Answer:
B
Step-by-step explanation:
if
x=3
y=2
-2xy²
3
2³=8
-2×3×8
= -48
d. If f¹(x+2) =X-1/x+1x not equal to 1 then find f(x) and f¹(4).
I assume by f¹, you actually mean f⁻¹ as in the inverse of f. I also assume you are asked to find f(x) (as in the inverse of f⁻¹) and f⁻¹(4).
Given that
[tex]f^{-1}(x+2) = \dfrac{x-1}{x+1}[/tex]
with x ≠ 1, we can find f⁻¹(x) by replacing x + 2 with x :
[tex]f^{-1}(x + 2) = \dfrac{x-1}{x+1} = \dfrac{(x+2) - 3}{(x + 2) - 1} \implies f^{-1}(x) = \dfrac{x-3}{x-1}[/tex]
Then when x = 4, we have
[tex]f^{-1}(4) = \dfrac{4-3}{4-1} = \dfrac13[/tex]
Of course, we also could have just substituted x = 2 into the definition of f⁻¹(x + 2) :
[tex]f^{-1}(4) = f^{-1}(2+2) = \dfrac{2-1}{2+1} = \dfrac13[/tex]
To find f(x), we fall back to the definition of an inverse function:
[tex]f^{-1}\left(f(x)\right) = x[/tex]
Then by definition of f⁻¹, we have
[tex]f^{-1}\left(f(x)\right) = \dfrac{f(x)-3}{f(x)-1} = x[/tex]
Solve for f :
[tex]f(x) - 3 = x (f(x) - 1)[/tex]
[tex]f(x) - 3 = x f(x) - x[/tex]
[tex]f(x) - x f(x) = 3 - x[/tex]
[tex](1 - x) f(x) = 3-x[/tex]
[tex]f(x) = \dfrac{3-x}{1-x} = \dfrac{x-1}{x-3}[/tex]
Find the area of the following sector. Round your answer to the nearest tenth.
The area of the sector is 188.9 km².
What is a sector?A sector is a plane figure enclosed by two radii and an arc between them.
To calculate the area of the sector, we use the formula below.
Formula:
A = ∅πr²/360................. Equation 1Where:
A = Area of a sectorr = Radius of the circle∅ = The angle sustained by the sector at the center of the circleFrom the diagram,
Given:
r = 19 km∅ = 60°π = 3.14Substitute these values into equation 1
A = 60×3.14×19²/360A = 188.9 km²Hence, the area of the sector is 188.9 km².
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Find the number of terms in the sequence.
-3, -3, -9, -15, ...,-9
Answer:
6
Step-by-step explanation:
I use the information I from my Nathan teacher
Could someone explain how to do this question?
Answer:
[tex]p\left( A|B\right) =0[/tex]
Step-by-step explanation:
Formula:
[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]
The only prime outcome is 3
Then
The set A = {3}
1 and 2 are the divisors of 2
Then
The set B = {1 , 2}
Therefore , p(A∩B) = 0
Also p(B) = 0.4+0.1 = 0.5
[tex]\Longrightarrow p\left( A|B\right) =\frac{0 }{0.5 }=0[/tex]
Question 1
What is the length of the diagonal from A to C of this rectangle? Round your answer to
the nearest tenth to a metre
Will mark Brainest!!
Answer: 17.2
Step-by-step explanation:
By the Pythagorean theorem,
[tex]10^{2}+14^{2}=(AC)^{2}\\\\(AC)^{2}=296\\\\AC=\sqrt{296} \approx \boxed{17.2}[/tex]
Brett draws the shape shown below.
He says the shape can be classified as a quadrilateral, parallelogram, rhombus, and square.
Is Brett correct? Explain.
The given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
What is a square?A square is a quadrilateral with all the sides equal and all the four sides are perpendicular to each other.
We know that it is a quadrilateral as a quadrilateral is having four sides and the sum of the angles is 180 degrees.
The given figure is a parallelogram as opposite sides of the figure are parallel and equal.
The given figure is a rhombus as all the sides are parallel and equal.
The given figure can not be a square as in the square all the four sides are perpendicular to each other.
Therefore given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
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What is 4:3 in the form of 1:n
Answer: 1:0.75
Step-by-step explanation:
Ratio 4 to 3 = 4:3
Simplified Ratio 4.00:3.00
Ratio in Form 1:n 1:0.75
Ratio in Form n:1 1.33:1
2(z + 5) + 5(z + 2) = 10 (z - 1)
Answer:
z = 10
Step-by-step explanation:
simplify to
2z + 10 + 5z + 10 = 10z-10
2+5z-10z=-10-10-10
-3z = -30
z = 10
give brainiest please!
hope this helps :)
Answer:
z = 10
Step-by-step explanation:
Distribute:
(2z + 5) + 5(z + 2) = 10(z - 1)
2z + 10 + 5(z + 2) = 10(z - 1)
and distribute again:
2z + 10 + 5(z + 2) = 10(z - 1)
2z + 10 + 5z +10 = 10(z - 1)
and add the 2 tens that are in bold.
2z + 10 + 5z +10 = 10(z - 1)
2x + 20 + 5z = 10(z-1)
Theres a lot more steps but just
comebine like terms
Distribute
Stubtract 20 from both sides
simplify
subtract 10z from both sides
simplfy
divide both sides by the same factor
and simplfy.
All the perfect squares and perfect cube numbers ranging from 1-500
help me pls i have 10 minutes left
Answer:
Rhombus
Step-by-step explanation:
Sides are parallel but have no right angles.
Answer:
parallelogram
Step-by-step explanation:
Opposite sides of the figure have the same slope (0 or 5/2), so are parallel. The product of the slopes is not -1, so the angles are not right angles. Adjacent sides are different lengths, so the figure is not a rhombus.
__
The figure is a parallelogram.
_____
Additional comment
The slope is the "rise" (change in y-coordinate) of the segment divided by its "run" (change in x-coordinate). The left and right sides have a rise of 7-2 = 5, and a run of 6-4 = 2 -0 = 2. Their slope is 5/2.
The top and bottom sides have a rise of 0, so a slope of 0.
When the product of the slopes of different segments is -1, those segments are perpendicular. The perpendicular to a horizontal line has "undefined" slope, so the product of the slopes would be (0)×(undefined). This is a special case of perpendicular lines where the product of slopes is not -1.
Find the value of x - Step by step answer please
Answer:
x = -2
Step-by-step explanation:
Given :
[tex]\frac{8}{x+1} = \frac{-16}{x+4}[/tex]
=============================================================
Cross multiplying the terms :
⇒ 8 (x + 4) = -16 (x + 1)
⇒ 8x + 32 = -16x - 16
⇒ 24x = -48
⇒ x = -2
the applicants for a soccer coaching position were asked how many years of coaching experience they had. here are the resuts 1,2,2,2,2,4,4,5,5,6,8,8,8,10
Answer:
Mean: 4.7
Mode: 2
Median: 4.5
Step-by-step explanation:
Which is the correct answer ?
Answer: D
Step-by-step explanation:
As the measure of the 75 degree angle is less than the measure of the 80 degree angle, rule out RS.
Also, the two triangles with the 80 degree angle are congruent, so PQ=QR.
This leavesc us with SP
Given that 1 ton is equal to 2,000 pounds, how many pounds does 5.9 tons equal?
59,000 pounds
11,800 pounds
1,180 pounds
5,900 pounds
Answer:
11,800 lb
Step-by-step explanation:
dnt worry i got my wayz :)
Answer:
11,800 lbs
Step-by-step explanation:
5.9x2,000=11,800
1712 is a odd or even number
1.)which of the following is the formula to find the volume of rectangular prism?
A. V =lwh
B. V = lw
C. 1/3(Bh)
D. 1/2(Bh)
2.)the volume of a cone is _____ the volume of a cylinder with the same base area (B) and height (h).
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Answer:
First answer:
A
Second answer:
I think A
Answer:
A and B
Step-by-step explanation:
1
the volume (V) of a rectangular prism is calculated as
V = lwh ( l is length, w is width, h is the height )
= Bh ( B is the area of the base )
2
the volume of a cone is [tex]\frac{1}{3}[/tex] the volume of a cylinder with the same base area (B) and height (h)
what is the solution to this equation ?
4(4x+1) = 3x - 4(6 - x) + 8
A. x = - 12/9
B. x = - 20/23
C. x = - 20/9
D. x = - 12/23
Answer:
x = -20/9
Step-by-step explanation:
First we need to distribute this equation 4(4x+1) = 3x-4(6-x)+8. After distributing we get 16x+4 = 3x-24+4x+8. Next we add like terms to get 16x+4 = 7x-16. Now subtract 7x on both sides to get 9x+4 = -16. Now subtract -4 on both sides to get 9x = -20. Now divide by 9 on both sides to get x= -20/9.
Hope that helps! :)
Solve the equation. 13x-5=1+11x
Answer:
x=3
13x-5=1+11x
(ADD 5 TO BOTH SIDES)
13x-5+5=1+11x+5
SIMPLIFY
13x=11x+6
SUBTRACT 11x FROM BOTH SIDES
13x-11x=11x+6-11x
SIMPLIFY
2x=6
DIVIDE BOTH SIDES BY 2
2x/2 = 6/2
SIMPLIFY TO GET FINAL ANSWER
x=3
A mother and daughter decided to add their ages together. The sum of their ages is 76. Six years ago, the mother was 3 times the age of her daughter. How old is the daughter now?
Answer: The answer will be 19
Answer: 23 years old
Step-by-step explanation:
PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS
Answer:
scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]
can you help me please?
prolly 4.36 just use the Pythagorean theorem
PLEASE HELP!!! EOC REVIEW!
From his eye, which stands 1.52 meters above the ground, Wyatt measures the angle of elevation to the top of a prominent skyscraper to be 28 degrees. If he is standing at a horizontal distance of 331 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
The height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper.
What is Trigonometric Ratio?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, h₀ = 1.52 m, angle of elevation = 28⁰
d = 331 m
Now, tan 28⁰ = h/d
h = d. tan 28⁰
h = 331 X 0.5317
h = 175.99 m
Total height = h + h₀
= 175.99 + 1.52
= 177.51 m
Thus, the height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper..
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Answer:
Step-by-step explanation:
The answer is 177.5 dont add the .1
PLEASE HELP! 50 POINTS! IF YOURE NOT GOING TO ACTUALLY ANSWER, PLEASE DON'T SAY ANYTHING.
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
There are 18 students on the debate club. How many ways can the club send 4 students to the next debate
There are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have the total number of students = 18
The number of ways the club send 4 students to the next debate is:
= C(18, 4)
[tex]= \rm \dfrac{18!}{4!(18-4)!}[/tex]
= 3060
Thus, there are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
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1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
catergorize the graph as linear decreasing, linear increasing, exponential growth or exponetnial decay
i cant help you with that bc there is no graph so...
The sum of negative eighteen and a number is eleven. What is the number?
Which equation could be used to solve the problem?
Answer:
-18 + x = 11
x = 29
Step-by-step explanation:
To solve this, you can use the formula of a + b = c
[tex]-18 + x = 11\\-18 = 18\\11 + 18 = 29\\x = 29[/tex]
Answer:
29
Step-by-step explanation:
Your equation can be -18+x=11. Since we don't know the number, we can use x. We are trying to find out a number that when it's added to -18, the answer will be 11.
Now, we solve the equation:
-18+x=11
x=11+18
x=29. Answer
To check this answer:
we can use our equation and substitute 29 for x.
-18+x=11
-18+(29)=11
11=11.
They are equal. Therfore, the answer is correct.
The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
Joey wants to buy a gym membership. He visits two gyms with two different fees. Gym A has a $40
sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month. How
many months will he have to belong to each before the costs are the same?
Answer:
2 months
Explanation:
50 - 40 = 10
25-20 = 5
10/5 = 2
The months for which Joey have to belong to each before the costs are the same are 2 months.
What is equation modelling?
Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.
Given is different fees structure of two gyms → Gym A has a $40 sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month.
Assume that the months for which Joey have to belong to each before the costs are the same be x.
Then -
For Gym A -
Total cost for x months = C[A] = 25x + 40
For Gym B -
Total cost for x months = C[B] = 20x + 50
For same cost -
C[A] = C[B]
25x + 40 = 20x + 50
25x - 20x = 50 - 40
5x = 10
x = 2
Therefore, the months for which Joey have to belong to each before the costs are the same are 2 months.
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What is the product of 3x(x²+4)?
Ox²+3x+4
O 3x³ +4
O 3x³ + 12x
O 3x² + 12x
Answer:
3x³ + 12x
Step-by-step explanation:
3x(x² + 4)
3x³ + 12x