If (tan^3 theta -1) / (tan theta - 1) - sec^2 theta +1 = 0, find cot theta.
a. -1 b.0 c. 1 d. sec theta
Answers
Check the attachment.
Hope it helps you :)
Answer:
Option A. [tex]cot\theta = -1[/tex]
Step-by-step explanation:
[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]
we have to the value of [tex]cot\theta[/tex]
We further solve the equation
[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex] [a³- b³= (a-b)(a² + b²+ ab)]
[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]
[tex]\frac{1}{cot\theta }=-1[/tex]
[tex]cot\theta = -1[/tex]
Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.
Related Questions
Which of the following is the correct way to write 6 * 6 * 6 as a base and exponent?
Answers
[tex] 6^{3} [/tex] .
6 to the 3rd power, or 6 cubed, would equal :
6 x 6 x 6 = 216.
Hope this helps.
One fifth the total of a number and 4 is 2, find the number
Answers
Answer:
-10
Step-by-step explanation:
(1/5)x+4=2
5(1/5)x+4=2)
x+20=10
x = -10
596.282 ×_____ = 5,962.82
A) 1
B) 10
C) 100
D) 1,000
Answers
5,962.82 ÷ 596.282 = 10
Traverion wants to find the answer to the question “how much money does the average college professor make?” He surveys 50 professors from the university in his hometown. Which best describes whether or not the results of his survey would represent the responses from the entire propulatiob of college professors?
Answers
Traverion's survey would not represent the responses from the entire population of college professors.
SurveyA survey is conducted in order to collect a piece of specific information from a group of people chosen from the entire population who denotes the entire population for those questions.
Given informationTraverion wants to find the answer to the question “how much money does the average college professor make?” He surveys 50 professors from the university in his hometown.
Traverion wants to know “how much money does the average college professor make?”, so, in the survey, he wants to know the average for the entire population.The information is been collected from his town only, therefore, the data represents the average college professor's salary for his town only.Hence, Traverion's survey would not represent the responses from the entire population of college professors.
Learn more about Survey:
https://brainly.com/question/13532910
the sum of two numbers equals 49.The sum of the larger number and twice the smaller number is 70. what are the numbers.
Tell me the steps!
Answers
[tex]x = 49 - y[/tex]
Substitute that into,
[tex]49 - y + 2y = 70 \\ y = 21[/tex]
Substitute that into,
[tex]x = 49 - 21 \\ x = 28[/tex]
Answer check :
[tex]21 + 28 = 49 \\ 28 + 2(21) = 28 + 42 = 70[/tex]
Answer : The numbers are 21 and 28.
Hope this helps. - M
The problem is solved using a system of equations to find that the two numbers in question are 21 and 28.
To solve the problem involving two numbers where the sum equals 49 and the sum of the larger number and twice the smaller number equals 70, we need to form a system of linear equations and solve for the unknowns. Let's denote the smaller number as s and the larger number as l.
The sum of the two numbers is 49: s + l = 49.The sum of twice the smaller number and the larger number is 70: 2s + l = 70.Subtract the first equation from the second to find the value of s.
2s + l - (s + l) = 70 - 49
Which simplifies to:
s = 21
Substitute the value of s into the first equation:
21 + l = 49
And solve for l:
l = 28
Therefore, the smaller number is 21 and the larger number is 28.
Jamie is 5 years older than Ella. Jamie's age is 11 years less than three times Ella's age. The system below models the relationship between Jamie's age (j) and Ella's age (e):
j = e + 5
j = 3e – 11
Which of the following methods is correct to find Jamie's and Ella's age? (4 points)
Solve j + 5 = 3j – 11 to find the value of j.
Write the points where the graphs of the equations intersect the x-axis.
Write the points where the graphs of the equations intersect the y-axis.
Solve e + 5 = 3e – 11 to find the value of e.
Answers
The correct method is to use the equation
e + 5 = 3e - 11
on solving, we get e = 8 and j = 13
Other methods are complicated.
Which expression repressents “6 more than x”?
Answers
Hope this helps I would appreciate brainliest
Short answer: C. x + 6
Why?
When you're referring to addition, you can use words like 'more than, higher than, added, etc.' In this case, we have 6 more than x, so the correct answer would be the one that shows addition, which is x + 6.
Hope this helped you! ♥
A bag is filled with marbles. You take out and mark 80 marbles. Then you put the marbles back in the bag and mix the marbles. In a sample of 20 marbles, 4 of the marbles are marked. About how many marbles are in the bag?
Answers
help me in 25 no...I am not getting
Answers
14.7 = 19.6t -4.9t²
4.9t² -19.6t +14.7 = 0 . . . . . put the equation in standard form
4.9(t² -4t +3) = 0 . . . . . . . . . factor out 4.9 to simplify the numbers
(t -1)(t -3) = 0 . . . . . . . . . . .. divide by 4.9 and factor
The solutions to this are ...
t = 1, t = 3
After 1 second, the ball will reach the height of 14.7 meters.
25b. This question asks you to find the value of t that make h = 0.
0 = 19.6t -4.9t² . . . . . . substitute the given numbers
0 = 4.9t(4 -t) . . . . . . . . factor
The solutions to this are ...
t = 0, t = 4
The ball will hit the ground after 4 seconds.
_____
As you can see from the graph below, a graphing calculator can be helpful for solving problems of this sort.
A survey shows that 67% of peanut butter lovers prefer chunky-style. Out of 850 people surveys, how many can be predicted to say they prefer chunky-style peanut butter?
Answers
All you have to do is make you % into a decimal is multiply by 850
Hope this helps :-)
I like to use this formula cause it's really useful when it comes to these problems:
Part Percent
________ = _________
Whole 100
So, you basically plug in the numbers into the equation, it's really easy:
??? 67%
________ = ________
850 100
Then, you cross multiply. 67% x 850 = 56,950 / 100 =
And the answer to your question is: 569.6 or rounded is 570.
Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x – 3)?
Answers
Answer:
(-6,0) and (3,0)
Step-by-step explanation:
we have the function [tex]f(x)=(x+6)(x-3)[/tex] and the x-intecept of the function will be when y=0 then:
[tex]f(x)=(x+6)(x-3)\longrightarrow 0=(x+6)(x-3)[/tex]
Then the result will be 0 when x=-6 or x=3
Kara and Steven are biking around a 1,800 kilometer path. They start biking from the same place, at the same time, and in the same direction. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take before Steven and Kara will be at the same place of the path next time?
Answers
Time taken before the cyclist are on the same sport will be found as follows:
time=distance/(relative speed)
distance=1800 km
given that the cyclist will be riding towards the same side, then
relative speed=(Steve's speed-Kara's speed)=30-15=15 km/h
thus time taken will be:
time=1800/15
=120 hours
Please help me!
Which of the following is the best definition of the sample space of a probability event?
Answers
Answer: D. The set of all possible outcomes
Step-by-step explanation:
The set of all possible outcomes is the collection of all possible outcomes of an experiment.In the theory of probability the sample space of an random experiment is the set of all possible results of that particular experiment.Therefore, the best definition of the sample space of a probability event is the set of all possible outcomes.
Solve the inequality and describe the solution set:
y-6 ≥ 12
Answers
You want to get the y only on one side of the equation. To get rid of the -6 you have to add 6 to both sides to even out the equation.
y-6≥12
+6 +6
y ≥18
Answer: The solution set is y≥18.
Step-by-step explanation:
Since we have given that
[tex]y-6\geq 12[/tex]
We need to first find the inequality and find the solution set.
[tex]y-6\geq 12\\\\y\geq 12+6\\\\y\geq 18[/tex]
So, the solution set for this would be all the values of y which is greater than 18.
i.e. y≥18.
A rectangle has vertices at these coordinates. (5, −3), (5, −8),(8, −3) What are the coordinates of the fourth vertex of the rectangle? Enter the coordinates in the boxes.
will give brainlest
Answers
Answer:
Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).
Step-by-step explanation:
Given Vertices of Rectangle are ( 5 , -3 ) , ( 5 , -8 ) , ( 8 , -3 )
To find: Coordinate of Fourth Vertex of the rectangle.
First, Plot all given three points on the graph.
Graph is attached.
We know that Opposite sides of the rectangle are equal and parallel.
Also All angles of rectangles are right angle.
So to satisfy these properties of rectangle.
4th coordinate must be on line x = 8 and y = -8.
⇒ Fourth coordinate = ( 8 , -8 )
Therefore, Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).
you flip two coins and roll a number cube what is the probability of flipping two tails and rolling as even number
Answers
P(even number) = 1/2
P(tail, tail, even) = (1/2) (1/2) (1/2) = 1/8
Answer: 1/8
so 1/2 x 1/2 = 1/4 probability of getting 2 tails
a single die has 3 even numbers so you have a 3/6 = 1/2 probability of getting an even number
multiply both together for probability of 2 tails and an even number: 1/4 x 1/2 = 1/8 probability
What is the value of x in the solution to this system of linear equations? 4x - 3y = 3
Answers
x-y=2
Multiply the bottom equation by -3
4x-3y=3
-3x+3y=-6
Add the two equations together
The y’s cancel each other out
So your left with:
X=-3
The value of x is -3
How many lawns were mowed?
What is the difference between the greatest amount and least amount of gasoline used to mow lawns?
Answers
11 lawns because there are 11 x’ s
What is the difference between the greatest amount and least amount of gasoline used to mow lawns ?
4/8 of to simplify it’s 1/2
factor 3x^3+3x^2+x+1
Answers
3x^3+3x^2+x+1= (3x^3+3x^2)+(x+1)=
3x^2(x+1)+(x+1)=
= (x+1)(3x^2+1)
Have a good day
3x²(x + 1) + 1(x + 1)
(3x² + 1)(x + 1)
Factored form: (3x² + 1)(x + 1)
An electrolyte solution has an average current density of 1 ampere per square decimeter (A/dm^2). What is the current density of the solution in A/m^2?
Answers
1 m = 10 dm
∴ 1 m² = 100 dm² ⇒⇒⇒ 1 dm² = 0.01 m²
For the given dimension
1 (A/dm²) = [tex] 1 \frac{A}{dm^2} = 1 \frac{A}{0.01 \ m^2} = 1 * \frac{1}{0.01 } \frac{A}{m^2} = 100 \ \frac{A}{m^2}[/tex]
note: 1/0.01 = 100
the density of electrolyte solution is 100 ampere per square meter
Step-by-step explanation:We know that the Average current density of the solution = 1 ampere per square decimeter and we need to find the average current density of the solution in ampere per square meter. So
x – y ≥ -4.
2x – y ≤ 5.
2y + x > 1
Answers
Explain why the equation 5z + 2 = 5z has no solution.
Answers
Answer : This is because when 5z minus 5z, it is nullified, with no way to determine the value of z. 5z - 5z = 0
That is why there is no solution for this equation.
Hope this helps. - M
Find sine cosine and tangent
Answers
SOHCAHTOA (used for reference).
[tex]Sin A = \frac{8}{10} = \frac{4}{5} \\Cos A = \frac{6}{10} = \frac{3}{5} \\Tan A = \frac{8}{6} = \frac{4}{3} \\Sin B = \frac{6}{10} = \frac{3}{5} \\Cos B = \frac{8}{10} = \frac{4}{5} \\Tan B = \frac{6}{8} = \frac{3}{4} \\[/tex]
What is 51-50.1? Explain your answer.
Answers
This was a basic subtraction problem.
Enter the value of m when the expression 13.5x+m is equivalent to 2.7(5x-3.6)
Answers
13.5x+m =2.7(5x-3.6)
13.5x+m =2.7*5x-2.7*3.6
13.5x+m=13.5x-9.72
if the expression (13.5x+m) is equivalent to 13.5x-9.72
then
m=-9.72
the answer is
m=-9.72
just answer question, No need to explain. THANKS
Answers
The -3 means it’s shifted to the right 3 units
The 4 means it shifted up 4 units
f (x) = x ^ 2
We have the following information:
Horizontal translations
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right
f (x) = (x-3) ^ 2
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = (x-3) ^ 2 + 4
Answer:
f (x) = (x-3) ^ 2 + 4
option C
simplify this expression 6q/20(q+r)
Answers
6q / 20 (q + r)
Rewriting the expression we have:
(6/20) (q / (q + r))
Simplifying we have:
(3/10) (q / (q + r))
Answer:
The simplified expression is given by:
(3/10) (q / (q + r))
Equation:
6q / 20 (q + r)
=(6/20) (q / (q + r))
Simplify it :
(3/10) (q / (q + r))
The simplified expression is given by:
(3/10) (q / (q + r))
The movie theater add 352 people in it.if the people split into eight even groups to watch different movies how many people Will watch each movie
Answers
So the answer is 44
Hope this Helps:)
Who can help me with this algebra 2 work Need help
Answers
Note:
log_a c=b can be written as:
aᵇ=c
hence:
1. log₄ 16=2
will be written in exponential as:
4²=16
2. 25^(1/2)=5
will be written in logarithmic form as:
log₂₅5=1/2
3. Which function represents exponential growth?
#N/B For an exponential function:
y=a(b)^x
when b>1 it exponential growth
when b<1 it is an exponential decay
F: y=1/20(4)ˣ
b=4>1
exponential growth
G: y=16(0.4)ˣ
b=0.4<1
exponential decay
H: 20(1/8)ˣ
b=1/8<1
exponential decay
I. y=8x³
The above function does not have a growth factor, thus
it is a polynomial function not an exponential function.
4. Solve log₄3+log₄x=log₄18
when we add log functions we can multiply them as follows:
log₄(3*x)=log₄18
the log₄ will cancel and we shall remain with:
3x=18
solving for x we get:
(3x)/3=18/3
thus
x=6
5. Solve log₇36x-log₇2=log₇9
Dividing log functions is like subtracting them, thus we shall have:
log₇(36x/2)=log₇9
simplifying this we get:
log₇ 18x=log₇9
log₇ will cancel because of the same base and we shall have:
18x=9
thus
x=9/18
x=1/2
Expand the following:
Remember:
Multiplying logs is the same as adding them
Subtracting logs is the same as dividing them
thus
6. log₃ 4xy
expanding the above give us:
log₃4+log₃x+log₃y
Answer: log₃4+log₃x+log₃y
7. log₅ (xy²)/3
expanding this gives us:
log₅x+log₅y²-log₅3
Answer: log₅x+log₅y²-log₅3
Condense the following logarithms:
Using the concept from 6 and 7 we shall have:
8. log₈2+log₈7-log₈x
condensing this will give us:
log₈[(2*7)/x]
simplifying gives us:
log₈(14/x)
9. log₇9+3log₇y-4log₇2
Condensing the above gives us:
log₇9+3log₇y-4log₇2
=log₇9+log₇y³-4log₇2
=log₇(9*y³)/2
=log₇(9y³/2)
a roll of one die has six possible outcomes. Use the product counting principle to determine the total number of outcomes for a toss of two die explain your response
Answers
There are 6 outcome for the first die and 6 outcomes for the second die. The fundamental counting principle states that to find the total number of outcomes of these independent events, we multiply:
6(6) = 36