Answers
The inverse of the function are respectively; f⁻¹(3) = 2 and f⁻¹(8) = 8.5
How to find the inverse of a Function?The formula to find the equation of this function using two coordinates is;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Using the first 2 coordinates, we have;
(y - 1)/(x + 1) = (3 - 1)/(2 + 1)
(y - 1)/(x + 1) = 2/3
3y - 3 = 2x + 2
3y = 2x + 5
y = ¹/₃(2x + 5)
Thus, the inverse is;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(3) = (3*3 - 5)/2
f⁻¹(3) = 2
Similarly;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(8) = (3*8 - 5)/2
f⁻¹(8) = 8.5
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Related Questions
Review the four points shown on the polar coordinate
system.
5ad6
B
C
76
27/3
4/3
2
3/2
N
4
50/3
A
6
D
11/6
Which point represents (-6.II) ?
Opoint A
Opoint B
Opoint C
Opoint D
Answers
The answer is Point B.
6.62607004081818181818181 X 10^-34
Answers
The solution to this is 6.62607e-34.
How to solve for exponentialsWe have the value is raised to the power of -34
We have to solve this using a calculator
This is similar to
[tex]6.62607004081818181818181*\frac{1}{10000000000000000000000000000000000}[/tex]
The number of zeros are 34
We would have 6.62607e-34 as the final solution.
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Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
Answers
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
Step-by-Step Solution:
In the Right Triangle formed to the extreme right, lets mark the angles as
∠1, ∠2 and ∠3.
Therefore, from the Figure :-
∠1 = 73°
∠2 = 90°
By Angle Sum Property :-
∠3 = 180 - (73 + 90)
∠3 = 180 - 163
=> ∠3 = 17°
The Angle which forms a Linear Pair with ∠3 is the Corresponding Angle of ∠r, and Corresponding Angles are Equal.
Therefore,
=> 180 - ∠3
= 180 - 17
=> 163°
Therefore, the Angle that forms the Linear Pair with ∠3 is 163°
This Angle is Corresponding to ∠r and hence they are Equal ie. ∠r = 163°
Hence, ∠r = 163°
need help with this question.
Answers
We have this equation:
[tex]\log(x) + \log(x + 99) = 2[/tex]
First, combine both logarithms using the multiplication property and simplify the expression.
[tex]\log[x(x + 99)] = 2[/tex]
[tex]\log[ {x}^{2} + 99x ] = 2[/tex]
Now, use the definition of logarithm to transform the equation.
[tex] {10}^{2} = {x}^{2} + 99x[/tex]
[tex] {x}^{2} + 99x - 100 = 0[/tex]
Finally, use the quadratic formula to solve the equation.
[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]
With this, we can say that the solution set is:
x = 1x = -100We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
Un constructor tiene un predio, por lo que está considerando que los terrenos sean rectangulares con un perímetro de 64 metros.
Answers
Based on the perimeter of the rectangle, and the adjustments to make the plot a square, the sides are 13m and 19m.
What are the sides of the plot?The perimeter is:
2(L + W) = 64
L + W = 32
The adjustment to make the plot a square would mean that both sides can be equal:
L + 3 = W - 3
L = W - 6
Substituting in the original formula gives:
L + W = 32
W - 6 + W = 32
2W = 38
W = 19 m
L would be:
L + W = 32
L + 19 = 32
L = 13m
The rest of the question is:
No obstante, para que los terrenos puedan ser cuadrados, se tendría que aumentar el ancho en 3 m y disminuir 3 m de largo. Entonces, ¿cuánto mediría el ancho y el largo del terreno rectangular?
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How did I do? for one of the questions I assumed you didnt take in count for the base so I just did lateral area
Answers
The area of the exposed surface is 442 square feet
What is a right square pyramid?A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.
Analysis:
The exposed surface is the area of the four triangles.
The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft
Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.
In conclusion, area of exposed surface is 442 square feet.
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!!!!!!!A dress pattern uses the scale 2 inches : 1 foot.if the model is 12 inches long how long is the dress!!!!!!pls Hurry
Answers
Using the scale ratio, the length of the dress is: 6 ft.
How to Apply Scale to Measurement?Given a scale for the dress pattern as, 2 inches : 1 foot, it means 2 inches of the model equals 1 foot of the actual dress.
Therefore, using the scale ratio, let x represent the length of the dress. We would have:
2/1 = 12/x
x = (12 × 1)/2
x = 6 ft.
The length of the dress is: 6 ft.
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I’m super confused please help me
Answers
Answer:
See below
Step-by-step explanation:
Look at it from the front and the side as shown in the diagram and draw what you would see:
22POINTS PLEAS ANsewer
Answers
Answer:
2y>-y+5
Step-by-step explanation:
because it has a eligible number at the right hand side
what is the lcd of 1/4 and 1/6
Answers
Answer:
12
Step-by-step explanation:
LCD of 1/4 and 1/6 is the least common denominator that is divisible by 4 and 6 at the same time and is the least.
So it the same to find least common multiple of 4 and 6 that is 12.
The answer is 12.
an a horizontal number line, positive numbers are____
On a vertical number line, negative numbers are_____
The number 0 is
Answers
Answer:
Positive number are located above 0 and negative numbers are located below 0 on a vertical number line
Answer:
On a horizontal number line, positive numbers are down from ANS= 0 to the left of 0✔ to the right of 0X up from 0.On a vertical number line, negative numbers are ✔ ANS=down from 0 to the left of 0to the right of 0up from 0.The number 0 is a negative numbera positive number✔Ans= neither positive nor negative.
Step-by-step explanation:
yw
What is the domain and range of this graph?
Answers
Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10
Answers
Hello,
Step-by-step explanation:
[tex]f(x) = ln(x) {}^{4} [/tex]
[tex](ln(u)') = \frac{u'}{u} [/tex]
[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]
[tex]f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} [/tex]
[tex]f(10) = ln(10) {}^{4} [/tex]
[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]
[tex]y = f'(a)(x - a) + f(a)[/tex]
which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answers
Answer:
d
Step-by-step explanation:
it's kinda hard to explain
if 3²× = 27 what is x
Answers
Answer:
3
Step-by-step explanation:
whenever solving for x, you have to work backwards…like so:
3 squared is 9
27 divided by nine is 3
x=3
To double check the answer, substitute the value that we just found into x
(3x3)x3=27
Answer:
[tex]x=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]3^{2x}=27[/tex]
Rewrite 27 in exponential form with base 3:
[tex]\implies 3^{2x}=3^3[/tex]
As both exponents have the same base,
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies 2x=3[/tex]
Divide both sides by 2:
[tex]\implies x=\dfrac{3}{2}[/tex]
Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run ?
Answers
Answer:
6 1/12 miles total
Step-by-step explanation:
3 1/4 = 13/4
2 5/6 = 17/6 to ADD fractions, you must have a common denominator
I will use 12 for these
13/4 = 39/12
17/6 = 34 /12
now you can add and simplify 39/12 + 34/12 = 73/12 = 6 1/12 miles
What is the volume of the pyramid shown
in the diagram?
12 cm³
15 cm³
21 cm³
45 cm³
Please help urgent
Answers
Answer:
volume = 15 cm^3
Step-by-step explanation:
Volume of pyramid = 1/3 base area * height
= 1/3 ( 3 x 3 ) * 5 = 15 cm^3
if f(x)=4x-x^2 find f(x+h)-f(x+h)/2h
Answers
Answer:
0
Step-by-step explanation:
numerator are the same the difference between same number or variable will be zero
The value of x. if (3x +3) : (9x + 7) is duplicate ratio of 3:5 is
Answers
Answer:
(3x + 3) (9x + 7) is the duplicate ratio of 3:5 . the value of x is 2.
What is the end behavior of the function f of x equals negative 2 times the cube root of x? as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0. as x → [infinity], f(x) → [infinity], and as x → –[infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity].
Answers
The end behavior of the function is as:
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The end behavior of a function will describe the behavior of the graph of the function at the "ends" of the x-axis.
How do determine the end behavior of a function?By determining the highest degree of the polynomial function. As the highest degree term will grow faster than the other terms as x gets very large or very small, its behavior will dominate the graph.
The graph of the function is f(x)=2∛x
the function leads to infinity so the end behavior of the function is
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
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You enter an elevator on the ground floor, which is labeled 0. You get off on the floor labeled +4. What is your location?
A four floors above the ground floor
B. four floors below the ground floor
C. four floors near the ground floor
D. four floors around the ground floor
Answers
Answer:
A. four floors above the ground floor
Step-by-step explanation:
if you start at 0 which is the ground floor and go up 4, that would be +4, since, in theory, going up would be considered positive. So the answer is A.
brainliest!!!!!!
Question 4(Multiple Choice Worth 1 points)
(06.05 MC)
Given the functions k(x) = 2x² - 5 and p(x) = x - 3, find (k. p)(x).
(kop)(x) = 2x² - 6x + 4
(kop)(x) = 2x² - 12x + 13
(kop)(x) = 2x² - 12x + 18
(kop)(x) = 2x² - 8
Answers
Answer:
2x² - 12x + 13
Step-by-step explanation:
Given following:
k(x) = 2x² - 5p(x) = x - 3Start solving from right to left across the function.
Steps:
k[p(x)]k[x - 3]2(x - 3)² - 52(x² - 6x + 9) - 52x² - 12x + 18 - 52x² - 12x + 13Answer:
2x² - 12x + 13
Step-by-step explanation:
Steps:
k[p(x)]
k[x - 3]
2(x - 3)² - 5
2(x² - 6x + 9) - 5
2x² - 12x + 18 - 5
2x² - 12x + 13 pls brainlest
Simplify, using the distributive
property.
5f + 16f = (5 +?)f=?f
Answers
Applying the distributive property, we would simplify the expression as: 5f + 16f = (5 + 16)f = 21f.
How to Apply the Distributive Property?The distributive property states that, ab + ac = (b + c)a.
Using the distributive property, we have:
5f + 16f
= (5 + 16)f
= 21f
Therefore, 5f + 16f is simplified as 21f.
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What is the simple interest that is missing from the table?
I
?
p
$375
r
2.2%
t
3 years
Answers
Answer:
SI =PXRXT/100
Step-by-step explanation:
THIS WOULD HELP YOU
Dilate ∆ABC about the origin using the scale factor n. Measure and compare the lengths of the sides of the dilated triangle, ∆A'B'C', with those of ∆DEF. Take a screenshot of your dilation, save it, and insert the image below the table.
Answers
The attached graph represents the image of the triangles
How to dilate the triangle?To do this, we make use of the following coordinates
A = (1, 0)
B = (5, 0)
C = (1, 6)
The lengths of the triangle are calculated using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]
[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]
[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]
Using the scale factor of 2, we have the image of the dilation to be:
D = (2, 0)
E = (10, 0)
F = (2, 12)
The lengths of these sides are
DE = 8
EF = 14.4
DF = 10
See attachment for the image of the triangles ABC and DEF
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134 A financial analyst believes that if interest rates decrease in a given period then the
probability that the stock market will go up is 0.08. The analyst further believes that
interest rate have a 0.40 chance of decreasing during the period in question. Given the
above information, what is the probability that the market will go up and interes: rate
will go down during the period in question?
Answers
The probability that the market will go up and interest rate will go down during the period in question is 0.03.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the market will go up and interest rate will go down = 0.08 X 0.40 = 0.03
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en un proyecto de innovacion, se deben determinar montos para varios gastos, Se gasta un 25% en equipamiento, un quinto en salarios, un 35% en publicidad, qudando un remanente de $1.500.000 para gastos varios
Answers
The amount that's was attributed to the project from the start based on the percentage is $7,500,000.
How to calculate the percentage?From the information given, the remaining percentage will be:
= 100% - (25% + 20% + 35%)
= 100% - 80%
= 20%
Let the total amount be x.
Therefore, 20% of x = 1,500,000
0.2x = 1,500,000
x = 1500000/0.2
x = 7500000
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A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!"
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items?
d. If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive?
e. Is it better to apply the 60% discount first or the 20% discount first?
Answers
Answer:
a the assumption is that after the 60% discount, the 20% will contribute to the old price, not the adjusted price
b this is incorrect because the 20% discount will be added on after the 60% discount has been used
c the 500 dollars would turn to 100 dollars
d 40
e it would be best to first apply the 60% coupon first over the 20% coupon
For what value of y does 125 =
(1/25)^y-1
Answers
Answer:
[tex] y = -\dfrac{1}{2} [/tex]
Step-by-step explanation:
I assume that y - 1 is an exponent, and the equation is
[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]
[tex] 5^3 = (5^{-2})^{y - 1} [/tex]
[tex] 5^3 = 5^{-2y + 2} [/tex]
[tex] -2y + 2 = 3 [/tex]
[tex] -2y = 1 [/tex]
[tex] y = -\dfrac{1}{2} [/tex]
The model for the height of the balloon captured from the ground with a balloon launcher can be represented by the function… how long will it take for the balloon to hit the ground after it’s launched?
Answers
Answer:
2 seconds
Step-by-step explanation:
To find the time it takes for the balloon to reach the ground, you need to set the equation equal to 0. This is because the ground technically has a height of 0.
h(t) = -16² + 128t <----- Original expression
0 = -16² + 128t <----- Plug 0 in for h(t)
16² = 128t <----- Add 16² to both sides
256 = 128t <----- Solve 16²
2 = t <----- Divide both sides by 128
Therefore, if t = 2, it will take the balloon 2 seconds to reach the ground.
==========================================================
Explanation:
The balloon is on the ground when the height is zero.
Replace h with 0 and solve for t.
[tex]h(t) = -16t^2 + 128t\\\\0 = -16t^2 + 128t\\\\-16t^2 + 128t = 0\\\\-16t(t - 8) = 0\\\\-16t = 0 \ \text{ or } \ t-8 = 0\\\\t = 0/(-16) \ \text{ or } \ t = 0+8\\\\t = 0 \ \text{ or } \ t = 8\\\\[/tex]
Ignore t = 0 because this is when the balloon is initially on the ground. In other words, the balloon starts on the ground, so it makes sense that t = 0 leads to h = 0.
The other solution t = 8 is what we're after. The balloon touches the ground again at the 8 second mark. This is the length of time the balloon is in the air.
A quick way to determine and confirm the answer is to use graphing software. Check out the diagram below. We have a parabola with x intercepts of 0 and 8.