Mathematics High School

Find the exact value of Cosine (alpha + beta) given sin Alpha = two-fifths for Alpha in Quadrant II and Cosine Beta = one-third for Beta in Quadrant IV.

Answers

Answer 1

The exact value of cos (α + β) is (4√2-21) / 15.

What is angle?

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Sin α = 2/5, and α is in second quadrant,

cos β = 1/3 , and β is in fourth quadrant

Since, α is in second quadrant, the value of cos α will be negative.

The value of cos α, by right angle triangle property,

cos α = -√21 / 5

Since, β is in the fourth quadrant, the value of sin β will be negative.

The value of sin β = - 2√2 / 3

Cos (α + β) = cos α.cos β - sin α. sin β

Substitute the values here,

Cos (α + β) = (-√21 / 5) . 1/3 - 2/5. ( - 2√2 / 3)

= -21/15 + 4√2/15

= (4√2-21) / 15

The value of cos (α + β) is (4√2-21) / 15.

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Answer 2

Answer:

Step-by-step explanation:

Related Questions

PLEASE HELP!!! 60 points will be rewarded to the person that answers this question correctly.

The two figures below have the same perimeter. What is the value of x?

1. Write an equation that can be used to represent the situation above

2. Solve the equation

3. Prove the solution by plugging it into both sides of the equation

Answers

Answer:

3 or 5

Step-by-step explanation:

Because follow the problem

Put x = 4 + y in slope-intercept form.

Answers

Answer:

y=x-4

Step-by-step explanation:

I graphed this out and got the equation.

6 blue slabs have a mean weight of 7 kg. 3 yellow slabs have a mean weight of 5 kg. 1 grey slab has a mean weight of 9kg. work out the mean of 10 slabs

Answers

Answer: 6.6kg

Step-by-step explanation:

6 blue slabs have a mean weight of 7 kg. The total weight of the 6 blue slabs will be:

= 6 × 7kg

= 42 kg

3 yellow slabs have a mean weight of 5 kg. The total weight of the 3 yellow slabs will be:

= 3 × 5kg

= 15kg

1 grey slab has a mean weight of 9kg.

To get the mean of the 10 slabs, we add their total weights together and divide by 10. This will be:

= (42kg + 15kg + 9kg)/10

= 66kg/10

= 6.6kg

Based on the information given the mean of 10 slabs is 6.6 kg.

Formulate

(9+5×3+6×7)/10

Calculate the quotient

9+15+6×7/10

9+15+42/10

Calculate the sum or difference

24+42/10

66/10

Reduce the fraction

33/5

Hence:

Mean=6.6 kg

Inconclusion the mean of 10 slabs is 6.6 kg.

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what is the equation of the graphed line?

Answers

Answer:

y=mx+b

Step-by-step explanation:

you need to find the y intercept and the slope in order to write the equation in y intercept form slope is the change of u over the change in x

PLS HELP ASAP I WILL GIVE BRAINLYEST...
20 Points...

Answers

Answer:

True

False

True

Step-by-step explanation:

What is 325.623 rounded to the nearest tenth

Answers

325.6 is your answer :

If the number that comes before it is smaller than 5, you keep the number the same. If it’s larger than 5, then you boost it up one. For example, if it was 325.683, you’d round that to 325.7.

Hope that helps!

Answer: 325.6

Step-by-step explanation: 6 is in the tenth place and you don't round up the two

Find the slope and y-intercept of the graph. y=5x-3

Answers

Answer:

Step-by-step explanation:

y=mx+b

your m is the slope and your b is the y-intercept

so for y=5x-3 your slope would be 5 and your y-intercept would be -3

The equation y = 5x - 3 represents a line with a slope of 5 and a y-intercept of -3.

How to Find the Slope and the Y-intercept of a Graph?

The equation of a graph can be expressed as y = mx + b, which is in the slope-intercept form. This means that:

m is the slope

b is the y-intercept of the graph.

The line described by the equation y = 5x - 3 has a slope of 5, meaning that as x increases by 1, y increases by 5. The y-intercept, represented by the constant term -3, indicates that the line intersects the y-axis at the point (0, -3).

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Plz help!!!!

5. (a) A vehicle travels 240km in 4 hours. Find Its average speed in km/h.

(b) How far does it travel between 1pm and 5pm?

(c) How long does it take to travel 100km at the speed in (a) above

Answers

Answer:

a) 60 km

b) if it means 1 pm to 5 pm than answer will be 240 again

c)100/60

A model of a tree is made using a scale of 1 inch = 25 feet. What is the height of the actual tree if the height of the model is 4 1/4 inches? Actual height of the tree is feet.

Answers

Answer: 4 1/4 inches = 106.25 ft

Step-by-step explanation:

1inch = 25 ft

4 inch = 100 ft

1/4 inch = 6.25 or 6 1/4

100+ 6.25= 106.25 ft

write and equation of the line that passes through the point (4, -2) and has a slope of -1/2.

Answers

Answer:

−

(

)

Step-by-step explanation:

The point-slope form of a linear equation is:

(

−

)

(

−

)

Where

(

)

is a point on the line and

is the slope.

Substituting the values from the point in the problem and the slope provided in the problem gives:

Answer:

y=-1/2x

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=-1/2(x-4)

y+2=-1/2x+4/2

y+2=-1/2x+2

y=-1/2x+2-2

y=-1/2x

What are the dimensions of the rectangle shown on the coordinate plane?

The answers for me to choose from is on the pictures.
please help running out of time

Answers

Answer:

answer might be part b of the answers

what is x
7x-21=4x-36

Answers

Answer:

x = -5

Step-by-step explanation:

WILL MARK BRAINLIEST SHOW ALL YOUR WORK

Answers

Answer:

y = 1/3x - 4

Step-by-step explanation:

the line crosses the y-axis at -4

To calculate the gradient of a straight line we choose two points on the line itself. From these two points we calculate: The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates)

If we take the points (9,-1) and (6,-2), we do:

-1-(-2) = 1

9-6=3

which gives 1/3

Answer:

y = 1/3x - 4

Y- intercept = -4

Slope = 1/3

Step-by-step explanation:

Y intercept is where the line intercepts/passes through the y axis

Slope is how many units it takes HORIZONTALLY (side to side) to go up ONE unit VERTICALLY (up down)

It took the line 3 horizontal units to go up 1 vertical unit. So you divide 1 by 3 which gives you 1/3

Select the correct graph of ABC

Giving brainliest

Answers

Answer:

I think it is B.

Step-by-step explanation:

pls make me brainliest and that is the only answer that matches each statement

Distance between y=2 and y=-6

Answers

Answer:

[2] +[-6]

2 + 6 = 8

Step-by-step explanation:

list three numbers that are larger than 20 but smaller than 50 and only have 2 factor

Answers

Answer:

23, 29, 31 I think. yeeeee good luck

Please hurry bb :) Please don't put the wrong answer if u don't know <3

Answers

The answer is bestbuy because at AT&T the phone would cost $809.10 and the phone at bestbuy would be $
799 and that’s less.

1. Place a value under the radical symbol to make the statement true.

Answers

Answer:

Step-by-step explanation:

2 cuberoot 6 is equal to

2^2 times 6 which is 24

What are the last 3 digits of 5 to the power of 2020?

Answers

Answer:625

Step-by-step explanation:

simply the following equations
a. -5(-3x - 2y +1)

b. 6(x + 3y -5)

Answers

15x + 10y -5

6x + 18y -30

Which of the following statements is true about the graphs of f(x) = 1 and g(x) = f(5x)?

a)The graph of g(x) is less steep than the graph of f(x).
b)The graphs of g(x) and f(x) have the same slope.
c)The graphs of g(x) and f(x) have different y-intercepts.
d)The graph of g(x) is steeper than the graph of f(x).

Answers

Answer:

okay i will answer but i dont see the question

Step-by-step explanation:

Gavin read 6 books in 3 months. If he reads at a constant rate, how many books did he read each month? Give your answer as a whole number or a FRACTION in simplest form.

Answers

Answer:

2 books in one month

Step-by-step explanation:

Answer:

2 books per month .

Step-by-step explanation :

6 divided by 3 = 2

So 1 book per month = 2 , 2 books per month = 4 , 3 per month = 6 ( counting by 2 )

Hope that helped :)

!!30 points!!
The container that
holds the water for
the foorball team s 1/3
full. After pouring in 12
gallons of water, it is
7/9 full.

After pouring in 12
gallons of water, it is
7/9 full. How many
gallons can the
container hold?

Answers

Your answer would be 27 Gallons.

Anwer is 27 gallons answered for your question

In a deli the ratio of ham subs sold to cheese subs sold in a day was 9:4. If 36 cheese subs were sold how many ham subs were sold?

Answers

Answer:

oolollololollolollo

Step-by-step explanation:

The number of ham subs sold is given by the proportion equation A = 81

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the number of ham subs sold be represented as A

Now , the proportion will be

The ratio of ham subs sold to cheese subs sold = 9 : 4

And , the number of cheese subs sold = 36

Substituting the values in the equation , we get

number of ham subs sold A / number of cheese subs sold = 9 / 4

On simplifying the equation , we get

A / 36 = 9 / 4

Multiply by 36 on both sides of the equation , we get

A = ( 9 x 36 ) / 4

A = 9 x 9

A = 81 ham subs

Therefore , the value of A is 81 ham subs

Hence , the number of ham subs sold is 81

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Steph is a baker.
She bakes 42 white rolls and 60 brown rolls.

Write the ratio of white rolls to brown rolls in its simplest form.
white rolls:brown rolls

Answers

Answer:

42:60

Step-by-step explanation:

Answer:

7:10

Step-by-step explanation:

Simplify the ratio until you can't divide it anymore

Replacing one regular light bulb with a
compact fluorescent bulb will save 151.56
pounds of carbon dioxide per year. If you
replace 25 regular light bulbs, then how
many pounds of carbon dioxide will you save
per year?

Answers

Answer:

3789 pounds of carbon dioxide

multiply 151.56 by 25

Answer:

3789

Step-by-step explanation:

edge 2020

answer the question below, 100 points (and brainliest if it lets me, im desperate)

Answers

It will take the diver 6.24 seconds

GIVING BRAINIEST EXPLAIN ANSWER

Answers

It’s a I’m doing this exact same thing in math too

In △ACD, if AC≅AD, m∠A = 3x − 4, m∠C = 5x + 1, and m∠D = 7x − 27, find x and the measure of each angle.

Answers

Answer: x= 14

A= 38

C= 71

D= 71

what property is 9+-9=0

Answers

I think it’s zero. Yeah I’m sure it’s zero

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