Answer:
To find the inverse of:
[tex]f (x)=\dfrac{4}{x-2}-1[/tex]
Set the function to y:
[tex]\implies y=\dfrac{4}{x-2}-1[/tex]
Rearrange to make x the subject:
[tex]\implies y+1=\dfrac{4}{x-2}[/tex]
[tex]\implies (y+1)(x-2)=4[/tex]
[tex]\implies xy-2y+x-2=4[/tex]
[tex]\implies xy+x=2y+6[/tex]
[tex]\implies x(y+1)=2y+6[/tex]
[tex]\implies x=\dfrac{2y+6}{y+1}[/tex]
Swap x and y:
[tex]\implies y=\dfrac{2x+6}{x+1}[/tex]
Change y to the inverse of the function sign:
[tex]\implies f[/tex][tex]\:^{-1}(x)=\dfrac{2x+6}{x+1}[/tex]
Rewrite g(x) as a fraction:
[tex]g(x)=\dfrac{3}{x+2}-2[/tex]
[tex]\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2(x+2)}{x+2}[/tex]
[tex]\implies g(x)=\dfrac{3-2x-4}{x+2}[/tex]
[tex]\implies g(x)=-\dfrac{2x+1}{x+2}[/tex]
Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other
Which of the following is a geometric series? 40 50 60 70 40 42 44 46 40 80 40 120 40 20 10 5
The given series 40 + 20 + 10 + 5 is a geometric series.
What is the geometric series?The geometric series the ratio of consecutive terms is equal and the ratio is called the common ratio of the geometric series.
Let us find the ratio of consecutive terms of each of the given series.
For the series 40 + 50 + 60 + 70
50/40 = 5/4
60/50 = 6/5
Since, 5/4 ≠ 6/5 hence, it is not a geometric series.
For the series 40 + 42 + 44 + 46
42/40 = 21/10
44/42 = 22/21
Since, 21/10 ≠ 22/21 hence, it is not a geometric series.
For the series 40 + 80 + 40 + 120
80/40 = 2
40/80 = 1/2
Since, 2 ≠ 1/2 hence, it is not a geometric series.
For the series 40 + 20 + 10 + 5
20/40 = 1/2
10/20 = 1/2
Since, 1/2 = 1/2 hence, it is a geometric series.
Therefore, D is the correct option.
To learn more about the geometric series visit:
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In a class of 90 students, the ratio of boys and girls is 4:5 Find the number of boys and girls
Step-by-step explanation:
Number of students in class = 90
ratio of boys and girls = 4:5
sum of ratios = 9
Number of boys = 4/9 × 90
= 360/9
= 40
Number of girls = 5/9 × 90
= 450/9
= 50
Hope it helpz~
Complete the statement using <, >, or =.
36% of 150 ____ 27% of 200
Answer: =
Step-by-step explanation: 54 =54
3/100 ×150=54
2/100 ×200=54
Easy answer!! Simplify
Answer:
\frac{5}{6}\quad \left(\mathrm{Decimal :0.83333
Step-by-step explanation:
[tex]\bold{Heya!}[/tex]
[tex]\sf{\sqrt\frac{23}{36}[/tex]
[tex]\sf{Apply \: radical \: rule:} \: \sqrt{\frac{a}{b}[/tex] [tex]\sf{= \sqrt{\frac{\sqrt{a}}{b}[/tex] [tex]\sf{a \geq 0, b \leq 0[/tex]
[tex]\sf{\sqrt{\frac{23}{\sqrt{36}}[/tex]
[tex]\sf{\sqrt{36} = 6}[/tex]
[tex]\sf{= {\frac{\sqrt{23}}{6}[/tex]
Hopefully This Helps ! ~
#LearnWithBrainly
[tex]\underline{Answer :}[/tex]
Jaceysan ~
After a dilation with center (0,0) the image of DB is D’B’ if DB=6 and D’B’=2 the scale factor of dilation is what ?
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corrresponding sides. image to original.
scale factor = [tex]\frac{D'B'}{DB}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Which answer is correct?
Answer:
D and B
Step-by-step explanation:
Because D is saying the negative number is less than, we know it is true.
Because B states that -7.1 is more, it is correct. -7.1 is closer to zero than -7.8, making it a larger number.
Answer:
B. -7.1 > -7.8
D. -6[tex]\frac{3}{5}[/tex] < 6[tex]\frac{2}{5}[/tex]
both B. and D. are correct!
The data set shows the number of cats owned by the members of Taylor's basketball team.
2,0, 1, 2, 4, 1,4,0,3,2
The value that could best measure the center of this data is
Answer:
Mean
Step-by-step explanation:
2,0, 1, 2, 4, 1,4,0,3,2
in ascending order we have
0 0 1 1 2 2 2 3 4 4
There are no outliers here so I would say the mean.
Actual mean = 1.9
Please help!!! I dont understand this
Answer:
x=120
Step-by-step explanation:
so if you look at a angle ruler you will see it's 120 so now if you look one up and put it to 120 it would match i wouldn't know how accurate it is but from what i know its 120
4. What is the height of a triangular sail whose base is 4 meters and area is 20 square meters?
Answer:
pa branliest
Step-by-step explanation:
The height of a triangle is 4 inches more than twice the length of the base
5 0
·
5 –3
= how do i do this
Michelle is interested in knowing how often girls in her class at school use their cell phones to instant message their friends.
Which of the following methods could Michelle use to conduct a simple random sample to answer her question?
A. Give the survey to the first fifty girls on a list of all the students in her class.
B. Post her survey on the Internet and ask only girls to respond.
C. Write the name of each girl in her class on a card and then draw 10 cards from a hat.
D. Identify which homeroom each girl in her class is in and then choosing a sample from each homeroom based on the number of girls in the homeroom.
Answer:
it is NOT d
Step-by-step explanation:
I did it and got it wrong
NOT D
What is the area, in square meters, of the trapezoid below?
Step-by-step explanation:
A = 1/2*h(base + base)
Plugging everything in gives you:
1/2*(6.8)(7.5 + 13.7 + 5.3)
((13.7 + 5.3) gives you the bottom base)
First, adding inside the parentheses:
1/2*(6.8)(26.5)
Multiply 6.8 by 26.5(h times bases):
1/2*(180.2)
Lastly, multiply:
A= 90.1 m^2
Hope this helps :)
Find the value of
46
83
An outside angle equals the sum of the two opposite inside angles.
x = 83 + 46 = 129
What is the area of this trapezoid?
168 ft
221 ft
248 ft
261 ft
Answer:
248
Step-by-step explanation:
18-13 =5
16*5=80/2 because it is a triangle = 40
40+16*13=
40+208+
248
Answer:
248
Step-by-step explanation:
k12 :)
the point ( 8 , 5 ) lies on a line with a slope of 1/4 write the equation of the line
Answer:
[tex]y=\frac{1}{4} x+3[/tex]
Step-by-step explanation:
[tex]y-5=\frac{1}{4} (x-8)[/tex]
[tex]y=\frac{1}{4} x-2+5[/tex]
[tex]y=\frac{1}{4} x+3[/tex]
Hope this helps
Answer:
y = [tex]\frac{1}{4}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (8, 5 ) into the partial equation
5 = 2 + c ⇒ c = 5 - 2 = 3
y = [tex]\frac{1}{4}[/tex] x + 3 ← equation of line
If the dimensions of a rectangular prism are 3 cm , 4 cm, and 10 cm, then it’s surface area is
Answer:
As Per Provided Information
Dimensions of rectangle prism are 3 cm , 4 cm and 10 cm .
We have been asked to determine it's surface area.
[tex] \underline{\boxed{\bf \: Surface \: Area_{(Rectangular \: Prism)} = 2(lw + hl + hw}}[/tex]
where,
w denote width
h denote height
l denote length
[tex] \longrightarrow\sf \: Surface \: Area_{(Rectangular \: Prism)} = \: 2(3 \times 4 + 4 \times 10 + 10 \times 3) \\ \\ \\ \longrightarrow\sf \: Surface \: Area_{(Rectangular \: Prism)} = \:2(12 + 40 + 30) \\ \\ \\ \longrightarrow\sf \: Surface \: Area_{(Rectangular \: Prism)} = \:2(82) \\ \\ \\ \longrightarrow\sf \: Surface \: Area_{(Rectangular \: Prism)} = \:164 \: {cm}^{2} [/tex]
Therefore,
Surface area of rectangular prism is 164 cm².Answer:
Surface area of rectangular prism is 164cm²
Step-by-step explanation:
Given :-
Dimensions of rectangular prism is 3cm , 4cm, and 10cmTo find:-
Surface area of rectangular prismSolution:-
Surface area of rectangular prism :-
2(lb + bh + hl)
putting the known values ,
Surface Area = 2(3×4+4×10+10×3) cm²
Surface area = 2(12+40+30) cm³
Surface area = 164cm²
Round your answers to one decimal place, if necessary.
Find the mean and median of these data: 2,7, 13, 15, 19, 21.
The mean is
The median is
Answer:
the mean is 12.83333333333 ans so many more 3's
the median is 14 because the two middle numbers are 13+15=28 and divided by 2 is 14
Step-by-step explanation:
if it is right, please can i have the brainliest
13 - (19,500 - (672 x 29)] =
Answer:
1
Step-by-step explanation:
im know it ive dine the problem 10 times
If the area of a circle measures 16cm2 what is the circumference
Answer:
14.18 cm
Step-by-step explanation:
Area = pi r^2
sqrt ( area/pi) = r
diameter is 2 x r and circumference is pi * d
circumference pi * 2 * ( sqrt area/pi) = 14.18 cm
. Shanovia drew a card from a standard deck of 52 playing cards. What is the probability Shanovia drew 1 of
the 4 aces?
Answer:
not answered this question
work out 9 over 13 of 182 (9 over 13 is supposed to be a fraction)
Answer:
126
Step-by-step explanation:
In math, "of" usually means multiplication.
9/13 of 182 means 9/13 × 182.
9/13 × 182 = 9/13 × 182/1 = (9 × 182)/(13 × 1) = 1638/13 = 126
Answer: 126
Answer:
126
Step-by-step explanation:
To find 9/13 of 182, we would divide 182 by 13 and multiply the quotient by 9.
182 ÷ 13 = 14
14 • 9 = 126
To double-check our answer, we can divide 126 by 182 and see if the fraction is congruent to 9/13.
126 ÷ 182 = 0.6923
9 ÷ 13 = 0.6923
I hope this helps.
Simplify the expression.
Answer:
1/81
Step-by-step explanation:
9 to the power of 7 is 4782969
and 9 to the power of 9 it 387420489
and when u divide it u get 1/81 I beleve
Answer:
1/81 or 0.01 that is rounded to the nearest hundredth
Step-by-step explanation:
Your welcome
WILL MARK BRAINLIEST!!!!!!
Answer:
40π m² and 125.6 m²
Step-by-step explanation:
the area (A) of the sidewalk is calculated as
A = outer area - inner area
(a)
A = πr₁² - πr₂² ( r₁ is radius of outer circle and r₂ the radius of inner circle )
A = π × 11² - π × 9²
= 121π - 81π
= 40π m²
(b)
A = 40 × 3.14 = 125.6 m²
4.) Which is a statistical question?
(a) How many weeks are in November?
(b) How many students are on the roster for Morehouse Homeroom?
(c) How tall is Reggie?
(d) How many minutes do students wait in line to go home after school?
Answer:
How many students are on the roster for Morehouse Homeroom?
(Easy) b. When will function h exceed both function f and function g?
Answer:
Is their like any opions? or no
Step-by-step explanation:
35. Mathematical Connections A streamer is
launched 3 s after a fuse is lit and lands 8 s
after it is lit.
у
100
80
60
Height (ft)
40
20
0
0
X
8 10
2 4 6
Time (s)
a. What is a quadratic equation in factored
form that models the situation?
Launching the fuse is an illustration of a quadratic model, and the equation of the quadratic model is f(x) = 15(x - 3)(x - 8)
How to model the quadratic equation?From the complete question, the zeros of the quadratic function are:
x = 3 and x = 8
Rewrite as:
x - 3 = 0 and x - 8 = 0
So, the quadratic equation is:
f(x) = a(x - 3)(x - 8)
Also from the graph, we have the following point
(x,y) = (4,60)
Substitute 4 for x and 60 for f(x) in the function
a(4 - 3)(4 - 8) = 60
Evaluate the difference
a(1)(-4) = 60
Evaluate the product
-4a = 60
Divide both sides by 4
a = -15
Substitute a = -15 in f(x) = a(x - 3)(x - 8)
f(x) = -15(x - 3)(x - 8)
Hence, the equation of the quadratic model is f(x) = 15(x - 3)(x - 8)
Read more about quadratic models at:
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When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 7c – 4c2 – 3c 4 –4c2 4c 6 –7c2 10c 6 –4c2 4c 8 –7c2 7c 6
The simplified and standard form of the considered polynomial is -4c^2 -4c + 6
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
The given polynomial is:
[tex]2 + 7c - 4c^2 - 3c + 4[/tex]
Simplifying it gives:
[tex]2 + 7c - 4c^2 - 3c + 4 = 2+4 + (7-3)c - 4c^2 = 6 -4c -4c^2[/tex]
Writing it in the order of increasing to decreasing powers:
[tex]6 -4c -4c^2 = -4c^2 -4c + 6[/tex]
Thus, the simplified and standard form of the considered polynomial is [tex]-4c^2 -4c + 6[/tex]
Learn more about standard form of a polynomial here:
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Answer 1 and 2 and I'll mark you brainliest
Which of the following is equal to the expression listed below?
14 + 21
A.7 + (2 × 3)
B. (7 × 2)(7 × 3)
C. 7(2 + 3)
D. (7 + 2)(7 + 3)
Answer: C
Step-by-step explanation: The answer is C because unbending suing distributive property, the equation becomes (7 x 2) + (7 x 3). Solving for these parentheses, the equation becomes 14 + 21. I hope this helps!
Slow and steady wins the race. The leatherback sea turtle is the fastest known reptile, with a maximum
speed of 21.92 miles per hour (mph).
Which of the following equations, where d is distance in miles and t is time in hours, represents a speed
that is less than that of the leatherback sea turtle?
Choose all answers that apply:
PLEASE HELP!!
Answer:
A and B
Step-by-step explanation:
See explanation below