I REALLY NEED THIS ONE IT'S MY LAST ONE.
Verify the identity. Justify each step.
please help and show your work.
Answers
[tex]\bf \cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}-\frac{cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}+\frac{cos(\theta )}{sin(\theta )}}\implies \cfrac{\frac{1}{cos(\theta )}}{\frac{1-cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1+cos(\theta )}{sin(\theta )}} \\\\\\ \cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1-cos(\theta )}-\cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1+cos(\theta )}[/tex]
[tex]\bf \cfrac{sin(\theta )}{cos(\theta )[1-cos(\theta )]}-\cfrac{sin(\theta )}{cos(\theta )[1+cos(\theta )]} \\\\\\ \cfrac{sin(\theta )[1+cos(\theta )]~-~sin(\theta )[1-cos(\theta )]}{cos(\theta )[1+cos(\theta )][1-cos(\theta )]} \\\\\\ \textit{notice that }[1+cos(\theta )][1-cos(\theta )]\textit{ is a difference of squares}[/tex]
[tex]\bf \cfrac{\underline{sin(\theta )}+sin(\theta )cos(\theta )\underline{-sin(\theta )}+sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]} \\\\\\ \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]}\\\\ -------------------------------\\\\ \textit{recall that }sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\qquad thus\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[sin^2(\theta )]}\implies \cfrac{2\underline{sin(\theta )cos(\theta )}}{\underline{cos(\theta )sin(\theta )} sin(\theta )}\implies \cfrac{2}{sin(\theta )} \\\\\\ 2\cdot \cfrac{1}{sin(\theta )}\implies 2\cdot csc(\theta )\implies 2csc(\theta )[/tex]
Related Questions
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
(A.) {(-8, -12)}
(B.) {(3, 2)}
(C.) {(-4, 6)}
Answers
x + 2y = 7
+ x - 2y = -1
—————————
2x = 6
Now that we eliminated 2y because they cancel out, we are left with 2x = 6. Divide both sides by 2 in order to get x.
The answer is: x = 3.
Now that we know the numerical value of x, all we have to do is plug x into either system of equation in order to find the numerical value of y.
x + 2y = 7
3 + 2y = 7
2y = 4
y = 2
The solution to the problem is (3, 2).
Final answer:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 is found by eliminating y, yielding x=3 and y=2, which is option B, (3, 2).
Explanation:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 can be found by adding or subtracting the two equations to eliminate one of the variables. By adding the two equations, we eliminate y and get 2x = 6, which results in x = 3. Substituting x = 3 back into either of the original equations yields y = 2. Therefore, the solution to the system is (3, 2), which corresponds to option B.
Multiply. (−4−7i)(3−5i)
Answers
Explanation: Use FOIL
-4*3-4(-5i)-7i*3-7i(-5i)
Simplify and combine like terms
=-47-i
Simplifying the problem would equal -47 - i
I hope this helps! :>
***PLEASE HELP*** ***50 POINTS***
Construct a system of two linear equations where (−2, 3) is a solution to the first equation but not to the second equation, and where (5, −2) is the solution to your system.
You need to write the equations of your system and graph them on the same graph.
Explain how your graph shows that your system satisfies the 2 required conditions.
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see attached picture:
Math quest after a winter storm, the depth of the snow on cherry street was 10 \text{ cm}10 cm10, space, c, m. but then, the snow started melting at a rate of \dfrac{1}{3} \text{ cm}31 cmstart fraction, 1, divided by, 3, end fraction, space, c, m per hour.what was the depth of the snow on cherry street after 333 hours?
Answers
We are given that the initial depth of snow is 10 cm while the rate of melting is 1/3 cm per hour. So the melted ice after 3 hours is:
melted = (1/3 cm/hr) * 3 hours = 1 cm
Hence the depth left is:
depth = 10 cm – 1 cm = 9 cm
Answer:
9 cm
Answer:
9 cm.
Step-by-step explanation:
Let x be the number of hours.
We have been given that after a winter storm, the depth of the snow on cherry street was 10 cm. Then, the snow started melting at a rate of [tex]\frac{1}{3}[/tex], so the snow melted in x hours will be [tex]\frac{1}{3}x[/tex].
Since initially there was 10 cm of snow, so the depth of snow after x hours will be:
[tex]10-\frac{1}{3}x[/tex]
To find the depth of snow after 3 hours we will substitute [tex]x=3[/tex] in our expression.
[tex]10-\frac{1}{3}\times 3[/tex]
[tex]10-1[/tex]
[tex]9[/tex]
Therefore, the depth of the snow on cherry street after 3 hours will be 9 cm.
Assume that the set s has 8 elements. how many subsets of s have at most 2 elements?
Answers
The subsets of S that have 0, 1 or 2 elements include C(11,0) empty set, (C11,1) 1-element sets and (C11,2) 2-element sets.
C(11,0) = 11! / 0! 11! = 11! / 1×11! = 1
C(11,1) = 11! / 1! 10! = 10!×11 / 1×10! = 11
C(11,2) = 11! / 2! 9! = 9!×10×11 / 2×9! = 10×11/2 = 55
The total number of subsets of S that have at most 2 elements is
1 + 11 + 55 = 67
If 40% of a given number is 8, then what is 15% of the given number?
Answers
0.40x = 8
x = 8 / 0.40
x = 20....so 20 is the given number
what is 15% of 20...
0.15(20) = 3 <==== ur answer
Solve 10x-3=6x+85 give a reason to justify each statement
Answers
4x = 88
x = 22
10x-3 = 6x+85
add 3 to each side
10x=6x+88
subtract 66x from each side
4x = 88
divide 88 by 4 to get x
x - 88/4 = 22
x = 22
six times the reciprocal of a number equals 2 times the reciprocal of 6. find the number.
Answers
6x/1 = 1/3
6x/1 * 1/6 = 1/3 * 1/6
x = 1/18
the reciprocal of 18 is 1/18
so the number is actually 18
@spongebobdid91
True?
Answers
Based on the exterior angle theorem, where the outside angle is the sum of the two remote interior angles
hope this helps
Morgan needs gas for her jeep, which gets 26 miles per gallon for gas mileage. When she stops at the gas station, she already has 10 gallons of gas in her tank. She buys more gas for $1.60 per gallon. If Morgan spends $21 on gas, what is the total distance she could travel? Round, if necessary, to the nearest tenth.
Answers
Answer:
The answer 601.3 miles.
Step-by-step explanation:
tenesa bought a 50 pound bag of flour for her bakery. she used 13.65 pounds of flour. how many pounds of flour are left in the bag?
Answers
work:
50 - 13.65 = 36.35
36 1/3 pounds of flour are left.
A cab charges 1.45 for the flat fee and 0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has 35 dollars to spend
Answers
.55m + 1.45 [less than or equal to] 35
subtract 1.45
.55m = 33.55
divide by .55
m = 61 miles or less
b: A cab charges 1.45 for the flat fee
a: and 0.55 for each mile
x: miles she can travel
y: total money she has (35$)
so: 35>0.55 x + 1.45
solve for x:
0.55 x < 35 - 1.45
x< 61
Two angles are supplementary. one angle measures 12 degrees less than 5 times the other. find the measure of each angle
Answers
a + b = 180
a = 5b - 12
5b - 12 + b = 180
6b - 12 = 180
6b = 180 + 12
6b = 192
b = 192/6
b = 32 <=== one angle is 32 degrees
a = 5b - 12
a = 5(32) - 12
a = 160 - 12
a = 148 <=== the other angle is 148
The measures of the two supplementary angles are 32 degrees and 148 degrees, respectively.
Explanation:The question is about finding the measures of two supplementary angles given the relationship between them. Supplementary angles are two angles whose measures add up to 180 degrees. If we let x be the measure of the first angle, then the measure of the second angle is 5x - 12 degrees, according to the problem statement.
Since the angles are supplementary, we can set up the following equation: x + (5x - 12) = 180. This simplifies to 6x - 12 = 180. Solving for x gives us x = 32, so the first angle measures 32 degrees.
Substitute x = 32 into the equation for the second angle gives us: 5x - 12 = 5(32) - 12 = 148 degrees. Therefore, the two angles measure 32 degrees and 148 degrees, respectively.
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How many 3 digit positive integers are odd and do not contain the digit 5?
Answers
Assume n=a*100+b*10+c un integer positive odd with no 5.
a∈{1,2,3,4,6,7,8,9} ,#8
b∈{0,1,2,3,4,6,7,8,9},#9
c∈{1,3,7,9},#4
Number of integers searched: 8*9*4=288
A dime has the same value as 10 pennies.Marley bought 290 pennies to the bank.How many dimes did Marley get
Answers
How can you use distance and slope formulas to classify quadrilaterals?
Answers
Plz answer ASAPPP tyyy
Answers
890 - 870
20
Hope this helped!
the development of cars has pros and cons. the car has allowed for better transportation but it is also responsible for a great deal of pollution. which activity can help reduce through pollution through the use of new technology?
A)increasing taxes on cars that pollute the most
B)making an app that allows people to share rides
C)persuading people to use existing public transportation
D)building cars that can better withstand collisions
Answers
If tap and bre are supplementary and bre is its own complement, find the measure of tap. explain how you arrived at your answer
Answers
m∠bre + m∠bre = 90°
m∠bre = 45°
Then, for the relationship of bre and tap, we have the equation,
m∠bre + m∠tap = 180°
45° + m∠tap = 180°
m∠tap = 135°
The measure of tap is equal to 135°.
Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function? It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable. It is nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.
Answers
Answer:
It is nonlinear because linear functions increase or decrease at the same rate.
Step-by-step explanation:
A linear function is a function with a constant rate of change. This means it increases or decreases at the same rate.
Since this function decreases quickly and then more slowly, it does not have a constant rate of change; it is not linear.
Answer:
D
Step-by-step explanation:
edge 23
Find the equation in standard form of the line with slope − 4 7 -47 that passes through the point ( 2 , 5 ) (2,5)
Answers
y = mx + b
where m = the slope
b = y-intercept
The slope is -47, therefore
y = -47x + b
The line passes through (2,5), therefore
-47*2 + b = 5
-94 + b = 5
Add 94 to each side.
b = 5 + 94 = 99
The equation is y = -47x + 99
Answer: y = -47x + 99
A radio station plays 3 1/2 minutes of commercials every 1/4 hour. At this rate, how many minutes of commercials does this radio station play in one hour?
Answers
A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.
Answers
y= a(x - 2)^2 + 3 where a is some constant.
We can find the value of a by substituting the point (0.0) into the equation:-
0 = a((-2)^2 + 3
4a = -3
a = -3/4
so our equation becomes y = (-3/4)(x - 2)^2 + 3
The required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The parabola has vertex (2, 3) which is given in the question
Here h = 2,and k = 3
Substitute the values of h = 2 and k = 3 in the above equation
y - 3 = a(x - 2)²
y = a(x - 2)² + 3
If the parabola contains the point (0, 0)
Substitute the point (0, 0) in the above equation
0 = a((-2)² + 3
4a = -3
a = -3/4
Thus, the equation becomes y = (-3/4)(x - 2)² + 3
Hence, the required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
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Let f ( x ) = 2 x − 1 , g ( x ) = 3 x , and h ( x ) = x ^2 + 1 , what is g (h ( 24 ) ) ?
Answers
576+1= 577
g(577)= 577x3= 1731
At the beginning of the year Jason had $80 in his savings account. Each month he added $15 to his account. Write in expression for the amount of money and Jason saving account each month. Then use the expression to find the amount of money in his account at the end of the year
Answers
a model rocket is 3 inches long. the real rocket is 120 feet long. what is the unit rate that describes the relationship of the real rocket to the model rocket? a.360 ft/in. b.360 in./ft c.40 in./ft d.40 ft/in.
Answers
Which expression means 7 more than a number?
A.
d × 7
B.
d + 7
C.
d ÷ 7
D.
d – 7
Answers
whenever you hear a seven (or any other number) MORE THAN, think of adding that number!
Hope this helps :)
Factor polynomial 2x^2-11x+15
Answers
2x^2-11x+15
x^2-11x+30
(x-6)(x-5)
(x-6/2)(x-5/2)
(x-3)(2x-5)
Final answer: (2x-5)(x-3)
━━━━━━━☆☆━━━━━━━
▹ Answer
(2x - 5) * (x - 3)
▹ Step-by-Step Explanation
2x² - 11x + 15
Rewrite:
2x² - 5x - 6x + 15
Factor:
x(2x - 5) - 6x + 15
x(2x - 5) - 3(2x - 5)
Factor:
(2x - 5) * (x - 3)
Hope this helps!
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━━━━━━━☆☆━━━━━━━
Sam's bedroom has a perimeter of 46 feet. If the length of the bedroom is 11 feet, what is the width of the bedroom?
Answers
=24/2
= 12
HIJK is a rectangle. Find the value of x and the length of each diagonal. HJ=x and IK= 2x-7
Answers
By definition of rectangle, the diagonals are congruent or equal.
HJ=IK
x=2x-7
-x+x=2x-x-7
0=x-7
0+7=x-7+7
7=x and 2x-7=2 (7)-7=14-7=7
Diagonals are equal and are equal to 7
The value of x will be equal to 7 for the two diagonals HJ and IK.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.
Given that the length of each diagonal is HJ=x and IK= 2x-7
HJ and IK are diagonals.
By definition of the rectangle, the diagonals are congruent or equal.
HJ=IK
x=2x-7
-x+x=2x-x-7
0=x-7
0+7=x-7+7
7=x and 2x-7=2 (7)-7=14-7=7
For the two diagonals, the value of x is 7.
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