Write the expression as either the sine, cosine, or tangent of a single angle
Answers
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
where in this case,
x = pi/3
y = pi/5
So,
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(pi/3-pi/5) = cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(pi/3-pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(5pi/15-3pi/15)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(2pi/15)
------------------------------------------------------------
The answer is cos(2pi/15) which can be written as [tex]\cos\left(\frac{2\pi}{15}\right)[/tex]
Related Questions
10 POINTS + BRAINLIEST ANSWER
The scatterplot below shows the distances and times spent traveling for 22 trips by a driver. What is the time, in hours, of the trip represented by the data point farthest from the line of best fit (not shown)
A. 4
B. 6
C. 8
D. 10
Answers
Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
(Edit I have to repost this question bc i really need it answered. I'm offering more points now!
Answers
Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)
There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
(5x ) (x ) = 5x^2 +
2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3
3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.
For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6. This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.
As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.
-------------------------------------------------------------------------------------------------
Problem # 2
Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
4x^2 (x - 3) (x - 4)
To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x )(x ) and guessing for which numbers will add to -7x and multiply to 12
Write a pair of integers whose sum gives
(a) a negative integer (b) zero
(c) an integer smaller than both the integers. (d) an
integer smaller than only one of the integers.
(e) an integer greater than both the integers,
Answers
Answer:
The pairs below satisfy the five questions. A) -2 & 1. -2 + 1 = -1 B) -2 & 2. -2 + 2 = 0 C) -1 & - 2. -1+ -2 = -3 D) -3 & 1. -3 + 1 = -2 E) 1 & 2. 1 + 2 = 3.
Step-by-step explanation:
hope this helps have an amazing day
sav meh pl0x ty fam
Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23
Shift 1
18
25
56
42
29
38
54
47
35
30
Shift 2
23
19
50
49
67
34
30
59
40
33
Shift 3
19
22
24
40
45
29
33
29
39
59
Shift 4
21
23
25
40
35
19
70
40
22
23
The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
A) Shift 1
B) Shift 2
C) Shift 3
D) Shift 4
Answers
Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23
To obtain the sample that is closest to the mean we shall proceed as follows:
Shift 1:
18,25,56,42,29,38,54,47,35,30
The mean of the sample is:
(18+25+56+42+29+38+54+47+35+30)/10
=374/10
=37.4
Shift 2:
23, 19, 50, 49, 67,34,30,59,40, 33
The mean is:
(23+19+50+49+67+34+30+59+40+33)/10
=404/10
=40.4
Shift 3:
Shift 3
19, 22, 24, 40, 45, 29, 33, 29, 39, 59
The mean of the values
(19+22+24+40+45+29+33+29+39+59)/10
=339/10
=33.9
Shift 4:
21, 23, 25, 40, 35, 19, 70, 40, 22, 23
The mean of the values is:
(21+23+25+40+35+19+70+40+22+23)/10
=318/10
=31.8
From the calculations, the sample that has mean that is close to population mean is Shift 2
barb is making a bead necklace. she strings 1 white bead, then 3 blue beaads, then 1 white bead, and so on. write the numbers for the first eight beads that are white. what is a rule for the pattern.,
Answers
Panel 1 is the answer choice
Panel 2 is the question
Answers
A = (0,s)
B = (r,0)
Add up the x coordinates to get 0+r = r. Then cut that in half to get r/2
Similarly, do the same for the y coordinates: s+0 = s ---> s/2
So the location of point D is (r/2, s/2)
Answer: Choice C
Which equations are true for x = –2 and x = 2? Check all that apply.
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0
Answers
equation 4
Answer:
x2 – 4 = 0
4x2 = 16
Step-by-step explanation:
Simplify by using fractional exponents.[tex] \sqrt[3]{ x^{2} } [/tex]
Answers
[tex] \sqrt[3]{ x^{2} } [/tex]
Converting radical sign to fractional exponent:
[tex] ( x^{2} )^{ \frac{1}{3} } [/tex]
Simplifying the expression, we get:
[tex] \sqrt[3]{ x^{2} } = x^{ \frac{2}{3} } [/tex]
Which equation is true for the value b = 2? 2b + 24 = 30 3b − 2 = 4 b + 4 = 8 2b − 3 = 0
Answers
Hope this helps.
Answer:
3(b – 2) = 24
Step-by-step explanation:
A recipe for punch says to use 4 1/2 of lemonade for each cup of ginger ale. If you use 1 2/5 cups of ginger ale, how much lemonade should you use?
Answers
What is the rule for the reflection?
Will mark brainliest!
Answers
Answer:
Option C is correct.
[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
Step-by-step explanation:
From the given figure:
Coordinate of Triangle ABC are:
A(-2, 1), B(-3, 4) and C(-4, 1)
And
Coordinate of Triangle A'B'C' are:
A'(1, -2), B'(4, -3) and C'(1, -4)
The rule of reflection across the line:
[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
then;
Apply the given rule of reflection on coordinate of triangle ABC
[tex]A(-2, 1) \rightarrow (1, -2) =A'[/tex]
[tex]B(-3, 4) \rightarrow (4, -3) =B'[/tex]
[tex]C(-4, 1) \rightarrow (1, -4) =C'[/tex]
Therefore, the rule of reflection used here is [tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?
Please round to the tenths place.
Please show work/steps and provide units with your answer.
Answers
Mark a line going from the base of the building to the person 34 feet.
Draw another line from the person to the top of the building. Label the angle between the two lines as 74o
Tan(74) = o / a
Tan(74) = o/34
o = 34*Tan (74)
o = 34 * 3.49
o = 118.6
The building is 118.6 feet tall.
Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
Answers
directrix y=-2
focus (2,6)
y=1/(2(6-(-2)) * (x-2)²+(6+(-2))/2
or y=(x-2)²/16+2
Compare the fraction by using the symbol < , <, or =. a. 4⁄9 _____ 5⁄9 b. 4⁄5 _____ 8⁄10 c. 7⁄12 _____ 7⁄15 d. 3⁄4 _____ 6⁄7
Answers
B. 4/5 = 8/10
C. 7/12 > 7/15
D. 3/4 < 6/7
Final answer:
To compare fractions, evaluate if they are equal or if one is greater by comparing the numerators and denominators.
a. 4/9 < 5/9
b. 4/5 = 8/10
c.7/12 > 7/15
d.3⁄4 < 6⁄7
Explanation:
In fractions, to compare two fractions, check if the fractions are equal, or if one is greater than the other by comparing the numerators and denominators.
a. 4/9 vs. 5/9: 4/9 < 5/9 since 5 is greater than 4.
b. 4/5 vs. 8/10: 4/5 = 8/10 since they are both equivalent fractions.
c. 7/12 vs. 7/15: 7/12 > 7/15 since 12 is greater than 15.
d. 3/4 vs. 6/7: 3⁄4 < 6⁄7 because converting to decimals, 3⁄4 is 0.75 and 6⁄7 is approximately 0.857, making 6⁄7 larger.
Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?
Answers
These problems are best done by rounding to easy numbers, then picking the closest value. Below I gave an example of how to round them and then picked the best answer.
1) 12 + 12 + 10 = 34 So 33.68 is the closest.
2) 94 - 6 = 88 So 87.42 is the closest.
3) 28 x 2 = 56 So 53.62 is the closest.
4) 60 / 100 = 0.6 So 0.641 is the closest.
5) 100 x 30 = 3000 So 355.12 is not reasonable.
What is the measure of ∠XBC?
1. m∠XBC = m∠BAC + m∠BCA
2. 3p – 6 = p + 4 + 84
3. 3p – 6 = p + 88
4. 2p – 6 = 88
5. 2p = 94
m∠XBC =
Answers
m∠ABC=180-[(p+4)+84]--------> 180-[p+88]=92-p
m∠ABC=(92-p)° equation 1
and
m∠ABC+(3p-6)=180----------m∠ABC=180+6-3p
m∠ABC=186-3p equation 2
(1)=(2)
(92-p)=186-3p-----------> 186-92=-p+3p--------------> 2p=94
p=47°
therefore
m∠XBC=(3p-6)°---------->(3*47-6)=135°
the answer is
m∠XBC=135°
The measure of an exterior angle of triangle is equal to the sum of measures of two interior angles of triangle that are not supplementary with this exterior angles.
In the case of this question this fact sounds as
m∠XBC = m∠BAC + m∠BCA (option 1).
Now if
m∠XBC=(3p-6)°m∠BAC=(p+4)°m∠BCA=84°,then
3p-6=p+4+84 (option 2),
3p-6=p+88 (option 3),
3p-p-6=p-p+88,
2p-6=88 (option 4),
2p-6+6=88+6,
2p=94 (option 5),
p=47.
Then m∠XBC=(3p-6)°=(3·47-6)°=135°.
Answer: m∠XBC=135°.
In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials.
7b + 3, -4b + 5 and -3+2
A.) 10b + 2
B.) 10
C.) 0
D.) b - 8
Please explain.
Answers
Selection B properly describes the sum.
Answer:
Terms containing b are added; terms not containing b are added. The sum of the b terms is 0, because 7-4-3 = 0. That leaves only the constant 3+5+2=10.
Selection B properly describes the sum.
Step-by-step explanation:
Which of these denominations in no longer made in the United States?
A. $1000
B. $50
C. $2
D. $100
Answers
Answer:
$1000
Step-by-step explanation:
the function f(x)=2^x and g(x)=f(x)+k. if k=2, what can be concluded about the graph?
the graph of g(x) is shifted vertically...
2 units to the left of the graph of f(x)...
Answers
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 2 ^ x
g (x) = f (x) + k
if k = 2
then,
the graph of g (x) is shifted vertically 2 units up
Answer:
the graph of g (x) is shifted vertically 2 units up
Answer:
Its shifted verticlly 2 and to the left 2.
Step-by-step explanation:
Its verticlly because when it says 2^x its going up if it said -2^x it would go down.
It goes left because it is 2^x=? so if you put it on the other side its negative which makes it to the left.
1. Given a || b , c || d, and . Find the measure of angles 1 through 12 in the complex figure.
Answers
To solve all of the angles that are listed you are going to have to set up and solve several equation involving supplementary angles and angles around traversals around parallel lines.
For example, you could set up the equation:
3 + 4 + 69 = 180
Also, angle 9 is 116 because they are alternate interior angles.
Also, angle 11 is 116 because the are corresponding angles.
Also, angle k can be solved with the equation: k + 12 + 90 = 180.
Good luck
In summary:
- Angle 1 = Angle 2 = Angle 3 = Angle 4 = 69°
- Angle 5 = Angle 6 = Angle 7 = Angle 8 = 116°
- Angle 9 = Angle 10 = 69°
- Angle 11 = Angle 12 = 116°
Let's analyze the complex figure with parallel lines and transversals. We have two parallel lines, a and b, intersected by two transversals. I'll break down the problem step by step:
1. Angle 1: This angle is formed by the intersection of a and the transversal. It is an **alternate interior angle** with the angle measuring 69°. Therefore, **Angle 1 = 69°**.
2. **Angle 2**: It is also an alternate interior angle with the same measure as **Angle 1**. Hence, **Angle 2 = 69°**.
3. **Angle 3**: This angle is formed by the intersection of **b** and the transversal. It is a **corresponding angle** to **Angle 1**. Therefore, **Angle 3 = 69°**.
4. **Angle 4**: It is a corresponding angle to **Angle 2**. Thus, **Angle 4 = 69°**.
5. **Angle 5**: This angle is formed by the intersection of **c** and the transversal. It is an **alternate interior angle** with the angle measuring **116°**¹. Therefore, **Angle 5 = 116°**.
6. **Angle 6**: It is also an alternate interior angle with the same measure as **Angle 5**. Hence, **Angle 6 = 116°**.
7. **Angle 7**: This angle is formed by the intersection of **d** and the transversal. It is a **corresponding angle** to **Angle 5**. Therefore, **Angle 7 = 116°**.
8. Angle 8: It is a corresponding angle to Angle 6. Thus, Angle 8 = 116°.
9. Angle 9: It is a vertical angle to Angle 1. Therefore Angle 9 = 69°.
10. Angle 10: It is a vertical angle to Angle 2. Thus Angle 10 = 69°.
11. Angle 11: It is a vertical angle to Angle 5. Therefore, Angle 11 = 116°.
12. Angle 12: It is a vertical angle to Angle 6. Thus, Angle 12 = 116°.
On a map, 2 inches represents 60 miles. What part of an inch represents 12 miles? Please show how you get you answer.
A. 1/10in.
B. 1/5in.
C. 2/5in.
D. 1/2in.
Answers
if 2 inches are 60 miles then 12 miles is a fifth of 2 inches.
The formula for the area of a triangle is A = 1/2bh, where b is the length of the base and h is the height. The equation solved for h is h =2a/b The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = . Find the height of a triangle that has an area of 30 square units and a base measuring
12 units. 3 units 5 units 8 units 9 units
Answers
the answer is 5 units i know this because i just took a test with this question
A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.
Answers
7² + x² = 25²
x² = 25² - 7²
x² = 576
x = 24
The adjacent side of the triangle is 24
Given that sin A = [tex] \frac{7}{25} [/tex]
Since sin A = [tex] \frac{o}{h} [/tex]
We can conclude that o = 7 and h = 25
cos A = [tex] \frac{a}{h} [/tex]
cos A = [tex] \frac{24}{25} [/tex]
[tex] \sin A = \dfrac{7}{25} = \dfrac{opp}{hyp} [/tex]
[tex] a^2 + b^2 = c^2 [/tex]
[tex] a^2 + 7^2 = 25^2 [/tex]
[tex] a^2 = 625 - 49 [/tex]
[tex] a = \sqrt{576} [/tex]
[tex] a = 24 [/tex]
[tex] adj = a = 24 [/tex]
[tex] \cos A = \dfrac{adj}{hyp} [/tex]
[tex] \cos A = \dfrac{24}{25} [/tex]
Find the amount paid for the loan.
$2400 at 10.5% for 5 years
Answers
Final answer:
$3,919.24
Explanation:
To calculate the total amount paid for a loan of $2,400 at an interest rate of 10.5% over 5 years, we will assume the interest compounds annually for simplicity. The formula to find the future value of a loan including interest is P(1 + r)^n, where P is the principal amount ($2,400), r is the annual interest rate (10.5% or 0.105), and n is the number of years (5).
Plugging the numbers into the formula gives us $2,400(1 + 0.105)^5. Calculating this gives us approximately $3,919.24. Therefore, the total amount paid for the loan over 5 years would be $3,919.24.
To find the amount paid on a $2400 loan at 10.5% interest for 5 years, calculate the simple interest and add it to the principal. The total interest is $1260, bringing the total repayment amount to $3660 over 5 years.
To find the amount paid for the loan of $2400 at 10.5% interest for 5 years, one would typically use the formula for the compound interest or an installment payment plan depending on whether the loan is paid off in a lump sum at the end of the term or through regular payments over the term. However, you have not specified the method of repayment (lump sum or installments), so let's consider a simple interest scenario which is often used for short-term loans.
The simple interest can be calculated as:
I = PRT
Where:
I = Interest
P = Principal amount ($2400)
R = Annual interest rate (10.5% or 0.105 in decimal)
T = Time in years (5)
Using the formula:
I = $2400 × 0.105 × 5 = $1260
Therefore, the total interest paid over 5 years is $1260. To find the total amount paid for the loan, add the interest to the principal:
Total Amount Paid = Principal + Interest
Total Amount Paid = $2400 + $1260 = $3660
The borrower would have to pay a total of $3660 after 5 years.
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Question 2(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "some number to the power of 5?"
5x
x5
5x
x + 5
Question 3(Multiple Choice Worth 3 points)
(06.02)
Translate the algebraic expression shown below into a verbal expression.
Fraction with variable x in numerator and 10 in the denominator.
The sum of ten and some number
The quotient of some number and ten
The product of some number and ten
The difference of ten and some number
Question 4(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "eight less than some number?"
8 − b
b − 8
Fraction 8 over b
Fraction b over 8
Question 5(Multiple Choice Worth 4 points)
(06.02)
Which verbal expression best describes the algebraic expression 4x ÷ 6?
The sum of four and some number divided by six
The quotient of four times some number and six
The product of some number and six divided by four
The quotient of four and some number times six
Question 6(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "seven more than the product of three and some number?"
7 + 3 + x
3 + 10 ÷ x
3x + 7
3 + 7x
Answers
2. x5
3. The quotient of some number and ten
4. b − 8
5. The quotient of four times some number and six
6. 3x + 7
1. x and -4 are multiplied by 12
2 raided to this 5th power is an exponent
3 quotient means division
4 less than means subtraction
5 division means quotient, list numerator first then the denominator
6 product of is multiplication and more is an addition.
I am just going to answer the first one
1. 12(x - 4)
What would a monthly payment be on a purchase of $12000 car at 4.9% for 5 years?
Answers
Answer: it's 225.41 but your answer helped!
Step-by-step explanation:
The monthly payment will be $249
Firstly, we will calculate the simple interest which will be:
= PRT/100
where,
P = principal = $12000
R = rate = 4.9%
T = time = 5 years
Simple Interest = PRT/100
= ($12000 × 4.9 × 5)/100
= $294000/100
= $2940
Then the total amount to be repaid will be: = Principal + Interest
= $12000 + $2940
= $14940
We'll convert 5 years to months and this will be: = (5 × 12) = 60 months.
The monthly payment will then be:
= $14940/60
= $249
In conclusion, the monthly payment will be $249
Read related link on:
https://brainly.com/question/18860244
A club has members from three grades. It has 36 members from sixth grade, 24 members from seventh grade, and 30 members from eighth grade. What is the ratio of the club's seventh graders to eighth graders?
Answers
Answer:
the correct answer is 4/5!
have a great day!
simplify: 27k^5m^8/(4k^3)(9m^2)
Answers
You are paying 11% interest on a credit card balance of $2,000. Which of the following best estimates the interest you are paying each month?
a) $11.00
b) $13.33
c) $15.33
d) $18.33
Will fan and medal,
Answers
$220/12 (months in a year)=$18.33
d) $18.33
PLEASE PLEASE PLEASE PLEASE HELP ME!
suppose ruth ann has 3 routes she can travel between the school to the library and 5 routes from the library to her home. how many routes are there from ruth anns school to her home with a stop at the library.
a. 9
b. 60
c. 15
d. 25
Answers
There are 3 routes between school and the library.
There are 5 routes from the library to her home.
Therefore, there are 3 x 5 = 15 total routes