Answers
Answer:
We have that [tex]f(a) = f(b)[/tex] if [tex]a = \pm b[/tex], which does not respect the condition for the existence of an inverse function, which means that [tex]f^{-1}(x)[/tex] does not exist for this function.
Step-by-step explanation:
Existence of an inverse function:
An inverse function will exist if: f(a) = f(b) only if a = b.
In this question:
[tex]f(a) = -\frac{1}{7}\sqrt{16 - a^2}[/tex]
[tex]f(b) = -\frac{1}{7}\sqrt{16 - b^2}[/tex]
[tex]-\frac{1}{7}\sqrt{16 - a^2} =-\frac{1}{7}\sqrt{16 - b^2}[/tex]
[tex]\sqrt{16 - a^2} = \sqrt{16 - b^2}[/tex]
[tex](\sqrt{16 - a^2})^2 = (\sqrt{16 - b^2})^2[/tex]
[tex]16 - a^2 = 16 - b^2[/tex]
[tex]a^2 = b^2[/tex]
[tex]a = \pm b[/tex]
We have that [tex]f(a) = f(b)[/tex] if [tex]a = \pm b[/tex], which does not respect the condition for the existence of an inverse function, which means that [tex]f^{-1}(x)[/tex] does not exist for this function.
Related Questions
Find the sum of the arithmetic series given a1=8,a14=99,n=14.
Answers
Answer:
The sum of the series is: 749
Step-by-step explanation:
Given
[tex]a_1 = 8[/tex]
[tex]a_{14} = 99[/tex]
[tex]n = 14[/tex]
Required
The sum of the series
This is calculated using:
[tex]S_n = \frac{n}{2}[a_1 + a_n][/tex]
Substitute 14 for n
[tex]S_{14} = \frac{14}{2}[a_1 + a_{14}][/tex]
[tex]S_{14} = 7[a_1 + a_{14}][/tex]
Substitute values for a1 and a14
[tex]S_{14} = 7[8 + 99][/tex]
[tex]S_{14} = 7*107[/tex]
[tex]S_{14} = 749[/tex]
The diameter of a circle is 15 ft. Find its circumference in terms of \piπ.
Answers
Answer:
47.1 ft
Step-by-step explanation:
dx[tex]\pi[/tex]=C
15x3.14=
47.1
Answer:
18
Step-by-step explanation:
Carlos is building a screen door. He height of the door is 1 foot more than twice the width. What is the width of the door if the height is 7 feet?
Answers
Answer:
The answer is 3 feet.
Step-by-step explanation:
First, the height is 7 right. Then take away 1 foot since is said 1 foot more than twice the width. Then divide by 2 meaning twice. Meaning 7-1=6 6/2=3. There you go! Hope these formulas helped!
Answer:
3 feet
Step-by-step explanation:
To relate the height and width of the door, we can write an equation, which is derived from what is given in the problem. If we define w as the width and h as the height, the words, "1 foot more than twice the width" can translate to:
2w + 1, and this is equal to the height, so
2w + 1 = h
Now, we are given the height is 7. We substitute 7 where the height, h, is.
2w + 1 = 7
We can subtract 1 from both sides and divide by 2 to isolate x:
2w + 1 = 7
-1 -1
2w = 6
w = 3 - the width is 3 feet
20 POINTS HELP FAST
What is the total surface area of the square pyramid below?
A square pyramid. The square base has side lengths of 6 meters. The triangular sides have a height of 8 meters.
132 m2
144 m2
160 m2
228 m2
Answers
Answer:
https://brainly.com/question/16576809
Step-by-step explanation:
Answer:
144 m2
Step-by-step explanation:
A seamstress charges 25$ for an initial visit and then 18$ per hour of work. Emma paid 88.00$ to make a dress. How long did it take to seamstress Emma's dress
Answers
3.5 hours of work
Write 1.5 : 6 as a whole number ratio in it's simplest from.
Answers
Answer: 1.5 : 6 = 1 : 4
Step-by-step explanation: Change values to whole numbers.
Convert any decimal numbers to integers by multiplying both sides by 101 = 10 to eliminate all, 1, decimal places.
We then have:
1.5 : 6 = 15 : 60
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 15 and 60 is 15
Divide both terms by the GCF, 15:
15 ÷ 15 = 1
60 ÷ 15 = 4
The ratio 15 : 60 can be reduced to lowest terms by dividing both terms by the GCF = 15 :
15 : 60 = 1 : 4
Therefore:
1.5 : 6 = 1 : 4
illmakeubrainlessforthecorrectanswer
Answers
Answer:
THE CORRECT ANSWER IS B- 73 FEETThe given condition in question will form a right angle triangle
and the length of sides of triangle are given 55ft, 48ft and missing one.
Now using pythagoras theorem,55²+48²= x²
x² = 3025 + 2304
x² = 5329
Taking square root of 5329 will give 73 ft!
Jennifer is picking a ball out of a box without looking. The probability of picking a green ball is 1/12.
Which option best describes the likelihood of Jennifer picking a green ball?
Answers
Answer:
it's a
Step-by-step explanation:
Paula dives into a swimming pool from a diving board 2 feet above the water's surface. She descends to a depth 7 feet below the diving board. How far is Paula from the surface of the water:
1. What integer represents Paula's starting height above the water?
2. What integer represents the total distance Paula descends?
3. Write an addition expression to represent Paula's distance below the water's surface
4. At the end of her dive, Paula is ____feet below the surface of the water
5. Yolanda owes her friend $15. She also earns $8 each week in allowance. Write and solve an addition equation to show how the total amount of money that Yolanda has will change if she pays her friend back this week.
Answers
1) The integer representing Paula's starting height above the water is 2.
2) The integer that represents the total distance Paula descends is 7.
3) An addition expression to represent Paula's distance below the water's surface is 2 + 3.
4) At the end of her dive, Paula is 5 feet below the surface of the water.
5) If Yolanda pays her friend back this week, she will owe her only $7.
What is an integer?An integer is a whole number. It can be positive, negative, or zero but without fractions.
Addition expressions combine two or more addends with the addition operand and equation mark (=) to determine the sum (or the result of the addition operation).
Paula:Height of diving board = 2 feet
Depth of descent below the diving board = 7 feet
Distance below the water's surface = 5 feet (7 - 2)
5 feet = 2 + 3
Yolanda:Debt to a friend = $15
Earnings per week = $8
Total amount after paying friend = 8 - 15
= -$7
Learn more about addition operations at https://brainly.com/question/4721701
#SPJ1
If a number cube numbered 1-6 is tossed 300 times about how many times would you expect to land on the number 3?
50
200
150
100
Answers
explanation: the average for 300 flips on a 6 numbered cube is 50
A teacher wrote this experssion on the board (-6)(2)+(-8÷4) what is the vaule of this expression
Answers
Answer:
-14
Step-by-step explanation:
(-12)+(-2)
You solve using Pemdas, doing the (-8/4) first, and then doing (-6)(2)
The answer is the two values added together.
what is 23^a x 23^b= Pls I need the answer
Answers
Answer:
23^(a+b)
Step-by-step explanation:
23^a x 23^b =23^(a+b)
PLEASE HELP MARKING BRAINLIST
Answers
Answer:
82?
Step-by-step explanation:
Sorry if wrong :> Please mark brainliest! Have a awesome day ^_^ You're a great person!!!!
three times four and four fifths
Answers
Answer:
the answer is 12.8
Step-by-step explanation:
Answer:
14 [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
3*4 [tex]\frac{4}{5}[/tex]
4 [tex]\frac{4}{5}[/tex] = [tex]\frac{24}{5}[/tex]
[tex]\frac{3}{1} * \frac{24}{5}[/tex]= [tex]\frac{72}{5}[/tex]
[tex]\frac{72}{5}[/tex] to a mixed number
[tex]\frac{72}{5}[/tex]= 14.4 =14
72-(5*14)=2
14 [tex]\frac{2}{5}[/tex]
At one school, the ratio of boys to girls in the seventh grade is 12:11. There are 66 girls in the seventh grade. How many boys are there?
Answers
Answer:68
Step-by-step explanation:
I guesses but most likely right lol
Help please I don’t get this problem
Answers
9514 1404 393
Answer:
920 square feet
Step-by-step explanation:
The surface area is the sum of the areas of the different surfaces of the solid. This solid has 5 surfaces: 2 triangular bases and 3 rectangular faces.
The area of a triangle is given by the formula ...
A = 1/2·bh . . . . . where b is the base of the triangle, and h is its height
The dimensions shown on the "front" of the figure tell you the triangle has a base of 15 ft and a height of 8 ft. Its area is ...
A = (1/2)(15 ft)(8 ft) = 60 ft²
__
The rectangular faces all have a width of 20 ft. So, the sum of their rectangular areas will be that width multiplied by the sum of their lengths. We call this the "lateral area" of the prism.
lateral area = (base perimeter) × (prism width)
= (8 ft + 15 ft + 17 ft) × (20 ft) = 800 ft²
The sum of the areas of the two base triangles and the lateral area is the total surface area of the figure:
total area = 2×60 ft² + 800 ft²
total area = 920 ft²
What is 15/7 an mixed number
Answers
[tex]2 \frac{1}{7} [/tex]
is the answer
Answer:
answer: 2 1/7
Hope this helps
What is the area, in square inches, of the isosceles trapezoid below?
Answers
Explanation-
14.2 - 6.4 = 7.8 (to get the length of the base without the top part)
7.8 • 5.2 = 40.56 (to find the area outside of our subtracted square that has the top part)
6.4 • 5.2 = 33.28 (to find the area of the inner square)
40.56 + 33.28 = 73.84 (adding together both parts to find the total area)
A = 73.84
2 friends want to equally share of a bag of chocolate cookies. What
fraction of the bag will will each friend get to eat?
Answers
Answer:
is this a joke question? it is very easy. one half or 1/2
Step-by-step explanation:
Without using the formula, work out the gradient of the graph shown.
Give your answer in its simplest form.
Answers
Why does Brainly need be to make these messages 20 characters long?
Which of these groups of relative frequencies will be best buy a pie chart
Answers
Answer: You are correct! Whatever adds up to 100% is the answer! :)
Please no files. I can give brainlest....
Answers
C. 4140
Thanks & im sorry ^^
Answer:
3960 degree is the answer
Step-by-step explanation:
180(n-2)
180(24-2)
180*22
3690
here,n =number of sides
What are the factors of -11x + 15 = -2/2 ?
a.y=(22+5)(2+3)
b.y= (2x - 5) (2 – 3)
c. y=(21 – 1) (2 – 15)
d.y= (2x + 1) (3 +15)
Answers
Answer:
c
Step-by-step explanation:
Answer the question please
Answers
explanation: the top square is 3x2=6 and the bottom one is 8x5=40
Distribute 6 ( 0.4x + 5)
Answers
Answer:
2.4x+30
Step-by-step explanation:
(6*0.4x)+(6*5)
2.4x+30
A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.
Hours Spent Studying Total Points Earned
45 40
30 35
90 75
60 65
105 90
65 50
90 90
80 80
55 45
75 65
a) Develop an estimated regression equation showing how total points earned is related to hours spent studying.
b) Test the significance of the model with alpha = .05.
c) Predict the total points earned by Mark Sweeney. He spent 78 hours studying.
d) Develop a 95% prediction interval for the total points earned by Mark Sweeney.
Answers
Answer:
ansber 5 good by. ............
 PLEASE HELPPPPP ME PLEASE I DONT KNOW WHAT TO DO ☹️#7
Answers
Given:
The function is:
[tex]f(x)=-2x+5[/tex]
To find:
The inverse of the given function, then draw the graphs of function and its inverse.
Solution:
We have,
[tex]f(x)=-2x+5[/tex]
Step 1: Substitute [tex]f(x)=y[/tex] .
[tex]y=-2x+5[/tex]
Step 2: Interchange x and y.
[tex]x=-2y+5[/tex]
Step 3: Isolate variable y.
[tex]2y=5-x[/tex]
[tex]y=\dfrac{5-x}{2}[/tex]
Step 4: Substitute [tex]y=g(x)[/tex].
[tex]g(x)=\dfrac{5-x}{2}[/tex]
Hence, the inverse of the given function is [tex]g(x)=\dfrac{5-x}{2}[/tex] and the graphs of these functions are shown below.
can u please help me
Answers
Answer:
(a) x=45°
(b) If AD was parallel to BC, <A would be equal to (180-<B)=90 (corresponding angles). Since <A≠90, we can see that AD and BC aren't parallel.
Step-by-step explanation:
(a)
Angles in a quadrilateral add to 360:
<A+<B+<C+<D=360
2x+90+x+3x=360
6x=270
x=45°
(b)
If AD was parallel to BC, <A would be equal to (180-<B)=90 (corresponding angles). Since <A≠90, we can see that AD and BC aren't parallel.
Answer: Step-by-step explanation:
3x+2x+x=360-90
6x=270
x=45
∠DAB=2x=90° and ∠ABC=90° ⇒ AD║BC
3.2468 rounded to the nearest tenth.
please help me
Answers
Answer:
3.2
Step-by-step explanation:
Find the number in the tenth place
2
and look one place to the right for the rounding digit
4
. Round up if this number is greater than or equal to
5
and round down if it is less than
5
.
Reflect triangle A in the line Y = 1
Answers
Answer:
(1,2); (4,4); (1,4)
Step-by-step explanation:
Just reflect it directly across the y axis starting at x=1.