Answer: [tex]f^{-1} (x)=x^{2} -7[/tex]
Step-by-step explanation:
To find the inverse of a function replace f(x) with x and the original x with y
[tex]f(x)=\sqrt{x+7} \\x=\sqrt{y+7}[/tex]
Now we can solve for y
Square both sides so we can cancel out the root
[tex]x=\sqrt{y+7}\\x^{2} =\sqrt{y+7}^{2} \\x^{2} =y+7[/tex]
Now subtract 7 from both sides
[tex]x^{2} =y+7\\x^{2} -7=y+7-7\\x^{2} -7=y[/tex]
Now replace y with the inverse of f(x), [tex]f^{-1} (x)[/tex]
f⁻¹=x²+7
Solution:In order to find the inverse of a function, we should first replace f(x) with y, then switch x and y places, like so:y=√x+7x=√y+7Now, solve the equation for y.Square both sides in order to get rid of the square root:x²+7=yy=x²+7And finally, replace y with f⁻¹:f⁻¹=x²+7Also, inverse functions do the opposite thing in the opposite order.So if we have f(x)=x+7, the inverse function is: f⁻¹=x-7Hope it helps.
Do comment if you have any query.
write the inequality from the given number line.
Answer:
[tex]3 \leqslant - 3[/tex]
HELP / 100 POINTS
This shape has _______ faces.
This shape has 5 vertices.
This shape has 8 edges.
Answer:
5 faces
Step-by-step explanation:
A traingular prism has 5 faces. The square on the bottom and the four traingles that make up the sides.
hope this helps :)
Answer:
5
8
5
step by step
Love your pfp
The table below represents the scores of ten students in Ms. Williams’s class on a math and science test.
Answer: the answer is A or the 1st one
Step-by-step explanation:
Answer:
the answer is the frist one
Step-by-step explanation:
Part A
The distance that Eric can travel by driving to work can be represented by a linear equation because he sets his cruise control and is moving at a constant rate. He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.
What is the linear equation that can be used to find the distance that Eric travels each day? In the equations d = distance traveled, r = rate and t = time taken.
A. d = rt
B. d = t/r
C. d = r/t
D. d = r + t
E. d = r/75
Part B
What is the total distance that Eric travels each day?
A. 37.5 miles
B. 75 miles
C. 112.5 miles
D. 150 miles
E. 187.5 miles
WILL GIVE BRAINLIEST AND 40 POINTS
Answer:
Step-by-step explanation:
There's a saying to this kind of equation: Rate + Time = Distance and B best fits the saying, so B must be right (Don't quote me on that, it may be wrong)
the linear equation that can be used to find the distance that Eric travels each day is A. d = rt & the total distance that Eric travels each day is C. 112.5 miles.
What is speed?Speed is measured as distance moved over time.
here, given that,
He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.
so, the linear equation that can be used to find the distance that Eric travels each day is A. d = rt
i.e. d= 75*1.5
=112.5
& the total distance that Eric travels each day is C. 112.5 miles.
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Subtract. Write the answer as a fraction simplified to lowest terms.
41/40 - 3/8 =
Hey there!
41/40 - 3/8
= 41/40 - 3 × 5 / 8 × 5
= 41/40 - 15/40
= 41 - 15 / 40 - 0
= 26 / 40
= 26 ÷ 2 / 40 ÷ 2
= 13 / 20
Therefore, your answer is: 13/20
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help !
∆ABC is similar to ∆DEF. The measure of AB = 6, the measure of DE = 18, the measure of BC = 12, and the measure of DF = 15.
Find the measures of AC and EF.
AC =
_______________
EF =
[tex] \frac{ab}{de} = \frac{bc}{ef} = \frac{ac}{df} [/tex]=k
[tex] \frac{6}{18} = \frac{12}{ef} [/tex]
[tex]ef = 36[/tex]
from this[tex] \frac{12}{36} = \frac{ac}{15} [/tex]
[tex]ac = 5[/tex]
[tex] \frac{6}{18} = \frac{12}{36} = \frac{5}{15} = \frac{1}{3} [/tex]
I hope it helps
Using substitution, what is the solution for the system of equations below?
Hey there!
Substitute x = 2 to y = 3x - 1
=> y = 3(2) -1
=> y = 6 - 1
=> y = 5
x = 2,y = 5
Find the volume of the specified cone. Use 3.14 for , and round your answer to the nearest whole numbe
Diameter = 3 cm, Height = 7 cm
a 44 cu, cm
b. 66 cu, cm
c. 99 cu, cm
d 16 cu, cm
Answer:
Your answer is D 16 cu, cm
Step-by-step explanation:
A researcher is studying the relationship between stress and diet among college students. The researcher recruits students by sending out an e-mail blast, and then includes in the sample the first 100 male and 100 female students who volunteer to participate. What type of sampling did the researcher use
Using sampling concepts, it is found that convenient sampling was used by the researcher to find the volunteers to participate.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, the first 100 male and first 100 female students sampled are the ones who volunteer to participate, and volunteering is associated with convenient sampling.
More can be learned about sampling concepts at https://brainly.com/question/25122507
In an arithmetic sequence of numbers a1 = -4 and a6 = 46. Which of the following is the value of a12?
Answer:
a₁₂ = 106
Step-by-step explanation:
Given
a₁ (first term) = -4a₆ = 46Formula for nth term
aₙ = a₁ + (n - 1)dUsing that to expand a₆ and find d
a₆ = a₁ + (n - 1) d46 = -4 + (6 - 1)d50 = 5dd = 10Finding a₁₂
a₁₂ = a₁ + 11da₁₂ = -4 + 11(10)a₁₂ = 110 - 4a₁₂ = 106Answer:
[tex]a_{12}=106[/tex]
Step-by-step explanation:
Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
[tex]a_1=-4[/tex][tex]a_6=16[/tex]To find the common difference (d), substitute the given values into the general formula and solve:
[tex]\begin{aligned}\implies a_6=(-4)+(6-1)d & =46\\ 5d-4 & =46\\ 5d & = 50\\ d & =10\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}[/tex]
To find the 12th term, substitute n = 12 into the equation:
[tex]\implies a_{12}=10(12)-14=106[/tex]
Natalie Albert deposited checks totaling $1,735,97 into her savings account. She withdrew $100.00 while
depositing some coins. If her total deposit was $1,668.71, how much did Natalie deposit in coins?
Natalie Albert deposited checks totaling $1,735,97 into her savings account, she withdrew $100.00 while depositing some coins. If her total deposit was $1,668.71 then Natalie deposited $32.74 in coins.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the amount Natalie deposited in coins "x".
We know that her total deposit was $1,668.71,
so we can write an equation:
1,735.97 - 100.00 + x = 1,668.71
Simplifying, we get:
1,635.97 + x = 1,668.71
Subtracting 1,635.97 from both sides, we get:
x = 32.74
Therefore, Natalie deposited $32.74 in coins.
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The manufacturer of color televisions can sell 1900 sets to his dealers at $575 each. If the price is $470, he can sell 2600 sets. The total cost of producing x television sets is C(x)=3300+608x−0.09x^2. Assuming the demand function is linear, find the price per set that will maximize profit. Round your answer to the nearest cent, if necessary.
Answer:
$545
Step-by-step explanation:
Finding the price that maximizes profit requires several steps. We need the demand function that tells quantity sold in terms of selling price. With this, we can express the cost and revenue functions in terms of selling price. The profit will be the difference between revenue and cost.
__
demandThe demand (q) is said to be a linear function of price (p). The equation for that can be written ...
q(p) = (q2 -q1)/(p2 -p1)(p -p1) +q1 . . . . . for two points (p1, q1) and (p2, q2)
Using the given demand points, this can be ...
q(p) = (1900 -2600)/(575 -470)(p -470) +2600
q(p) = -20/3(p -470) +2600
q(p) = -20/3p +5733 1/3
__
costThe cost function in terms of selling price can be found by substituting the q(p) equation for x in c(x). For the purpose of finding the maximum profit, we only need the marginal cost function:
c(q(p))' = c'(q(p))·q'(p) = (608 -0.18(q(p)))·(-20/3) = (608 -0.18(-20/3p +5733 1/3))(-20/3)
c'(p) = -8p +2826 2/3
__
revenueAs with cost, the function we need for finding the maximum profit is the marginal revenue function. Revenue is the product of price and demand, so the marginal revenue is ...
r(p) = p·q(p)
r'(p) = q(p) +p·q'(p) = (-20/3p +5733 1/3) +p(-20/3)
r'(p) = -40/3p +5733 1/3
__
maximum profitThe maximum profit is found where the marginal profit is zero. In turn, that is found where the difference between marginal revenue and marginal cost is zero:
P = R -C
P'(p) = 0 = r'(p) -c'(p) = (-40/3p +5733 1/3) -(-8p +2826 2/3)
0 = -16/3p +2906 2/3
16p = 8720 . . . . . multiply by 3, add 16p
p = 545 . . . . . . . price for maximum profit
The price per set that maximizes profit is $545.00.
Sophia goes to an icecream shop to get a medium ice cream that costs $4.50, Sophia only has $6.40 and toppings are $0.75 each. Write an inequality to find how many toppings Sophia can get .
Answer:
x ≤ 2
Step-by-step explanation:
4.5 = medium ice cream
0.75x = toppings, x = amount of toppings
Sophia has $6.4, so 4.5+0.75x has to be less or equal to that.
4.5 + 0.75x ≤ 6.4, solve
0.75x ≤ 1.9
x ≤ 2 8/15
BUT you cannot get half a topping or a fraction of a topping,
so, x ≤ 2 toppings.
Sophia can get 2 or less toppings.
Which statement describes the transformation of figure 2 into figure 3?
Answer:
2 reflection across the y axis
(-x^2 -2) + (2x^2 + -1)
Answer:36
Step-by-step explanation:
x2 - 10x + 25 = 0 2x2 - 2x - 5 = 0 x2 - 16x = 36. This problem has been solved!
need help really please somebody
Answer:
70/100 ; 3/10 ; 50/100
Step-by-step explanation:
You need to multiply numbers to make them equivalent.
1st Question:
7/10 has to multiply by 10/10 because the denominator of the other one is 100 and 10 x 10 is 100.
7 x 10 = 70
70/100 shall be your answer.
2nd Question:
This time you need to find your starting point.
A way to do this is to divide/simplify the fraction in order to make it equivalent.
You need to divide by 10 because your quotient and denominator at your starting point is 10 and 100/10 is 10.
30 divided by 10 is 3
Your Answer for this one is: 3/10
3rd Question:
Same thing as the 1st one.
Multiply by 10.
5 x 10 = 50
50/100 is your answer.
what is the reciporcal of 7/6
Answer:
6/7
Step-by-step explanation:
you juts switch the top and bottom
Brainleist please
i need serious help lol
Answer:
A, C, can't see full answers
Step-by-step explanation:
a. 15/3=5 plus 10 is 15
true or false in order to find the surface area of a cube you could find the area of one face and multiply by six
Answer:
True
Step-by-step explanation:
The surface area of a cube is the total area on each side of the cube. SInce there are 6 sides of a cube, the surface area is equal to six times the area of one of the sides, because they are all the same.
PLEASE HELP i realy don’t understand this at all
Check the picture below, recall that the radius of a circle is always the same length in the circle.
50 PTS I WILL MARK BRAINLIEST PLS HELP! A book store manager took several random surveys of customers to determine which book genre they purchased most frequently. This table shows the average of each survey.
Based on the data shown in the table, which conclusions can be made about the frequency that customers purchase a genre?
Select each correct answer.
On average, 1 out of 6 customers purchase fantasy books most frequently.
On average, 24% of the customers purchase autobiographies most frequently.
On average, 22% of the customers purchase romance books most frequently.
On average, 2 out of 10 customers, purchase health and wellness books most frequently.
Book Genre Average of Surveys
Autobiographies 24
Mystery 11
Romance 22
Health and Wellness 18
Fantasy 15
NEED HELP WITH THIS QUESTION QUICK!!!
Answer:
56 degrees
90-34=56
Right-angle triangle, so the 2 angles should add to 90 to make 180 degrees
Hope this helps!
The sum of two number is −16. One number is 20 less than the other. Find the numbers.
Answer:
-50 is your answer it is really easy just try to get -50
fifty million of 94 million households watched the last episode of a popular television show. What percentage of households were not watching the show?
The percentage of households that were not watching the show were 46.81%.
Step-by-step explanation:In this case, we need to find the percentage of households that don´t watch the show. First, we need to know how much households don´t watch the show, this is:
[tex]94,000,000-50,000,000=44,000,000[/tex]
So, the households that were not watching the show were 44 million.
Now we can calculate the percentage, to find a percentage we use a division and to introduce the percentage units we multiply by 100.
[tex]\frac{44,000,000}{94,000,000}[/tex] × [tex]100=46.81[/tex]The percentage of households that were not watching the show were 46.81%.
Explain why a balance of less than -$10 represents a debt greater than $10.
Answer:
tbh I'm in 6 grade-_- and it's maybe higher than 10$
A tabletop in the shape of a trapezoid has an area of 7,367 square centimeters. Its longer base measures
127 centimeters, and the shorter base is 85 centimeters. What is the height?
The height of the tabletop is
centimeters.
Answer:
69.5 cm
Step-by-step explanation:
Area trapezoid = 1/2 (b1+b2) * h = 7367
1/2(127+85) h = 7367 h=
The base of a prism are right triangles with leg lengths of 7 inches and 5 inches. the prism height is 12 inches. what is the volume of the prism?
A 105
B 203
C 210
D 420 [but we know for certain d is wrong]
Answer:
The volume formula is length x width x height. 7x5x12=420 cubic inches
Step-by-step explanation:
find the area sector of AOB
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=12\\ \theta = 70 \end{cases}\implies \begin{array}{llll} A=\cfrac{(70)\pi (12)^2}{360}\implies A=28\pi \\\\\\ A\approx 87.96~cm^2 \end{array}[/tex]
HELP!
You own a square plot of land and you want to determine its surface area. You know that one side of land measures 10 longer than what the appraisers estimated, but you lost the paperwork with the information. Write an expression to represent the area of your land.
What is the area of the property if x = 12?
The area of the property is the product of its dimensions, and the expression for the area is (x + 10)²
How to determine the expression for area?The area of the land is the product of its dimensions.
Let the length and the width of the land be x.
So, the area measured by the appraisal is:
Area = x²
One side of the land is 10 more than the measured length.
So, we have:
Area = (x + 10)²
Substitute 12 for x
Area = (12 + 10)²
Evaluate
Area = 484
Hence, the area of the property is 484
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Write an equation in slope-intercept form for the line shown.
The equation in slope-intercept form is _______ .
To write the equation in slope-intercept form
⇒ must know what is the slope-intercept form
⇒ [tex]y = mx + b[/tex]
m: the value of the slopeb: the value of the y-interceptLet's find the slope first:
⇒ must know the slope's formula
⇒ [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) --> one point on the line(x2, y2) --> another point on the line that is not (x1, y1)Let's choose (0,1) and (-3,0)Now let's find the slope⇒ [tex]\frac{0-1}{-3-0}=\frac{-1}{-3} =\frac{1}{3}[/tex]
Now let's find the y-intercept
⇒ which occurs where the x-value of the coordinate is 0
⇒ that point is (0,1)
⇒ thus b = 1
Now let's set up the equation in slope-intercept form
[tex]y = \frac{1}{3} x+1[/tex] <-- Answer
Hope that helps!
Answer:
y-1/3x+1:
hope it helped