Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to verify that:
[tex]\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)[/tex]
Note that cot(x) = cos(x) / sin(x). Hence:
[tex]\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)[/tex]
Multiply:
[tex]\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:
[tex]\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Split:
[tex]\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Simplify:
[tex]\csc(x)-\sin(x)=\csc(x)-\sin(x)[/tex]
Problem 2)
We want to verify that:
[tex]\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Square:
[tex]\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:
[tex]\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out the sin²(x) from the denominator:
[tex]\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (perfect square trinomial):
[tex]\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (difference of two squares):
[tex]\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out a negative from the first factor in the denominator:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Cancel:
[tex]\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Distribute the negative into the numerator. Therefore:
[tex]\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}[/tex]
Alan and Margot each drive from City A to City B, a distance of 147 miles. They take the same route and drive at constant speeds. Alan begins driving at 1:40 p.m. and arrives at City B at 4:15 p.m. Margot’s trip from City A to City B can be described with the equation y = 64x, where y is the distance traveled in miles and x is the time in minutes spent traveling. Who gets from City A to City B faster?
Answer:
Margot gets from A to B faster
Step-by-step explanation:
Alan takes 2 hr and 35 min = 2. 58... hr
Margot takes 147/64 hr = 2.296.. hr
An example for my question before
Answer:
angle c is 82 degree because 82 degree and angle c are corresponding angles.
Step-by-step explanation:
note :corredponding angles are always equal.
the sum of co interior angle id 180 degree.alternate angle are equalthe sum of co exterior angle is 180 degreethe sum of alternate exterior angle is 180 degreeGuys I need help on all three please
Answer:
graph 1 proportional
graph 2&3 is non proportional
i think
A mountain has a 21-degree slope. The mountain reaches an altitude of 468 feet. If you hike to the top of the mountain, starting at sea level, how far will you hike?
Answer:
1306 feet
Step-by-step explanation:
sin∅ = opp/hyp
sin21 = 468/hyp
hyp = 468/sin21
hyp = 1305.920355304657206
Rounded
1306 feet
Find the perimeter of the triangle in terms of b.
I’m marking branliest
Answer:
7b - 2 = 6b
3b + 7 = 10b
6b + 6b + 10b +10b
12b + 20b
34b
A diagram shows a kite and its frame.
Answer:
indeed it does
Step-by-step explanation:
wheres the diagram exactly?
DUS is a 30°-60°-90° triangle with short leg SU. If SU = x, determine the
length of the long leg and the length of the hypotenuse.
Answer:
SD = 2x
UD = x[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The hypotenuse of a 30-60-90 triangle is 2 times the length of the shorter leg.
SU is the shorter leg = x
So, SD = 2x
The longer leg of a 30-60-90 triangle is [tex]\sqrt{3}[/tex] times the shorter leg.
So, UD = x[tex]\sqrt{3}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
In a 30-60-90 triangle the sides are in the ratio 1:√3:2 so if the shortest side SU = x then the long leg = √3x and the hypotenuse = 2x.
If the data represented by the graph is normally distributed, what are the endpoints of the middle 68% of the data?
Answer: -1.8 and 11.4
Step-by-step explanation:
Trust me or don’t lol
Answer:
D. 2.6 and 7
Step-by-step explanation:
Plato course, did the test
please answer it soon
the ratio of sparrows to finches at the bird feeder is 3 to 4. If there were 12 sparrows, how many finches were there? explain
Answer:
16
Step-by-step explanation:
3 sparrows for every 4 finches
12 sparrows
12÷3= 4
4×4= 16
16 finches
PLEASE HELP ME I NEED THE ANSWER
Answer:
72 yd^3
Step-by-step explanation:
Answer:
Volume of this pyramid is 72.
How would I be able to solve for m
Answer:
131
Step-by-step explanation:
180-49= 131 therefore the answer is 131
A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost.
a. What equation models the total cost as a function of the number of T-shirts
ordered?
b. What does each variable represent?
c. What are the initial value and rate of change of the function? What does each
one represent?
Answer:
a)
We know that the total cost for the 150 shirts (plus a flat-rate of $25) is $1,825.
First, let's find how much costs each shirt.
First, the total cost of the shirts alone (neglecting the flat-rate) is:
$1,825 - $25 = $1,800
Then each shirt costs equal to the quotient of the cost and the number of shirts:
$1,800/150 = $12
Each shirt costs $12.
Then if you order T shirts, the total cost will be the flat-rate of $25 plus T times $12. The equation is:
C(T) = $25 + T*$12
b) C represents the cost
T represents the number of shirts ordered.
c) The initial value is the constant value, in this case, is $25
The rate of change is the coefficient that multiplies the independent variable (T), in the equation the rate of change is $12.
You are going to take a 10-question True/False test. How many ways can this test be answered if leaving questions blank is a viable option for each question?
Answer:
There are 59,049 different ways of answering the exam.
Step-by-step explanation:
The first thing we need to count is the total number of selections, then we need to count the number of options for each one of these selections. The total number of combinations will be equal to the product between all the numbers of options.
Here, the selections are each one of the 10 questions, so we have 10 selections.
And each one of these selections has 3 options (true, false, blank)
So, we have 10 selections with 3 options each, then the total number of combinations will be:
C = 3*3*3*3*3*3*3*3*3*3 = 3^10
C = 59,049
There are 59,049 different ways of answering the exam.
NO LINKS PLEASE
EXPLANATION REQUIRED
I WILL GIVE BRAINLIEST
DONT MINF MY PRO CROPPING. DEFF.
ALSO ITS NOT C
Answer:
B is the correct answer
Step-by-step explanation:
Subtract area of triangle from total area: 30 - 14 = 16Since the figure is a square, all the sides are equal. Therefore, we need to find the square root of 16: √16 = 4All the sides of the square are 4 cm longTo check, reverse application:4 x 4 = 1616 + 14 = 30need help asap will give brainlyest
Answer:
it in a is correct if im wrong it is B
Step-by-step explanation:
3x+5(2+x)=4x-7 help me out here?
Answer:
x = -17/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3x + 5(2 + x) = 4x - 7
Step 2: Solve for x
[Distributive Property] Distribute 5: 3x + 10 + 5x = 4x - 7[Addition] Combine like terms: 8x + 10 = 4x - 7[Subtraction Property of Equality] Subtract 4x on both sides: 4x + 10 = -7[Subtraction Property of Equality] Subtract 10 on both sides: 4x = -17[Division Property of Equality] Divide 4 on both sides: x = -17/4Answer:
x=[tex]\frac{-17}{4}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x+5(2+x)=4x−7
3x+(5)(2)+(5)(x)=4x+−7(Distribute)
3x+10+5x=4x+−7
(3x+5x)+(10)=4x−7(Combine Like Terms)
8x+10=4x−7
8x+10=4x−7
Step 2: Subtract 4x from both sides.
8x+10−4x=4x−7−4x
4x+10=−7
Step 3: Subtract 10 from both sides.
4x+10−10=−7−10
4x=−17
Step 4: Divide both sides by 4.
[tex]\frac{4x}{4}[/tex]=[tex]\frac{-17}{4}[/tex]
x=[tex]\frac{-17}{4}[/tex]
Triangle EFG is dilated by a scale factor of one half centered at (1, 1) to create triangle E'F'G'. Which statement is true about the dilation?
Answer:
A triangle is dilated by scale factor of 1/5
Step-by-step explanation:
A triangle has three sides. All the corresponding angles of triangle must be congruent. When the triangle is dilated it is rotated 90 degrees clockwise about its origin. The shape of the triangle will not change due to rotation of dilation.
Phillip helps his neighbors with various jobs. The table shows some jobs he did, the number
of hours he worked, and the amount he was paid. Is Phillip's pay proportional to the number
of hours he works?
Use the drop-down menus to explain your answer.
Job
Fixing a Fence
Pulling Weeds
Painting a Garage
Mowing a Yard
Hours Worked
5
4.5
6
1.5
Amount Paid ($)
75
54
78
18
Answer:
Is and his pay is always a multiple of 3
Step-by-step explanation:
I did the i-Ready
Answer: his pay is always a multiple of 3
Step-by-step explanation:
What is simplifying? I honestly know what it is, but I forgot the definition.
28.
If 30% of a number is 15, what is the number?
No links!!
I will report if say something wrong.
Will give brainlest
Answer:
50
Step-by-step explanation:
30% * n = 15
Change to decimal form
.30 *n = 15
Divide each side by .30
.30n/.30 = 15/.30
n =50
The number is 50
(1, -3) and (0,-1)
Equation: y=-2x-1
Slope:-2
Y-intercept:___?
Answer:
-1
Step-by-step explanation:
which ones plsss help
Simplify: (-7x - 5) - (-9x2 + 8x + 7). Choose the standard form of the answer.
Answer:
-15x - 12 + 9x^2
Step-by-step explanation:
(-7x - 5) - (-9x^2 + 8x + 7)
-7x - 5 + 9x^2 - 8x -7
-15x - 12 +9x^2
what is that 2 by the 9x
We will simplify the given expression to get:
9x^2 - 15x - 12
How to simplify the given expression?
Here we have the expression:
(-7x - 5) - (-9x^2 + 8x + 7)
To simplify it, we just perform the difference between the polynomials:
-7x - 5 + 9x^2 - 8x - 7
Now we group terms with correspondent powers of x:
9x^2 + (-7x - 8x) + (-5 - 7)
Now we simplify this:
9x^2 - 15x - 12
This is the quadratic equation simplified.
If you want to know more about simplification, you can read:
https://brainly.com/question/723406
A TV is priced at $475.25. There is a 7% sales tax rate. What is the sales tax for the TV in dollars and cents?
Answer:
$33.27
Step-by-step explanation:
What is the quotient of 6.58* 10^6 and 4.7×10^3
expressed in scientific notation?
Answer:
1.4 · 10³
Step-by-step explanation:
6.58 · [tex]10^{6}[/tex] ÷ 4.7 · 10³
6.58 ÷ 4.7 = 1.4
[tex]10^{6}[/tex] - 10³ = 10³
1.4 · 10³
Answer:
3.0926 x 10^10
Step-by-step explanation:
PLEASE HELP!!!
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget. Assume there are four weeks in a month.
If you think the data is inconclusive, explain why.
Answer:
Yes, they should increase the budget, because both 8 (Manuel) and 9 (Gretchen) are at least 8. 8 times per month is equivalent to 2 times per week.
Step-by-step explanation:
Answer from Plato
Hence, the answer is Plato.
What is the measurement?
Measurement is the process of finding a number that shows the amount of something. Time the ongoing sequence of events is time. We can measure time in seconds, minutes, hours, days, weeks, months, and years.
Here given that,
The club will base its decision about whether to increase the budget for the indoor rock climbing facility on
the analysis of its usage. The decision to increase the budget will depend on whether members are using
the indoor facility at least two times a week. Use the best measure of center for both of the original data
sets to determine whether the club should increase the budget.
As per this we get that,
Yes, they can increase the budget, because both Manuel has [tex]8[/tex] and Gretchen [tex]9[/tex] are at least [tex]8[/tex] and [tex]8[/tex] times per month is equivalent to the two times per week.
Hence, the answer is Plato.
To know more about the measurement
https://brainly.com/question/18076822
#SPJ2
Which leg is adjacent to angle L?
Answer:
1st answer is correct
Step-by-step explanation:
JL
hope this helps you
can I have the brainliest please?
?????????????????????????????????????????????????
Answer:
a) 0
b) -5
Step-by-step explanation:
We want to find f(x) = -4
This means find the value of x where y=-4
The value of x where y=-4 is x=0
Then find f(2)
This means find the value of y when x =2
The value of y when x=2 is -5
BRAIN TO CORRECT ANSWER!!
A clothing store conducts a survey to determine customer satisfaction.
Which of these methods will produce the most representative sample of the population of store customers?
A. Survey all customers as they arrive at the store on a Monday.
B. Survey all customers who purchase shoes
C. Survey every 10th customer to enter the store.
D. Survey all customers who leave the store without making a purchase
Answer:
C
Step-by-step explanation:
This method is the best because it will survey the customers under one condition : every 10. If the store gets a lot of customers, then this should be easier to do. The rest are mostly dependent on what they do and that influences the survey. However, C makes it so that every 10 people are surveyed.
Answer:
A isnt the correct answer. B doesnt seem reasonable because its one specific item. D means they arent exactly a customer since they didnt buy anything therefore the answer would be C
C is your answer.
not sure about it tho but its what i would put