
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 )
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
find k so that x-1 is a factor of x^3 -3x^2 + kx - 1
By the remainder theorem, if p(x) = x³ - 3x² + kx - 1 and x - 1 is a factor p(x), then the remainder upon dividing p(x) by x - 1 is p (1) = 0.
So we have
p (1) = 1³ - 3 • 1² + k - 1 = 0
Solve for k :
1 - 3 + k - 1 = 0
k = 3
Your town has seen a steady decrease of job opportunities by the amount of 10% every year. If the number of jobs available at the end of last year was estimated at 350,000, then how many jobs will there be by the end of the following year?
a.
45,000
c.
35,000
b.
385,000
d.
315,000
Answer:
c)35000
Step-by-step explanation:
10%of 350000
10/100×350000
0.1×350000=35000
Answer: D
Step-by-step explanation:
350,000 - 10% = 315,000
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?
what is 5.476; rounded to the narthest hundredths
Answer:
The answer is 5.48
Step-by-step explanation:
When rounding the hundredths (second number after the dot), you want to look at the number on the right. In this case, that number is 6.
Anytime the number to the right is more than 5, you make the number before it one number higher. Here, the 7 in 5.476 turns into 5.48.
After you've rounded, drop the number you looked at. So, no need for the 6 anymore!
That's it!
Which of the following is the radical expression 2d 7/10
Answer:
[tex]2d^{\frac{7}{10}}[/tex] [tex]= \sqrt[10]{2d^7}[/tex]
Step-by-step explanation:
Given
[tex]2d^{\frac{7}{10}}[/tex]
Required
Determine the radical expression
To do this, we apply the following law of indices:
[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]
By comparing the above to [tex]2d^{\frac{7}{10}}[/tex], we have:
[tex]m=7[/tex]
[tex]n = 10[/tex]
So, the solution becomes
[tex]2d^{\frac{7}{10}}[/tex] [tex]= \sqrt[10]{2d^7}[/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
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.
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.
. 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
diagram 7(i) shows a square with area of 64cm² formed using a string.The string is cut to form another two congruent rectangles with length 5 cm, as shown in diagram 7(ii).Calculate the area , one of the rectangles.If u guys can help me solve this, u guys really save my life.I need to submit tomorrow morning.
Answer:
The area of one rectangle is 15 cm²
Step-by-step explanation:
The given parameters are;
The area of the square = 64 cm²
The length of the rectangles = 5 cm
The formula for the area of a square = (Side length)² = S²
Therefore, whereby the side length of the given square = S, we have;
Area of the square = 64 = S × S = S²
S = √(64 cm²) = 8 cm
The side length of the square = 8 cm
The perimeter of a square = The length of the string = Side length × 4 = 8 cm × 4 = 32 cm
∴ The perimeter of a square = The length of the string = 32 cm
The length of the string = The perimeter of the two congruent rectangle = 32 cm
Therefore;
The perimeter of each rectangle = 32/2 cm = 16 cm
Given that the length, L of the side of each rectangle is L = 5 cm, we have;
The perimeter of a rectangle = 2 × L + 2 × W
Where;
W = The width
The perimeter of the rectangle = 16 = 2 × 5 + 2 × W
2 × W = 16 - 2 × 5 = 6
W = 6/2 = 3
W = 3 cm
The width, W, of each rectangle is W = 3 cm
The area of one rectangle = W × L = 3 cm × 5 cm = 15 cm²
The area of one rectangle = 15 cm².
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:
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.
66 cm cube of silver is drawn into a wire 1 mile in a diameter does length of wire will be
Answer:
The length of the wire is 3.24451394 × 10⁻⁹ cm
Step-by-step explanation:
The volume of the wire = 66 cm³
The diameter of the wire = 1 mile
We convert the volume from cm³ into mile³ to get;
66 cm³ = 1.5834 × 10⁻¹⁴ mile³
The volume = π × D²/4 × l
Where;
D = The diameter = 1 mile
l = The length of the wire
1.5834 × 10⁻¹⁴ = π × 1²/4 × l
The length of the wire = l = 1.5834 × 10⁻¹⁴/(π × 1²/4) = 2.0160475 × 10⁻¹⁴ mile
1 mile = 160,934.4 cm
2.0160475 × 10⁻¹⁴ mile = 2.0160475 × 10⁻¹⁴ × 160,934.4 cm = 3.24451394 × 10⁻⁹ cm
The length of the wire = 3.24451394 × 10⁻⁹ cm
2x+3y=12
find the missing values
What value of q is a solution to this equation?
-3(12+q)=-18
Answer: q= -6
Step-by-step explanation:
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
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
what is the solution to -3x=9?
Answer:
x=-3
Step-by-step explanation:
Step-by-step explanation:
-3x=9
x= -3 Hope this helps
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]
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:
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
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:
a box is 50 cm long. how long is the box in feet
Answer:
____1.64042 foot____
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:
A cyclist travels 7 miles in 15 minutes.
What is her average speed in mph?
Answer:
0.47 miles per hour
Step-by-step explanation: