Answers
For this case we must find the inverse of the following function:
[tex]f (x) = x ^ 2 + 7[/tex]
For this we follow the steps below:
Replace f(x) with y:
[tex]y = x ^ 2 + 7[/tex]
We exchange the variables:
[tex]x = y ^ 2 + 7[/tex]
We solve the equation for "y", that is, we clear "y":
[tex]y^ 2 + 7 = x[/tex]
We subtract 7 on both sides of the equation:
[tex]y ^ 2 = x-7[/tex]
We apply square root on both sides of the equation to eliminate the exponent:
[tex]y = \pm\sqrt {x-7}[/tex]
We change y by[tex]f ^ {- 1} (x):[/tex]
[tex]f ^ {- 1} (x) =\pm\sqrt {x-7}[/tex]
Answer;
Option A
Related Questions
what is the difference r+2/r+4-3/r+1
Answers
Answer:
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\frac{r+2}{r+4}-\frac{3}{r+1}[/tex]
We collect the least common multiple of the denominators to get:
[tex]\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}[/tex]
Expand the numerator:
[tex]\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Answer:
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
[tex]\frac{r+2}{r+4} - \frac{3}{r+1}[/tex]
To simplify the fractions we take common denominator
LCD is (r+4)(r+1)
we try to get same denominator on both fraction
multiply the first fraction by r+1 and second fraction by r+4
[tex]\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}[/tex]
(r+2)(r+1) becomes r^2 +3r+2
3(r+4) becomes 3r+12
[tex]\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}[/tex]
[tex]\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}[/tex]
combine like terms
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
y = 3x-5
6x + 3y= 15
Answers
y = 3x - 5
So substitute 3x-5 for y:
6x + 3(3x-5) = 15
Simplify:
6x + 9x - 15 = 15
15x - 15 = 15
x - 15 = 1
x = 16
THEN find y by plugging the value of x back into the first equation:
y = 3(16) - 5
y = 48 - 5
y = 43
Which expression is equal to (f - g)(x)?
Answers
ANSWER
[tex](f-g)(x) = 11 |x| - 32[/tex]
EXPLANATION
The functions are:
[tex]f(x) = 10 |x| + 26[/tex]
[tex]g(x) = 58 - |x| [/tex]
[tex](f-g)(x) = f(x) - g(x)[/tex]
Plug in the functions:
[tex](f-g)(x) = 10 |x| + 26 - (58 - |x| )[/tex]
[tex](f-g)(x) = 10 |x| + 26 - 58 + |x| [/tex]
[tex](f-g)(x) = 10 |x| + |x| + 26 - 58[/tex]
[tex](f-g)(x) = 11 |x| - 32[/tex]
The correct choice is A
Answer:
11|x|-32 hope this helps :D
Step-by-step explanation:
10|x|+26-(58-|x|)
10|x|+26-58+|x|
10|x|+|x|+26-58
11|x|-32
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. The events are not independent because the .
Answers
Answer:
The events are not independent because the product of their marginal probabilities is not equal to their joint probability
Step-by-step explanation:
Two events A and B are said to be independent with respect to probability if the product of their marginal probabilities is equal to their joint probability. In the question presented we have;
Pr(A) = 0.4
Pr(B) = 0.2
Pr(A n B) = 0.1
The product of their marginal probabilities is;
Pr(A) * Pr(B) = 0.4 * 0.2 = 0.08
Their joint probability is given as;
Pr(A n B) = 0.1
Clearly, Pr(A) * Pr(B) ≠ Pr(A n B) and thus the events are not independent.
Answer:
Product of P(A) and P(B) is not equal to P(A and B)
Step-by-step explanation:
it would be option C on E2020
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
Answers
22 feet is the answer I hope this helps
Answer:
Longest rope is 44 feet. 1 piece is 1/2(44)=22. 22+44=66
Step-by-step explanation:
15. Cody and his wife are purchasing a home. The cost
of the home is $145,900. They will be required to
pay a down payment of 5% of the purchase price
and to pay closing costs of 6% of the purchase
price. How much cash will they need for the down
payment and closing costs?
$16,049
$8,754
$7,295
$145,900
$161,949
Answers
They would need $16,049!
Price of the home is $145,900.
Percentage of the down payment is 5%
Subtract 5% from $145,900 = $138,605
That mean 5% of $145,900 is $7,295
Percentage of the closing cost is 6%.
Subtract 6% from $145,900 = 137,146
That mean 6% of 145,900 is $8,754
Add the down payment ($7,925) and closing cost ($8,745)
$16,049!
Mark me Brainliest!! Please!
they will need to pay $16,049
multiply $145,900 by 5%
multiply $145,900 by 6%
now add the totals to get $16,049
A ________ is a transformation of a figure by turning it around a given point.
A. dilation
B. reflection
C. rotation
D. translation
Answers
Answer:
Translation
Step-by-step explanation:
which is a prime number 7 63 33 27
Answers
The answer is seven
In a lottery game, a player picks six numbers from 1 to 20. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?
Answers
The expected value of the lottery game is -$0.62, suggesting a long-term average loss of 62 cents per game played. This value is calculated by considering the probability of each outcome and the associated gain or loss.
Explanation:In order to calculate the expected value of the lottery game, we must first understand what expected value truly represents. The expected value is essentially a description of the average outcome of a series of events if these events are repeated many times. It's a statistical concept used to predict the long-range behavior of random events, such as lottery games.
The expected value is calculated as the sum of all possible values each multiplied by the probability of its occurrence. For the lottery game described, there are two possible outcomes: a win of $30,000 or a loss of $1.
The probability of winning is extremely low. In this game, the player is attempting to choose the correct 6 numbers out of 20, which is a 1 in 38,760 chance. Whereas, the probability of losing is extremely high, practically 38,759 out of 38,760.
Thus, the Expected Value (E) can be calculated as follows: (probability of winning x winnings) + (probability of losing x loss). Plugging in our values gives us an expected value of -$0.62, rounded to the nearest cent. This figure indicates that if one were to play this game repeatedly, their average loss per game would be about 62 cents.
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Carly wins 1282 tickets at a arcade. For each group of 65 tickets she will receive a prize. Carl solve the problem 1282÷65 and determines that she has enough tickets right now for 19 prices. What is the least number of additional tickets that current needs to win to have enough tickets for a 20th prize?
Answers
18 is correct because 1300/65=20 1300-1282=18.
a penny is dropped from the top of the statue of liberty which is 305 feet tall . the height of the penny, (h,) at time (t) seconds can be repesented by the equation h(t) = -16t^2 + 305. After 4 seconds how much further does the penny need to travel before it hits the ground.
Answers
Answer: Penny need to travel 49 feet before it hits the ground.
Step-by-step explanation:
Since we have given that
[tex]h(t)=-16t^2+305[/tex]
Here, h denotes the height of the penny
t denotes the time in seconds.
Now, t = 4 seconds
So, the penny needs to travel before it hits the ground is given by
[tex]h(4)=-16(4)^2+305\\\\h(4)=-16\times 16+305\\\\h(4)=256-+305\\\\h(4)=49\ feet[/tex]
Hence, Penny need to travel 49 feet before it hits the ground.
After 4 seconds, the penny needs to travel an additional 49 feet before it hits the ground.
Explanation:The equation h(t) = -16t^2 + 305 represents the height of the penny at time t seconds. To find out how much further the penny needs to travel before it hits the ground after 4 seconds, we need to substitute t = 4 into the equation and solve for h.
h(4) = -16(4)^2 + 305
h(4) = -256 + 305
h(4) = 49 feet.
Therefore, the penny needs to travel an additional 49 feet before it hits the ground.
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The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?" Select all statements that correctly evaluate the report. The question is biased toward a Yes response.
A) The sample is biased because it does not represent the population.
B) The question is biased toward a No response.
C)The question is not biased.
D) The sample is not biased.
Answers
Answer:
the question is biased towards a no response, because they're asking participants "are you willing to spend the extra time to blah blah" obviously they're going to say no, and the second answer is the sample is not biased because they're not giving the consumers any reason to want the product they're selling.
Step-by-step explanation:
Answer:
The sample is not biased.
The question is biased toward a No response
Step-by-step explanation:
I took the test!
Mr. Ornelas needed to travel 400 miles to reach Chicago from his
home. He went to Chicago in 8 hours and came back at an average speed
of 52 miles per hour. Which part of his trip was faster and how do you
know?
Answers
Answer:
Driving to Chicago Driving Back
d=rt
400/8=r(8)/8
r=50 mph < r= 52 mph
Step-by-step explanation:
given f(x)=x+2 and h(x)=1/x-1 evaluate the following function at x=2
[h(x)]^2/f(x)
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Substitute x = 2 into both h(x) and f(x)
h(2) = [tex]\frac{1}{2-1}[/tex] = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
[tex]\frac{h(x)^2}{f(x)}[/tex] when x = 2
= [tex]\frac{1}{4}[/tex]
1/4 is the following function at x=2
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
Substituting x = 2 into both h(x) and f(x)
h(2) = 1(2-1) = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
h(x)²/f(x) when x = 2
=1/4
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Answer choices
F(x) or G(x)
for both A and B
Answers
Answer:
A. f(x)
B. g(x)
Step-by-step explanation:
The initial amount if the value of the function at x = 0.
Here that value is 2000 for the f(x) and 1000 for the g(x), so the f(x) has the higher initial value.
For the second part, by looking at the graph, you can determine that the function for the g(x) is 1000(3)^x (because the g(1) is 3000). Plugging in two for both the function, you get the f(x) = 8,000 and the g(x) = 9,000, so the g(x) has the greater amount of bacteria after two days.
Answer:
A. f(x)
B. g(x)
Step-by-step explanation:
The initial amount if the value of the function at x = 0.
Here that value is 2000 for the f(x) and 1000 for the g(x), so the f(x) has the higher initial value.
For the second part, by looking at the graph, you can determine that the function for the g(x) is 1000(3)^x (because the g(1) is 3000). Plugging in two for both the function, you get the f(x) = 8,000 and the g(x) = 9,000, so the g(x) has the greater amount of bacteria after two days.
Fraction less than 3/6
Answers
Well you shaded in two of the six, so it is 2/6.
2/6 would be less than 3/6
The ratio of red cars to blue cars in a parking lot was 5:3.if there were 40 red cars, how many blue cars were there??
Answers
Every 5 red cars there are 3 Blue cars,
So if there are 40 red cars,
there are going to be 24 Blue cars
40 divided by 5 which is 8
Multiply 3 × 8 which is ( 24 blue cars )
Answer:
24
Step-by-step explanation:
The 5 part of the ratio represents 40 cars, thus
40 ÷ 5 = 8 cars ← value of 1 part of the ratio
3 parts = 3 × 8 = 24 ← number of blue cars
What is the surface area of the cylinder in term of pi? Radius of 11 and height of 23
Answers
Answer:
The surface area of the cylinder is [tex]748\pi[/tex].
Step-by-step explanation:
Given : Radius of the cylinder is 11 unit and height of the cylinder is 23 unit.
To find : What is the surface area of the cylinder in term of pi?
Solution :
The formula of surface area of cylinder is
[tex]A=2 \pi r^2+2\pi rh[/tex]
Where, r is the radius of the cylinder r=11 unit.
h is the height of the cylinder h=23 unit.
Substitute the value in the formula,
[tex]A=2 \pi r^2+2\pi rh[/tex]
[tex]A=2\pi(r^2+rh)[/tex]
[tex]A=2\pi(11^2+11(23))[/tex]
[tex]A=2\pi(121+253)[/tex]
[tex]A=2\pi(374)[/tex]
[tex]A=748\pi[/tex]
Therefore, The surface area of the cylinder is [tex]748\pi[/tex].
In the figure, angle A measures 41° and angle D measures 32°. What is the measurement of angle E?
Answers
triangles angles always add up to 180° that being said,
41+32=73
180-73=107
angle e= 107°
hope this helps!
write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of the exponential function in the form
y = a[tex]b^{x}[/tex]
Substitute the given points into the equation and solve for a and b
Using (1, 7.5), then
7.5 = ab → (1)
Using (3, 16.875), then
16.875 = ab³ → (2)
Divide (2) by (1)
[tex]\frac{ab^3}{ab}[/tex] = [tex]\frac{16.875}{7.5}[/tex], hence
b² = 2.25 ( take the square root of both sides )
b = 1.5
Substitute b = 1.5 into (1)
1.5a = 7.5 ⇒ a = 5
The exponential function is y = 5[tex](1.5)^{x}[/tex]
If the mean of this distribution is 7, which could be the median? A) 1.5 B) 5 C) 8 D) 10
PLEASE HELP
Answers
Answer:
Tationia Rolon
Step-by-step explanation:
I think its C because the median is the number in the middle
Answer
6
Step-by-step explanation:
I got is correct on usatestprep
FIRST CORRECT ANSWER GETS BRAINLIEST!! (Please don't rush to answer, I've gotten a lot of incorrect answers from people who answer within the minute)
Which table shows a proportional relationship between x and y?
Answers
Answer:
B
Step-by-step explanation:
y is 3 times the x
Answer:
B
Step-by-step explanation
1/3=3
6/2=3
12/4= 3
15/5=3
Find the perimeter of the polygon ??
Answers
Answer:
35.5 m
Step-by-step explanation:
The perimeter of the polygon is the sum of all the sides of the polygon. The sides are given as
11 m , 5 m ,7.5 m , 5m and 7m
Hence the perimeter would be,
11+5+7.5+5+7
= 35.50 m
Find the missing side length. When the area is 12ft.
Answers
Answer: Since you are finding the missing side of a rectangle, it is 3.
Step-by-step explanation:
Area of rectangle= (l)(w)
The length of the missing side is 3ft.
What is Area ?Area is defined as the space occupied by a flat surface .
It is measured in square units.
It is given in the question
A rectangle with one side as 4ft.
Area of the rectangle = 12 sq.ft
Other side = ?
Area of a rectangle is given by Length * Breadth
Area = one side * other side
Substituting the values
12 = 4 * other side
other side = 3 ft.
Therefore the length of the missing side is 3ft.
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For your instagram ad, you will be paying 80 cents per click.You get 3,320 clicks what is your cost?
Answers
Answer:
I wont tell you the answer. But, the answer is 3320/.8
Step-by-step explanation:
Whats 3320/.80?
The total cost of clicks $2656.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Per click charges= 80 cents
Total clicks= 3320
So, charges for 3320 clicks
= 3320 x 80
= 265600 cents
= $2656
Hence, the total cost of clicks $2656.
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For the z-score for the 11.6 data point
Answers
Answer:
z = 1.3345
Step-by-step explanation:
The z-score for a given data point, say x, from a normal distribution with a given mean and population standard deviation is usually calculated using the formula;
[tex]z=\frac{x-mean}{standard deviation}[/tex]
The following information is available;
mean = 7
population standard deviation = 3.522
x = 11.7
We simply employ the above formula to determine the z-score associated with the 11.7 data point;
[tex]z=\frac{11.7-7}{3.522}=1.3345[/tex]
A fast food restaurant sells burgers, chicken sandwiches, and entree salads. If a customer buys a burger, the probability they buy french fries is 0.80. Fifty percent of customers who purchase a chicken sandwich also buy fries, but only 10% of those buying an entree salad buy fries. Of all customers, 65% buy a burger, 20% a chicken sandwich, the rest buy an entree salad.
What proportion of customers get a burger and fries?
Answers
Answer:
52%
Step-by-step explanation:
We are told that, of all customers 65% buy a burger. This would imply that the proportion of customers who buy a burger is 0.65.
Moreover, if a customer buys a burger, the probability they buy french fries is 0.80. This implies that the proportion of customers who buy fries given that they bought a burger is 0.8.
Therefore, the proportion of customers who get a burger and fries is simply the product of the two probabilities;
= 0.65*0.8
= 0.52
Therefore, 52% of all customers get a burger and fries
To the nearest hundred what is the value of X
Answers
Answer:
41.51
Step-by-step explanation:
We can find the value of x using the trigonometry identify.
Cos (41) = x/55
x = 55cos (41)
x = 41.51
ANSWER
[tex]x = 41.51[/tex]
EXPLANATION
The given triangle has a right angle.
We were given an acute angle that measures 41°
The hypotenuse of the given right triangle is 55.
Since x is adjacent to the given angle and we also know the hypotenuse, we use the cosine ratio to find x.
[tex] \cos(41 \degree) = \frac{x}{55} [/tex]
Therefore
[tex]x = 55 \cos(41 \degree) [/tex]
[tex]x = 41.509[/tex]
We round to the nearest hundredth to obtain,
[tex]x = 41.51[/tex]
Can someone help me on 8,12 please
Answers
Step-by-step explanation:
8.
[tex]\triangle CHF\sim\triangle YWS\\\\\angle C\cong\angle Y\\\angle H\cong\angle W\\\angle F\cong\angle S\\\\\dfrac{CH}{YW}=\dfrac{HF}{WS}=\dfrac{CF}{YS}[/tex]
Although it does not look like the picture.
From the picture ∠F ≅ ∠Y...
We must stick to the correct writing:
Δ → Δ
C → Y
H → W
F → S
12.
ΔMLK and ΔYWZ are not similar because they have different angles (different shape).
A triangle has angles measuring 15 degrees and 45 degrees what is the measure of the 3rd triangle’s 3rd angle?
Answers
Answer:
60
Step-by-step explanation:
15+45-180
120-180
60
Side 3=60
Answer:
120
Step-by-step explanation:
15+45=60
180-60=120