Which of the following is a solution to 3tan^3x=tanx?
PLEASE HELP

Answers

Answer 1
Answer:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Explanation:
3 tan³x = tan x
3 tan³x - tan x = 0
tan x (3 tan²x - 1) = 0
either tan x = 0
This means that:
x = 0 , π or 2π ...........> I

or 3 tan²x - 1 = 0
This means that:
3 tan²x = 1
tan²x = [tex] \frac{1}{3} [/tex]
tan x = ± [tex] \frac{1}{ \sqrt{3}} [/tex]
at tan x = [tex] \frac{1}{ \sqrt{3}} [/tex]
x = π/6 or 7π/6 ...................> II
at tan x = - [tex] \frac{1}{ \sqrt{3}} [/tex]
x = 5π/6 or 11π/6 ..............> III

From I, II and III, the solutions for x would be:
0, π, 2π, π/6, 5π/6, 7π/6 and 11π/6

Hope this helps :)
Answer 2

Answer:

its 150 degrees i think

Step-by-step explanation:

i could be wrong though but i'm like 80% sure im right


Related Questions

The function given by Upper A left parenthesis t right parenthesis equals 0.0265 t cubed minus 0.444 t squared plus 1.774 t plus 8.76A(t)=0.0265t3−0.444t2+1.774t+8.76​, 0 less than or equals t less than or equals 100≤t≤10​, can be used to estimate the​ amount, in billions of​ dollars, invested by large oil companies in exploration for new reserves t years after 19951995. Find the relative extreme​ points, and sketch a graph of the function.

Answers

A graphing calculator shows the relative extremes to be
.. (2.606, 10.837) . . . relative maximum
.. (8.564, 8.033) . . . . relative minimum

What is the area of the hexagon? Numerical answer only!

Answers

8 times 3 =24
3 times 2 =6

=30
From here you can split up the hexagon into 2 rectangles. Draw a line from D perpendicular to line AB. 

Area = length x width

We know the upper rectangle's dimensions are 2 by 3 because AB = CD + EF. Put in the numbers, 6 = CD + 3. Solve for CD which is 3. Multiply 2 by 3 to get the area of the upper rectangle. Answer: 6

The lower rectangle's dimensions are 8 by 3 (given). Multiply 8 by 3 to get the area of the lower rectangle. Answer 24.

Once you've calculated both areas, add them up to find the area of the entire figure.
Final Answer: 30 [tex] cm^{2} [/tex]

Sela's piano lesson starts at 4:45pm the lesson is 30 minutes long

Answers

The piano lesson would end at 5:15. Does this answer your question?

the piano lesson ends at 5:15

Find the radius of the circle whose equation is 3x² + 3y² = 75.

Answers

3x² + 3y² = 75
divide everything by 3
x² + y² = 25

This is a standard equation of a circle.
Center (0,0) and radius = 5

Answer: 5 units

Step-by-step explanation:

We know that the general equation of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given : The equation of a circle : [tex]3x^2 + 3y^2 = 75[/tex]

Taking 3 as common from the left side of the given equation , we get

[tex]3(x^2 + y^2) = 75[/tex]

Divide 3 on both the sides , we get

[tex]x^2 + y^2 = 25[/tex]

Comparing to the general equation of circle , we get

[tex]r^2 = 25\\\\\Rightarrow\ r=5[/tex]

Hence, the radius of the circle = 5 units

what is 5 1/2 × 2 1/3

Answers

Hello,

Here is your answer:

The proper answer to this question is "77/6".

Here is how:

First turn the mix numbers into fractions:

5 1/2=11/2
&
2 1/3=7/3

Now write the equation:

11*7=77
2*3=6

Your answer is 77/6!

If you need anymore help feel free to ask me!

Hope this help!

onsider the following pseudocode function. function Crunch(x R) if x ≥ 100 then return x/100 else return x + Crunch(10 · x) (a) Compute Crunch(4). Crunch(4) = (b) What happens if you try to compute Crunch(−23)? What does this suggest about an appropriate precondition for this function?

Answers

a) Crunch(4) = 4 +Crunch(40)
.. = 4 +40 +Crunch(400)
.. = 4 +40 +400/4
.. = 48

b) Crunch(-23) = -23 +Crunch(-230)
.. = -23 -230 +Crunch(-2300)
... terminates with overflow or memory exception

An appropriate precondition is x ≥ 0.

Two fair dice are rolled. what is the (conditional) probability that the first dice lands on an even number given that at least one of the dice lands on a 6?

Answers

The probability is 1/2

Is the sequence arithmetic? If so, identify the common difference. 15,22,35,46,...

Answers

The answer is no the sequence isn't arithmetic. I'm 100% pretty sure.

The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders.

Answers

Using the data presented in the problem, you are asked to predict the probability that future customers will cancel their preorders. To find the probability, you have to divide the number of people who cancelled their preorders by the total number of people who preordered.

35 people / 140 people = .25 or 25% probability that the future customers will cancel their preorders.

Answer:

A

Step-by-step explanation:

Which is a cubic function? a. f(x) = 3x + 1 b. f(x) = 3x2 + x + 2 c. f(x) = 5x3 + 2x + 1 d. f(x) = x3 + x4 + 5

Answers

A cubic function is a function with the highest degree of 3. So the answer is V

Answer:

Option C is a cubic function

Step-by-step explanation:

Given the options we have to choose the cubic function

Cubic function is the function with degree 3 i.e the highest power of variable is 3.

Option a: [tex]f(x)=3x+1[/tex]

The above polynomial has highest power 1 i.e of degree 1

∴ not a cubic function

Option b: [tex]f(x)=3x^2+x+2[/tex]

The above polynomial has highest power 2 i.e of degree 2

∴ not a cubic function

Option c: [tex]f(x)=5x^3+2x+1[/tex]

The above polynomial has highest power 3 i.e of degree 3

∴ above is a cubic function

Option d: [tex]f(x)=x^3+x^4+5[/tex]

The above polynomial has highest power 4 i.e of degree 4

∴ not a cubic function

Cecil Green sells golf hats. He knows that most people will not pay more than $20 for a golf hat. Cecil needs a 40% markup on cost. What should Cecil pay for his golf hats? (Round your answer to the nearest cent.) Cecil pays $

Answers

Final answer:

Cecil should pay $14.29 for his golf hats.

Explanation:

To determine what Cecil should pay for his golf hats, we need to calculate the cost price and apply the 40% markup. Let's assume the cost price is 'x'. Since Cecil needs a 40% markup on cost, the selling price will be 140% of the cost.

To find the selling price, we can use the equation: 140% of 'x' = $20. Solving this equation, we get: x = $20 / 1.4 = $14.29.

Therefore, Cecil should pay $14.29 for his golf hats.

Is 200 milliliter equivalent to 2 liters

Answers

No because,

1 liter = 1000 milliliter 
2 liter = 2 * 1000 = 2000 milliliter 
200 milliliter = 0.2 liter

Hope this helps :)

In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct?Check all that apply.m∠1 = 60°m∠13 = 80°m∠6 = 80°m∠5 = 60°m∠10 = 120°m∠ 14 = 100°

Answers

we are given

m∠3 = 120° and m∠12 = 80°

we will check all

Calculation of m∠1:

we can see that angles 1 and 3 are linear

so, their sum must be 180

m∠1+m∠3 = 180°

now, we can plug values

m∠1+ 120°= 180°

m∠1=60°

Calculation of m∠13:

we know that

angles 12 and 13 are alternate angles

so, they must be equal

m∠13=m∠12 = 80°

m∠13= 80°

Calculation of m∠6:

we know that

angles 3 and 6 are alternate angles

so, they must be equal

m∠3=m∠6 = 120°

m∠6= 120°

Calculation of m∠5:

we know that

angles 1 and 5 are corresponding angles

so, they must be equal

m∠1=m∠5 = 60°

m∠5= 60°

Calculation of m∠10:

we can see that angles 10 and 12 are linear

so, their sum must be 180

m∠10+m∠12 = 180°

now, we can plug values

m∠10+ 80°= 180°

m∠10=100°

Calculation of m∠14:

we know that

angles 10 and 14 are corresponding angles

so, they must be equal

m∠10=m∠14 = 100°

m∠14= 100°


Answer:

A, B, D, F

Step-by-step explanation:

Well to summarize what the previous person mentioned:

1 = 60

13 = 80

6 = 120

5 = 60

10 = 100

14 = 100

So given that information the correct answers are:

A, B, D, F

A school has 18 left-handed students. If 8% of the total number of students in the school are left-handed, what is the total number of students in the school?

Answers

Your answer is two hundred twenty-five
225 students.  18/0.08 = 225

What are the roots of the equation?

x^2+24=−11x

Enter your answers in the boxes.

Answers

The correct answers are:

x=-3 and x=-8.

Explanation:

We can first write this in standard form, ax²+bx+c=0. To do this, we will add 11x to both sides:
x²+24+11x=-11x+11x
x²+11x+24=0.

Now we can factor this. Look for factors of c, 24, that sum to b, 11. Factors of 24 are:
1 and 24 (sum 25)
2 and 12 (sum 14)
3 and 8 (sum 11)
4 and 6 (sum 10).

The factors we need are 3 and 8, since they sum to 11. This gives us factored form:
(x+3)(x+8)=0.

Using the zero product property, we know that in order to have a product of 0, one or both of the factors must be 0. This means we have:
x+3=0 or x+8=0.

Solving the first equation:
x+3-3=0-3
x=-3.

Solving the second equation:
x+8-8=0-8
x=-8.

Answer:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

Step-by-step explanation:

Given the equation:

[tex]x^2+24 = -11x[/tex]

Add 11x to both sides we have;

[tex]x^2+11x+24 = 0[/tex]

Split the middle terms we have;

⇒[tex]x^2+8x+3x+24 = 0[/tex]

⇒[tex]x(x+8)+3(x+8)= 0[/tex]

⇒[tex](x+8)(x+3)= 0[/tex]

By zero product property we have;

x+8 = 0 and x+3= 0

⇒x = -8 and x = -3

Therefore, the roots of the given equations are:

[tex]x_1 = -8[/tex]

[tex]x_2 = -3[/tex]

You borrow $350 from your aunt and agree to repay her $400 in 18 months. What interest rate (to the nearest tenth) are you paying?

Answers

I = P*r*t
r = I/(P*t) = (400 -350)/(350*1.5) . . . . . . 18 mo = 1.5 yr
r = 1/10.5
r ≈ 9.5%

You are paying about 9.5% simple interest.

Which is the most reasonable conjecture about the data shown in the scatter plot?



I think B? I'm not sure..

Answers

In this case, what you should notice is that there is an increase in salary according to years of experience.
 Notice that as the horizontal axis moves away from the origin of coordinates, the vertical axis also moves away from the origin of coordinates.
 Answer: 
 people with more experience, have to earn higher salaries. 
 option B.

Find the x-intercepts (if any) for the graph of the quadratic function.
6x^2 +12x+5=0
Give your answers in exact form. Show your work

Answers

we have that

6x^2 +12x+5=0
to find the x intercepts resolve the second order equation

x=[-b(+-)√(b²-4ac)]/2a
x1=[-12(+)√(12²-4*6*5)]/12---> [-12(+)√(144-120)]/12
=[-12(+)√(24)]/12--------> -1+√24/12-----> -1+√6/6

x1=-1+√6/6
so
x2=-1-√6/6

see the graph in the attached figure

the answer is
the x-intercepts for the graph of the quadratic function in exact form are
x1=-1+√6/6
x2=-1-√6/6

For a track meet, Tara ran the 1,600 m event at constant speed in 5 minutes and 20 seconds. What was her speed?

Answers

1600/320=5

Her speed was 5 meters/second

Tom and Sonya were comparing their answers on a math problem. It was an order of operations problem, and they each had a different answer. Tom had an answer of 11, and Sonya had an answer of 104. Which student correctly solved the order of operations problem given by the teacher?

(5^2 +6)–(7•4)+8

Answers

Hello!

The order of operations is PEMDAS or parenthesis, exponents, multiplication, division, addition subtraction.

So 5^2 is 25 + 6 is 31

7*4 is 28

31 - 28 = 3

and 3 + 8 is 11

Tom was right

Hope this helps!
Hey there!

Seeing that it's an order of operations problem, we can use our standard format of computing, PEMDAS. It stands for:

P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction

When we compute these problems, we must do it in this order. Therefore, when we do this problem, we start within the parentheses.

(5^2 +6)–(7•4)+8

Inside the parentheses, we have an exponent. Since it's second, we compute it first. 

(25 +6)–(7•4)+8

Next, we can simplify the multiplication problem in the other set of parentheses.

(25 +6)–(28)+8

Simplify first parentheses:

31 - 28 + 8

Subtract

3 + 8 = 

11

Notice how we subtracted first. That's because when we do PEMDAS, addition, and subtraction, along with multiplication and division, are on the same level- so you can do them in any order. This doesn't go for anything else though unless it's obviously commutative.

Hope this helps!

The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of $ 1 1 3 . 0 0 $113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 4 5 % 45%45, percent. At what price should the manager sell the couch?

Answers

Original $= $113
% mark up= 45%

=original $ + (original $ * 45%)
=113 + (113 * 45%)
=113 + 50.85
= $163.85

ANSWER: The manager should sell the couch for $163.85.

Hope this helps! :)
The answer is $163.85

Complete the expansion of (a + b)6 with a = 1 and b = 0.3.
(dont add everything together)
(1 + 0.3)^6 = (____)^6 + 6(____)^5(____) + 15(____)^4(____)^2 + 20(____)^3(____)3 + 15(____)^2(____)^4 + 6(___)(___)^5 + (____)^6

Answers

(1+0.3)^6=(1)^6+6(1)^5(0.3)+15(1)^4(0.3)^2+20(1)^3(0.3)^3+15(1)^2(0.3)^4+6(1)(0.3)^5+(0.3)^6

(1+0.3)^6=1+6(1)(0.3)+15(1)(0.09)+20(1)(0.027)+15(1)(0.0081)+6(0.00243)+0.000729

(1+0.3)^6=1+1.8+1.35+0.54+0.1215+0.01458+0.000729

Answer:

[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]

Step-by-step explanation:

This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that

[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]

Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula

[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]

where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].

What is the length of one leg of the triangle

Answers

Answer:

Step-by-step explanation:

The length measure of the second leg of the right-angle triangle is 12 units.

What is the measure of the missing leg length of the triangle?

Given the parameter:

Hypotenuse = 15 units

Length of leg1 = 9 units

Length of leg2 = x

To determine the measure of the missing side length of the right triangle, we use the Pythagoras theorem.

It is expressed as:

( hypotenuse )² =  ( leg 1 )² + ( leg 2 )²

Plug in the given values:

( 15 )² =  ( 9 )² + ( leg 2 )²

Simplifying, we get:

225 = 81 + ( leg 2 )²

( leg 2 )² = 225 - 81

( leg 2 )² = 144

Take the square roots:

leg 2 = √144

leg 2 = 12 units

Therefore, the second leg measures 12 units.

The question is not complete, the complete question is:

A right triangle's leg is 9 and the hypotenuse is 15, What is the length of of the other leg of the triangle?

Learn more about trigonometric ratio here: https://brainly.com/question/28038732

#SPJ3

Dr. Clarence invested $5000 in an account that draws 3.2% interest, compounded annually. What is the total value of the account after 5 years?

Answers

Given that the amount invested was compounded annually, the total value of the investment after 5 years will be:
FV=P(1+r/100)^n
where:
FV=future value
p=principle
r=rate
n=time
hence
FV=5000(1+3.2/100)^5
FV=$5,852.865

A student rolls a number cube whose six faces are numbered 1 through 6. What is the sample space for this experiment? S = {2, 4, 6} S = {1, 2, 3, 4, 5, 6} S = {6} S = {1, 2, 3, 4}


HURRY PLEASE HELP

Answers

S={1,2,3,4,5,6}
hope this helps

Answer: {1, 2, 3, 4, 5, 6}

Step-by-step explanation:

Sample space is the set of all possible outcomes for a certain experiment.

Given : A student rolls a number cube whose six faces are numbered 1 through 6.

Then, the possible outcomes of rolling it = 1, 2, 3, 4, 5, 6

Then , the sample space for this experiment = set of all possible outcomes

= {1, 2, 3, 4, 5, 6}

annual college tuition and fees are 8000$. Books and other charges cost 1000$ per year. If Tony receives a $4500 scholarship each year, how much more will he need to pay for 1 year of college?

Answers

Your answer would be $9,000.
Work; add up the total including the new $4,500 scholarship. Then subtract $4,500 from that. You get an answer of $9,000.

$8,000+$1,000+$4,500=$13,000-$4,500=x
X=$4,500

whats the equation of the line?

Answers

Is there an attachment? I can’t help.

which pair of angles are corresponding angles
a. 1 and 2
b. 1 and 5
c. 2 and 7
d. 2 and 5

Answers

angles 1 and 5 are corresponding

I believe your answer is 1 and 5 as they maintain the same relative position, but they're not equal as they are not parallel to each other

Find the fifth term of an=3n-5

Answers

For the fifth term, n = 5.
Just replace n with 5 in the expression.
Then evaluate the expression.

[tex] a_n = 3n - 5 [/tex]

[tex] a_5 = 3(5) - 5 = 15 - 5 = 10 [/tex]

In a normal distribution, the mean is ____ it's mean and mode

Answers

In a normal distribution, the median (I think you meant to say) is equal to the mean and mode.

Final answer:

In a normal distribution, the mean, median, and mode are all the same, since it is symmetric around the mean. The standard deviation affects the shape of the distribution, and the empirical rule states that most values lie within two standard deviations of the mean. Differences in symmetry may cause the mean, median, and mode to diverge, with the mean being most affected by skewness.

Explanation:

In a normal distribution, the mean is equal to the median and mode, by definition. This is because the normal distribution, which is also known as the Gaussian distribution, is symmetrically shaped like a bell curve around the mean (μ). The mean indicates the center of the distribution and the point of symmetry, while the median divides the data such that half of the values are above it and half are below. The mode is the most frequently occurring value in the data set, and in a perfect normal distribution, it coincides with the mean and median.

The standard deviation (σ) is a measure of the spread of the distribution. If the standard deviation is increased, the curve becomes wider and flatter, while a decrease in σ makes the distribution steeper and narrower. Additionally, the location of μ on the X-axis can shift the entire graph to the left or right, but the shape of the graph remains the same. The empirical rule helps us understand that approximately 95% of values lie within two standard deviations from the mean.

Drawing from the collaborative exercise provided, by recording the heights and creating histograms with smooth bell-shaped curves, one can calculate the mean and identify how characteristics such as skewness affect the mean, median, and mode, especially in non-symmetric distributions. In these cases, the mean can be influenced by the direction of the skew more than the median, pulling it towards the tail of the distribution.

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