If 2 tan x 1- tan2 x 1 V3 then x can equal: + MT B. X= A. x=112 x- 7 C. X = ST D. X=
Answers
Solve for x
[tex]\frac{2\tan (x)}{1-tan^2(x)}=\frac{1}{\sqrt[]{3}}[/tex]Step 1: Let tan(x) represent y
[tex]\begin{gathered} \frac{2y}{1-y^2}=\frac{1}{\sqrt[]{3}} \\ \text{cross multiply} \\ 1-y^2=2\sqrt[]{3}y \\ y^2+2\sqrt[]{3}y-1=0 \end{gathered}[/tex]Step 2: Using quadratic equation solve for y
[tex]\begin{gathered} y^2+2\sqrt[]{3}y-1=0 \\ y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=2\sqrt[]{3},c=-1 \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{(2\sqrt[]{3})^2-4(1)(-1)}}{2(1)} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{12+4}}{2} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{16}}{2} \\ y=\frac{2(-\sqrt[]{3}\pm2)}{2} \\ y=-\sqrt[]{3}\pm2 \end{gathered}[/tex]Since the y represents tan x
[tex]\begin{gathered} \tan \mleft(x\mright)=-\sqrt{3}-2,\: \tan \mleft(x\mright)=2-\sqrt{3} \\ x=\arctan \mleft(-\sqrt{3}-2\mright)+\pi n,\: x=\arctan \mleft(2-\sqrt{3}\mright)+\pi n \\ x\text{ in degrees} \\ \: x=-75^{\circ\: }+180^{\circ\: }n,\: x=15^{\circ\: }+180^{\circ\: }n \\ \: x=15^{\circ\: }+180^{\circ\: }n \end{gathered}[/tex]Therefore the correct answer is
[tex]x=\frac{\pi}{12}+n\pi[/tex]Hence the correct answer is Option B
Related Questions
please help you just solve the equation and list properties
Answers
EXPLANATION
To solve the given equation:
[tex]-4=\frac{v+6}{2}[/tex]Step 1:
Multiply both-side of the equation by 2 in other to eliminate the denominator.
[tex]-4\times2=\frac{(v+6)}{2}\times2[/tex]At the right-hand side of the equation, 2 add the numerator will cancel-out 2 at the denominator.
[tex]-8=\frac{(v+6)}{\cancel{2}}\times\cancel{2}[/tex]- 8 = v+ 6
step 2:
Subtract 6 from both-side of the equation.
That is;
-8 - 6 = v + 6 - 6
-14 = v
Hence, the value of v = -14
Sort the following into either terminating or non-terminating categories. 2%, 3/4, 105/15, 1/3, 15/7, 81/11
Terminating
Non-Terminating
Answers
The terminating category consists of 2%, 3/4, and 105/15.
The non-terminating category consists of 1/3, 15/7, and 81/11.
What are terminating and non-terminating decimals?Decimals with an end digit are said to be terminating decimals. The number of digits in a decimal, which it is, is finite (or terms). Examples include 0.15, 0.86, etc. The decimals without a terminal are known as non-terminating decimals. The number of terms in it is unlimited.Given: 2%, 3/4, 105/15, 1/3, 15/7, 81/11
To determine whether these fractions are terminating or non-terminating decimals,
2% = 2/100 = 0.02
It is a terminating decimal.
3/4 = 0.75
It is a terminating decimal.
105/15 = 7
It is an integer, hence terminating.
1/3 = 0.3333333...
It is a non-terminating decimal.
15/7 = 2.14285714
It is a non-terminating decimal.
81/11 = 7.36363636
It is a non-terminating decimal.
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Fargus deposits $366 in a savings account at City BankThe account pays an annual interest rate of 5 percent She makes no other deposits or withdrawalsAfter three months the interest is calculated. How much simple interest does her money
Answers
The Simple interest after three month $423.70
What is Simple Interest ?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
If she deposits $366 in the account and you receive interest, you must first calculate the interest for the current year before adding the sum to calculate the interest for the following month.
for instance, deposit plus interest equals the new amount for month one, month one amount plus interest equals amount for month two, and month two amount plus interest equals amount for month three.
The total would thus be $423.70 for the following month:
month 1
366+ (366*.05)=x
366+18.3=x
month 2
384.30+(384.30*.05)=x
384.30+19.22=x
month 3
403.52+(403.52*.05)=x
403.52+20.18=x
423.7 = x
Thus, total amount then would be $423.70
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A survey of 600 school employees yielded the following information: 449 were instructors, 325 were full-time faculty, and 260 of the instructors were full-time faculty. How many of the 600 surveyed school employees were instructors or were full-time faculty?
Answers
Answer:
260+325 = 585
260 where instructors that were full time and 325 were already full time. this is correct if I am reading your question correctly if not the answer is likely 260
Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive
integer coefficient.
Polynomial of lowest degree with lowest possible integer coefficients, and with zeros 3-2i and 0 (multiplicity 4).
Answers
Step-by-step explanation:
Let use the following rules to construct a polynomial,
Rule 1:
If r is a zero of some polynomial, f(x), then
[tex](x - r)[/tex]
is a factor of the polynomial
We first know that one of our zeroes are real, which is 0.
So since r=0
[tex](x - 0) = x[/tex]
is a factor
However, since the root ,0, has a multiplicty of 4, that basically means we have 0 as a root 4 times or basically we multiply the factor 4 times.
[tex]x \times x \times x \times x = x {}^{4} [/tex]
This leads to an another rule:
If a polynomial has a zero, r that has a multiplicty of k,
we represent the factor as
[tex](x - r) {}^{k} [/tex]
where k is all integers greater than 0.
So to reinforce myself, since 0 has a multiplicty of 4, we have
[tex](x - 0) {}^{4} = {x}^{4} [/tex]
So our first factor is
[tex] {x}^{4} [/tex]
Part 2: Complex Zeroes.
When dealing with complex zeroes, we must note this rule.
if (a+bi) is a zero of some polynomial, p then its conjugate (a-bi) is a factor as well.
So if 3-2i is a factor, then
3+2i is a factor as well.
Using Rule 1, our factors now become
[tex](x - (3 + 2i))[/tex]
and
[tex](x - (3 - 2i))[/tex]
So our factors are
[tex] {x}^{4} (x - (3 - 2i)(x - (3 + 2i))[/tex]
To simplify use FOIL Method,
[tex] {x}^{4} ( {x}^{2} - x(3 + 2i) - x(3 - 2i) + 9 - 4 {i}^{2} )[/tex]
[tex] {x}^{4} ( {x}^{2} - 6x + 13)[/tex]
[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]
So our polynomial is
[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]
how much does $3000 earn in 6 months at in interest rate of 4%, compounded quarterly?
Answers
The amount earned by $3000 deposited in the account after 6 months is $60.30
What does quarterly compounding mean?
Quarterly compounding means that the interest is computed and credited to the account every quarter, that is every 3 months, in other words, our future value formula would indicate quarterly interest rate rather than an annual interest rate
FV=PV*(1+r)^N
FV=the amount in the account after 6 months=unknown\
PV=initial amount deposited in the account=$3,000
r=quarterly interest rate=4%/4=0.01
N=number of quarters in 6 months=2
FV=$3000*(1+0.01)^2
FV=$3000*(1.01)^2
FV=$3000*1.0201
FV=$ 3,060.30
amount earned=FV-PV
amount earned=$3060.30-$3000
amount earned=$60.30
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4. The radius of a hydrogen atom is
0.000000000025 meter. How would you
express this radius in scientific notation?
Answers
Answer:
2.5×10^-11
Step-by-step explanation:
Put the point in the middle of 2 and 5 and count how many times you need to get there ...
like 0.05 to put point after 5 you have to jump 2 steps so it is 5×10^-2.
Scampini Technologies is expected to generate $75 million in free cash flow next year, and FCF is expected to grow at a constant rate of 7% per year indefinitely. Scampini has no debt or preferred stock, and its WACC is 12%, and it has zero nonoperating assets. If Scampini has 40 million shares of stock outstanding, what is the stock's value per share? Do not round intermediate calculations. Round your answer to the nearest cent
Answers
If Scampini has no debt or preferred stock, and its WACC is 12%, and it has zero nonoperating assets in which Scampini has 40 million shares of stock outstanding, the stock's value per share is $37.50.
Stock priceNext year CF = $75 millions
Growth rate of CF = 7%
WACC = 12%
Number of shares outstanding = 40 million shares
Estimated business valuation:
Valuation = Next year CF/ (WACC -growth rate)
Valuation = $75 million / (12% - 7%)
Valuation = $75 million /5%
Valuation =$1500 million
Estimated stock price:
Stock price = Valuation /Shares outstanding
Stock price = $1500 million / 40 million shares
Stock price = $37.50
Therefore the stock price is $37.50.
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The mean per capita income is $21,604 per annum with the standard deviation of $727 per annum. What is the probability that the sample mean will be less than $21,635 if a sample of 193 persons is randomly selected? Round your answer to four decimal places
Answers
Explanation
In the question, we are given that
[tex]\begin{gathered} \mu=21,604 \\ \sigma=$ 727 $ \\ n=193 \end{gathered}[/tex]First, we will get the standard deviation of the sample mean as
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{727}{\sqrt{193}}=52.3306[/tex]Then, we can find the probability that the sample mean will be less than $21,635 for a sample of 193 persons
[tex]\begin{gathered} P(\bar{X}<21635)=P(z<\frac{\bar{X}-\mu}{\sigma_x})=P(z<\frac{21635-21604}{52.3306}) \\ =P(z<0.59238) \end{gathered}[/tex]Therefore, using the z score calculator
[tex]P(z<0.59238)=0.7232[/tex]Answer: 0.7232
What is the approximate area of the shaded sector of the circle?
Answers
The formula for the area(A) of the sector is,
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Given:
[tex]\begin{gathered} \theta=139^0 \\ r=4m \end{gathered}[/tex]Therefore,
[tex]A=\frac{139^0}{360^0}\times\pi\times4^2[/tex]Simplify
[tex]\begin{gathered} A=\:19.40806\approx19.41\text{ \lparen2 decimal places\rparen} \\ \therefore A=19.41m^2 \end{gathered}[/tex]Hence,
[tex]A=19.41m^2\text{ \lparen OPTION D\rparen}[/tex]The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model is
Answers
the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
We are given the function as:
BSA = √( w h / 3600)
where:
h = height
w = weight
BSA = body surface area
1) Now, for w = 68 kg and BSA = 1.9, we get the height as:
1.9 = √( (68) h / 3600)
3.61 = 68 h / 3600
12,996 = 68 h
h = 12996 / 68
h = 191.12 cm
h ≈ 191 cm
2) for h = 165 cm and BSA = 2.2, we get the weight as:
2.2 = √( w (165) / 3600)
4.48 = 165 w / 3600
17424 = 165 w
w = 17424/ 165
w = 105.6 kg.
w ≈ 106 kg
Therefore, we get that, the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
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If using the method of completing the square to solve the quadratic equation
x^2+ 15x - 23 = 0, which number would have to be added to "complete the
square"?
Answers
Step-by-step explanation:
you would take half of 15 and then square it to get to number, which is 56.25
Answer:
[tex](\frac{15}{2} )^2=\frac{225}{4}[/tex]
Step-by-step explanation:
[tex]x^2+15x-23=0\\x^2+15x+(\frac{15}{2} )^2-(\frac{15}{2})^2-23=0\\(x^2+15x+(\frac{15}{2})^2)=23+(\frac{15}{2})^2\\(x+\frac{15}{2})^2=(23*4+15^2)/4=317/4\\x+\frac{15}{2}=+\frac{\sqrt{317}}{4}\\, -\frac{\sqrt{317}}{4}\\\\x=-\frac{15}{2}-\frac{\sqrt{317}}{4}\\\\, -\frac{15}{2}+\frac{\sqrt{317}}{4}\\\\[/tex]
Name all transformations of the following function
Answers
Notice that the parent function of y is:
[tex]f(x)=\sqrt{x}.[/tex]Now, recall that a function h(x) translated n units to the left is represented by:
[tex]h(x+n),[/tex]translated m units up :is represented by
[tex]h(x)+m,[/tex]reflected across the x-axis :is represented by
[tex]-h(x),[/tex]vertically compressed by a factor of 1/k :is represented by
[tex]\frac{1}{k}h(x).[/tex]Therefore, y is f(x) translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
Answer:y is its parent function translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
I8. Last night, you spent a total of 51 minutes working on your homework problems for math andbiology. Each math problem takes 5 minutes to complete and each biology problem takes 3minutes to complete. You completed a total of 15 problems. Write a system of equations thatdetermines how many math problems and how many biology problems you completed lastnight.
Answers
Let x represent the number of math problems that you completed.
Let y represent the number of biology problems that you completed
From the information given,
You completed a total of 15 problems. This means that
x + y = 15
If each math problem takes 5 minutes to complete, it means that the time to complete x math problems is 5 * x = 5x
If each biology problem takes 3 minutes to complete, it means that the time to complete y biology problems is 3 * y = 3y
If you spent 51 minutes working on your homework problems for math and
biology, it means that
5x + 3y = 51
Thus, the system of equations is
x + y = 15
5x + 3y = 51
The equation of a line is written below.
y=2x-3
The slope of the line is____
The y-intercept of the line is_____
Answers
Answer:
Slope: 2
Y-intercept: -3
Step-by-step explanation:
y=2x-3
The slope is always the number(s) before the x and the y-intercept is what is added or subtracted
answer this question please
Answers
a. Absolute value function the reference beam is g(x) = |8x/5|.
b. g(x) = +8x/5 ; x < 5 and g(x) = -8x/5 > 5.
What is defined as the absolute value function?An absolute value function is one that has an algebraic expression enclosed in absolute value symbols. Remember that a number's absolute value is its distance from 0 just on number line.For the given function;
Part a: The reference beam is passing from the points;
(x₁, y₁) = (5, 8)
(x₂, y₂) = (0, 0)
Then the slope of the line is -
m = (y₂ - y₁)/(x₂ - x₁)
Put the values ;
m = (0 - 8)/(0 - 5)
m = 8/5
The equation of the line is;
y - y₁ = m(x - x₁)
Put the values;
y - 0 = 8/5(x - 0)
y = 8x/5
Or in absolute modulus function for the path of reference beam; y = |8x/5|.
Part b: absolute function in terms of piecewise function;
g(x) = +8x/5 ; x < 5 as the slope is increasing.
and g(x) = -8x/5 > 5.; as the slope is decreasing.
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what is the slope and y intercept of 4x + 7y=18?
Answers
Answer:
-4/7, 18/7
Step-by-step explanation:
[tex]4x+7y=18 \\ \\ 7y=-4x+18 \\ \\ y=-\frac{4}{7}x+\frac{18}{7}[/tex]
12. Evaluate: 0.0512 x 104.
O 51.2
O 5120
O 512
O 0.00000512
Answers
8−8, minus
=-5=−5 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
Answers
Answer:
AAAAAAAAAA
Step-by-step explanation: AAAAAAAAAAAAAAAA
The equation |2x + 1 = 9 has two solutions, a and b, where a < b. Find the two solutions.
Answers
Answer:
Write down one equation or inequality that has more than two solutions, but not infinitely many solutions
Step-by-step explanation:
Jason is canoeing on a river that flows
downstream at a rate of 1 mile per hour. After
paddling 5 miles downstream, he turns around
and paddles 6 miles upstream to report the
condition of the river to the rest of his group. The
whole trip takes 3 hours.
a) Fill out the last column in table below by
writing an expression for time downstream and
for time upstream
Answers
An expression exists as a number, a variable, or a combination of numbers and variables, and function symbols. The speed in still water exists 4 mph.
What is meant by expression?The acronym BODMAS, which stands for brackets of, division, multiplication, addition, and subtraction, might be used to simplify the expression. It specifies how to answer a mathematical expression in a particular order.
Let x be the speed in still water
[tex]$&\frac{5}{x+1}+\frac{6}{x-1}=3[/tex]
LCD = (x + 1)(x - 1)
[tex]$&(x+1)(x-1) \cdot \frac{5}{x+1}+(x+1)(x-1) \cdot \frac{6}{x-1}=(x+1)(x-1) \cdot 3 \\[/tex]
simplifying the above equation, we get
5(x - 1) + 6(x + 1) = 3(x + 1)(x - 1)
5x - 5 + 6x + 6 = 3 x² - 3
3x² - 11x - 4 = 0
(3x + 1)(x - 4) = 0
x = -1/3 (speed is not negative);
then we get x = 4 mph
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An actress has a probability of getting offered a job after a try-out of 0.11. She plans to keep trying out for
new jobs until she gets offered one. Assume outcomes of try-outs are independent.
Find the probability she will need to attend more than 3 try-outs. Round your answer to 4 decimal places.
Submit Question
Answers
The probability she will need to attend more than 3 try-outs is 0.7049.
The probability of an actress getting a job after a tryout is 0.11.
The actress wants to keep trying out for new jobs until she gets offered one.
The number of trials necessary for success in a series of independent trials follows a geometric distribution with parameter p, where p is the probability of success in a single trial.
The probability mass function is given as:
[tex]P(X=k)=q^{k-1}p[/tex] where k = 1, 2, 3
We have p = 0.11
q = 1 - 0.11 = 0.89
If X is the number of tryouts,
[tex]P(X=k)=q^{k-1}p\\P(X=k)=(0.89)^{k-1}(0.11)[/tex]
[tex]P(X\leq r)=1-q^r\\P(X\leq r)=1-(0.89)^r[/tex]
Therefore, the probability that she will need to attend more than 3 try outs will be:
P = P( X > 3 )
P = 1 - P( X ≤ 3 )
P = 1 - [ 1 - 0.89³ ]
P = 1 - 1 + 0.89³
P = 0.704969
P = 0.7049
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A game is played using one die. If the die is rolled and shows 2, the player wins $25. If the die shows any number other than 2, the player wins nothing Complete parts (a) through (b) below
a. If there is a charge of $5 to play the game, what is the game's expected value?
$(Round to the nearest cent)
Answers
The game's expected value is -$0.83.
The game is played using one die.If the die is rolled and it shows 2, then the player wins $25.If the die is rolled and it shows any number other than 2, then the player wins nothing.The probability of getting 2 on the die is 1/6.The probability of not getting 2 on the die is 5/6.The cost of playing the game is $5.If the die shows 2, the player has a profit of $20.If the die doesn't show 2, the player has a loss of $5.The expected value is the sum of the product of the value of individual events and their respective probabilities.The expected value is 20(1/6) - 5(5/6).The expected value is - 5/6.The expected value is -$0.83.To learn more about probability, visit :
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Solve each equation mentally.
a. ½ ·x = 1
b.x = 1
c. 1 + 1 = x
Answers
A.) [tex]x = 2[/tex]
B.) [tex]x=1[/tex] (Nothing further can be done with this.)
C.) [tex]x=2[/tex]
_____________________________________
Hope this helps! If not, feel free to comment below on the matter and I'll see what else I can do to assist you further. If it did help though, feel free to lmk! Thanks and good luck!
Use subtraction
14x25x4
Answers
There are two possibilities for answers none of which require subtraction based on the expression given:
What is the explanation for the above solutions?
With the question none of which involves subtraction. First is that this is a simple multiplication in which case the answer is 1,400;
Second that the above expression actually means 14x * 25x * 4 in which case the answer is 1400x²
Explanation 1
14 x 25 x 4
= 350 x 4
= 1,400
Explanation 2
14x * 25x * 4
= 1400 * x * x
= 1400x²
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help with this please
Answers
Consider the given radical,
[tex]\sqrt[]{128}[/tex]Factorize the number,
[tex]128=2^7[/tex]Consider the following properties,
[tex]\begin{gathered} a^{m+1}=a^m\times a \\ a^{mn}=(a^m)^n \end{gathered}[/tex]Then the radical can be simplified as,
[tex]\sqrt[]{128}=\sqrt[]{2^7}=\sqrt[]{2^6\times2}=\sqrt[]{64\times2}=\sqrt[]{64}\times\sqrt[]{2}[/tex]Thus, the radical is simplified as,
[tex]\sqrt[]{128}=\sqrt[]{64}\times\sqrt[]{2}=8\sqrt[]{2}[/tex]The full-time year-round median salary for U.S. workers in
2000 was $30,846, compared to $52,800 in 2020.
Answers
The linear function that gives the full-time year-round median salary for U.S. workers in t years after 2000 is given by:
S(t) = 30846 + 1097.7.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change.The coefficient b is the y-intercept of the function, which is the initial value of the function.Linear functions are used in situations when the rate of change is constant, or can be interpreted as a constant, and this rate is called the slope, as we stated above.
In this problem, we have that:
The reference year is of 2000, hence the intercept is of b = 30846, as it was the median salary during the year of 2000.In 20 years, the median salary increased to $52,800, hence the slope is calculated as follows: m = (52800 - 30846)/20 = 1097.7.Hence the linear function that models the situation is given as follows:
S(t) = 30846 + 1097.7.
What is the missing information?The complete problem could not be found on any search engine, hence we are going to suppose that it asks for a linear function for the median salary in t years after 2000.
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Find the surface area of the ball shown to the right .The ball has a surface of _ cm2(Simplify your answer .Type an exact answer in terms of pie.)
Answers
Surface area of a sphere: 4 π r^2
Where:
r = radius = d/2 = 14/2 = 7
Replacing
SA = 4 π 7^2 = 4 π 49 = 196π cm2
Jackie has 9 stamps. Kevin has 36 stamps. Kevin says he has 5 times as many stamps as Jackie. Is Kevin correct? Explain your reasoning.
Answers
The most appropriate choice for linear equation will be given by -
Kevin is not correct
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let Kevin has x times as many stamps as stamp
Jackie has 9 stamps
Number of stamps Kevin has = 9x stamps
By the problem,
9x = 36
[tex]x = \frac{36}{9}[/tex]
x = 4
So Kevin has 4 times as many stamps as Jackie
But Kevin says he has 5 times as many stamps as Jackie.
So Kevin is not correct.
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Need some help!!!can you please explain?
Answers
iven:
he fucnction is,
[tex]f(x)=\frac{3}{4}\sqrt[3]{x+1}[/tex]xplanation:
he graph fo the function cnan be obtained by graph of cube root of x.
If we shift the graph of cube root by x by one unit left then then function changed to,
[tex]\sqrt[3]{x+1}[/tex]If the obtained graph shrink vertically by a factor of 3/4 then graph changed to function,
[tex]\frac{3}{4}\sqrt[3]{x+1}[/tex]This is the requied function for which we need the graph.
So graph can be obtained by horizontal shift of 1 unit to left, shrink by a factor of 3/4 and there is no vertical shift and graph will not flip over any axis.
Thus answer is, All statements are true.