I need help with this practice from my trigonometry prep bookI have attempted this problem previously but I am not too sure if my answer is correct so I’d like more clarification on this

Answers

Answer 1

The function is given as,

$\tan \alpha\text{ = }\frac{-12}{5}\text{ }(\text{ }\alpha\text{ lies in the second quadrant )}$

Calculating the value of h ,

$\begin{gathered} h\text{ = }\sqrt[]{12^2+5^2} \\ h\text{ = }\sqrt[]{144\text{ + 25}} \\ h\text{ = 13} \end{gathered}$

Calculating the values of the remaining functions :

$\begin{gathered} \sin \text{ }\alpha\text{ = }\frac{12}{13} \\ \cos \alpha\text{ = }\frac{-5}{13} \end{gathered}$

Now,

calculating the value of x ,

$\begin{gathered} x\text{ = }\sqrt[]{5^2-3^2} \\ x\text{ = }\sqrt[]{25\text{ -9 }} \\ x\text{ = }\sqrt[]{16} \\ x\text{ = 4} \end{gathered}$

$\sin \text{ }\beta=\text{ }\frac{-4}{5}$

Calculating the required functions ,

$\cos \alpha\cos \beta\text{ + sin}\alpha\sin \beta\text{ = cos(}\alpha-\beta)$

Therefore,

$\begin{gathered} \cos (\text{ }\alpha-\beta)\text{ =( }\frac{-5}{13})(\frac{3}{5})\text{ + (}\frac{12}{13})(\frac{-4}{5}) \\ \cos (\text{ }\alpha-\beta)\text{ = }\frac{-15}{65}\text{ }\frac{-\text{ 48}}{65} \\ \cos (\text{ }\alpha-\beta)\text{ = }\frac{-15\text{ - 48 }}{65} \\ \cos (\text{ }\alpha-\beta)\text{ = }\frac{-63}{65} \end{gathered}$

Thus the required answer is ,

$\cos (\text{ }\alpha-\beta)\text{ = }\frac{-63}{65}$

Related Questions

For every hour Sonia worked, she hand made 2 seashell necklaces for her gift shop. Graph and write an equation that describes the relationship.

Answers

Answer:

y=2x

Step-by-step explanation:

Let y be the number of necklaces. Let x be the hours she worked.

So the equation will be y=2x.

So if she worked 2 hours then its 2×2=4.

The value of y varies directly with x. If x=8 then y=80. What is the value of x when y = 120?

Answers

We know that y varies directly with x, this means that:

$y=kx$

If x=8 and y=80, then:

$\begin{gathered} 80=8k \\ k=\frac{80}{8} \\ k=10 \end{gathered}$

Hence:

$y=10x$

Now, if y=120, we have:

$\begin{gathered} 120=10x \\ x=\frac{120}{10} \\ x=12 \end{gathered}$

Therefore, if y=120 than x=12.

John and Jill collect 280 stamps. Out of this John collected three time as many as
Jill. How many stamps did Jill collected?

Answers

Answer:

Jill collected 70 Stamps

John collected 210 Stamps

Step-by-step explanation:

280/4=70

Please allow me to know if my answer helped you with a thank you!

<3Miss Hawaii

If Samantha moved point A 9 units down and 6 units to the right, at what point would she end up?

Answers

Based on the transformaion of point A, the coordinate of the point she would end up is (3, -4)

How to determine the point she would end up?

The complete question is added at the end of this solution

From the question, we have the following point

Starting point = (-3, 5)

The movement is given as

9 units down and 6 units to the right

The above can be represented mathematically as

(x, y) = (x + 6, y - 9)

When the above translation is applied on point A, we have the following equation

A' = (-3 + 6, 5 - 9)

Evaluate the sum and he difference in the above equation

A' = (3, -4)

Hence, the coordinate of the point she would end up is (3, -4)

Answers

Answer:

The answer that describes the pair of angles is Acute

Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.

If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.

Answers

The number 100 would land in column 2

The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In which row would the number 100 land?

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

The location of 100 in rows of 6 numbers

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Predicting the row and column 100 will land

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

Answers

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

In given figure AB is the diameter of circle. If ∠CAD = 32° and ∠CPB = 28°. Find ∠CDA.

Answers

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

use vieta's therom to solve each problem. the difference of two solutions of x^2-17x+c=0 is 1. find c

Answers

Using Vieta's Theorem the value of c = 72.

What is the Vieta Theorem?

Suppose we have a quadratic equation, in the following format:

ax² + bx + c, were a, b, and c are constant.

The roots are p and q.

As, The Theorem states that:

p + q= -b/a

pq= c/a

We have given the polynomial x²-17x+c=0

So, a= 1, b= -17

Since the difference of the solutions is 1, we have that:

p -q= 1

p = 1+ q

Now, using p + q= -b/a

1 + q + q= -(-17)/1

2q +1 = 17

2q= 16

q= 16/2

q= 8

and, p = 1+ q= 9

Again pq = c/a

8 x 9 = c/1

c= 72

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03 Multiple Choice
Select all of the expressions that are equivalent to (9x+6)-(8x-4).
M. 2(x + 1)
P. 2x+6
R. 2x + 2
S. 2(x + 3)
T.
8x
OE
0/20

Answers

Answer:

The answer is (x + 10)

Step-by-step explanation:

(9x + 6) - (8x - 4)

9x + 6 - 8x + 4

Rearrange it

9x - 8x + 6 + 4

Combine like terms

x + 10

Thus, The answer is (x + 10)

2x+2(3x-2)+4-2(3x+8)

Answers

Answer:

-14

Step-by-step explanation:

Answer:

2x - 16

Step-by-step explanation:

2x + 6x - 4 + 4 -6x - 16 = 2x - 16

What number is the opposite of 35?

Answers

Answer:

I believe its -35

Step-by-step explanation:

negatives are opposites or positives lmk ig I'm wrong

What single transformation maps ABC onto ABC?; Which rigid transformations can map triangle ABC onto triangle Fed?; What are the rigid transformations that will map โณ ABC to โณ DEF ?; Which pair of triangles can be proven congruent by the HL theorem?; Which rigid transformation S can map Triangleabc onto Triangledec ?

Answers

Single transformation maps ABC onto A'B'C' is reflection.

Given :

Reflection the single transformation maps ABC onto A'B'C' is reflection .

The rigid transformations can map triangle Δ ABC onto triangle Δ FED is reflection then translation .

The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .

pair of triangles can be proven congruent by the HL theorem is rotation then translation .

rigid transformation S can map Triangle abc onto Triangle dec is reflection then rotation .

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How many quarts of water does Zahara need to add to keep the consistency the same? Complete the ratio square.

Answers

ANSWER:
6 quarts

EXPLANATION: 6 quarts of water to keep the consistency the same

If you buy 10 pounds of lettuce for $70, what is the rate which one pound of lettuce costs?

Answers

Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

What is the measure of MBT?

Answers

$\\ \sf\longmapsto 17x-6=5x+18$

$\\ \sf\longmapsto 17x-5x=18+6$

$\\ \sf\longmapsto 12x=24$

$\\ \sf\longmapsto x=\dfrac{24}{12}$

$\\ \sf\longmapsto x=2$

Now

$\\ \sf\longmapsto \angle{MBT}$

$\\ \sf\longmapsto 5x+18$

$\\ \sf\longmapsto 5(2)+18$

$\\ \sf\longmapsto 10+18$

$\\ \sf\longmapsto 28$

Answer:

m∠MBT = 28°

Step-by-step explanation:

BN is an angle bisector. This makes ∠NBM and ∠MBT equal.

$17x-6=5x+18\\12x-6=18\\12x=24\\x=2$

Finally, substitute the value for the variable.

$5(2)+18\\10+18\\28$

Therefore, m∠MBT = 28°.

help agian!!!!!!!!! i will fall

Answers

Answer:

This net could form a Pyramid

will have 5 faces 5 points and 5 vertices

Step-by-step explanation:

Jacob ran 4 miles on Monday, 4.5 miles on Tuesday, and 3 on Wednesday.
How many total miles did Jacob run?

Answers

11.5 miles ..........11.5

what led to the creation of the free-soil party?

A. To stop immigrants from entering the United States

B. To promote slavery across the West

C. To stop the spread of slavery

D. To achieve Manifest Destiny

Answers

Answer:

The answer is C

Step-by-step explanation:

brainliest plss

Kerry invited 23 friends to his pool party. They played a game where everyone had to separate into groups. Each group had the same number of children.The game could not be played with all 24 children in one group and each group had to have more than two children. Which of the following are ways that they could divide into groups? Choose all that apply.

Answers

Answer:

24:
6 of 4
or

8 of 3

Step-by-step explanation:

6x4=24
8x3=24

24 - 6 of 4 or 8 of 3

what number when divided 6 gives you the same number as 450 divided by 9

Answers

Answer:

300

Step-by-step explanation:

450 / 9 = 50

50 x 6 = 300

300 is your answer

Hope this helps!

A cylindrical cup with a base diameter of 4 inches and a height of 12 inches is filled with orange juice that occupies 67% of the cup. What is the volume of the orange juice in the cup?

Answers

radius=r=4/2=2in

Volume

πr²hπ(2)²(12)48π150.7in³

Volume of orange juice

67% of 150.70.67(150.7)100.969in³

Answer:

101.0 in³ = 1.656 liters

Step-by-step explanation:

Formulas

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

$\textsf{Diameter of a circle}=2r \quad\textsf{(where r is the radius)}$

Given dimensions of cylinder:

diameter = 4 inheight = 12 in

First, calculate the radius by halving the diameter:

$\implies \textsf{Radius }(r)=4 \div 2=2\: \sf inches$

Substitute the given values into the formula to find the volume of the cup:

$\begin{aligned}\textsf{Volume of a cylinder} & = \pi r^2h\\ \implies \textsf{Volume of the cup} & = \pi \cdot (2)^2 \cdot 12\\& = \pi \cdot 4 \cdot 12\\& = 48\pi \sf \:\:in^3 \end{aligned}$

The cup is filled with orange juice that occupies 67% of the cup. To find the volume of orange juice in the cup, multiply the found volume of the cup by 67%:

$\begin{aligned}\implies\textsf{Volume of orange juice} & = 67\% \textsf{ of }48 \pi \\\\& = \dfrac{67}{100} \cdot 48 \pi \\\\& = \dfrac{3216}{100} \pi \\\\& = 101.0336197...\\\\& = 101.0\:\: \sf in^3\:(nearest\:tenth) \end{aligned}$

Liquid is usually measured in liters.

To convert cubic inches to liters, multiply by 0.016387064:

$\implies \sf 101.0336197...in^3 \times 0.016387064 = 1.656 \: liters\:(3\:dp)$

a triangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square centimeters. find its slant height.

PLEASE ANSWER ASAP

Answers

Answer:the slant height of the triangular pyramid is approximately 11.4132 centimeters.

Trigonometry: Measure tal Excel In Opt. Mathematics - Book 9 ) If the number of degrees of a certain angle added to the number of gra same angle is 152, find the angle in degrees.

Answers

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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hooke's law describes an ideal spring. many real springs are better described by the restoring force (fsp)s

Answers

The mathematical expression for the work performed by the spring and the cubic term is W=3.3488J C=%3.4

The spring's and the cubic term's labor Question Parameters:

How much effort is required to compress this spring 15 cm

Take into account a spring with k = 250 N/m and q = 900 N/m3.

In general, the mathematical formula for the force is given as

(FSp)s=−kΔs−q(Δs)^3

Location of Work done

W = int dxF.

Hence

W=3.3488J

b)Where a cubic term is mathematically given as

C={0.1139}/{3.3488}

C=%3.4

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A bag of trail mix weighs 1.625 pounds. Round 1.625 to the nearest hundredth. please guys give me correct answer i am doing a exam

Answers

Answer: 1.63

The hundredth place is the SECOND number after the decimal point. Make sure to follow rounding rules of rounding up if the number behind it is 5 through 9 or down if the number is 0 through 4.

normally id say no cause ur doing an exam but ive lost my sense of academic integrity so the answer is 1.63

nearest hundredth is 2 numbers after decimal place so it would be 1.63 cause the next number after the 2 in 1.625 is 5 which means u have to round up so yea 1.63 id the correct answer

11. Which of the following are not meaningful?
(b) XXXI
(a) VXXIX
(C) XLIV
12. Write 'Divide the difference of 91 and 7 by 6' using brackets and solve.
(d) CXCLXV

Answers

The answer to question 11 is (d) CXCLXV. Roman numerals are not meaningful when they are repeated more than three times.

The answer to question 12 is [(91 - 7) ÷ 6] = 14.

532,8 g = kg? [1]
O 5,328 kg
O 5 328 kg
O 0,532 8 kg
O 53,28 kg
O None of the given answers

Answers

The answer is 0,532 8 kg

Explanation:

Convert from g to kg by dividing by 1000.

532,8/1000 = 0,532 8kg

I hope this helps!!

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values. g There is a _____% chance that the high temperature will exceed 100 degrees on an August day. Please give your answer as percent, rounded to the nearest whole percent (e.g. 5, 72).

Answers

Answer:

There is a 10% chance that the high temperature will exceed 100 degrees on an August day.

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:

$P(X > x) = \frac{b - x}{b - a}$

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values.

This means that $a = 98, b = 118$

Probability that it exceeds 100 degrees:

$P(X > 100) = \frac{100 - 98}{118 - 98} = 0.1$

0.1*100% = 10%.

There is a 10% chance that the high temperature will exceed 100 degrees on an August day.

At the opening of a new movie 45% of the people in the theater were children.There were 187 adults were in the theater.What was the total number of people at the movie?

Answers

The number of people at the movie is 340

How to determine the number of people at the movie

Let's represent the total number people at the movie as "x".

We know that the number of adults in the movie is 187 and the percentage of children is 45%

So we can write:

187 = (1 - 45%) * x

This gives

187 = 0.55x

To solve for x, we can divide both sides by 0.55:

x = 187/0,55

Evaluate

x = 340

Hence, the number of people is 340