Is (3,8) a solution to the inequality 14x + 12y = 12?

First, recall that

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

so you just need to find cos(A) and sin(B).

Since both A and B end in the second quadrant, you know that

• cos(A) and cos(B) are both negative

• sin(A) and sin(B) are both positive

Then from the Pythagorean identity, you get

cos²(A) + sin²(A) = 1   ==>   cos(A) = -√(1 - sin²(A)) = -2√10/7

cos²(B) + sin²(B) = 1   ==>   sin(B) = +√(1 - cos²(B)) = √21/5

You'll end up with

cos(A - B) = (-2√10/7) (-2/5) + (3/7) (√21/5)

… = (4√10 + 3√21)/35

(which makes the last sentence in the question kind of confusing, because this expression doesn't get much simpler and it's certainly not a rational number)

The value of cos(A - B) is approximately 23/25

Given that A and B are in the second quadrant, we have

To find cos(A - B), we have to use trigonometric functions

cos(A - B) = cosAcosB + sinAsinB ...equation(i)

but

[tex]cos^2A + sin^2A =1 \\cos^2A = 1 - sin^2A\\cos^2A = 1 - (\frac{3}{7})^2 = 1 - \frac{9}{49}= cosA= -\frac{2\sqrt{5} }{7}[/tex]

Having the value of cos A, let's solve for cosB

cos B = -2/5

[tex]sin^2B = 1-cos^2B\\sin^2B = 1-(-\frac{2}{5})^2= 1-\frac{4}{25}\\sinB = \sqrt{\frac{21}{25} }=\frac{\sqrt{21} }{5}[/tex]

substituting the values if sinA, cosA, sinB, cosB into equation(i) above;

[tex]cos(A-B)=cosAcosB+sinAsinB\\cos(A-B)=(-\frac{2\sqrt{5} }{7})(-\frac{2}{5})+(\frac{3}{7})(\frac{\sqrt{21} }{5})\\cos(A-B)=\frac{3\sqrt{21}+4\sqrt{5} }{35} \\cos(A-B) = 23/35[/tex]

The value of cos(A-B) is given above

Learn more on trigonometric functions here;

https://brainly.com/question/4326804

Answer:

16

Step-by-step explanation:

First you calculate the value

(2)÷2^-2

Then you simplify

2^4

=16

Answer:

The LCM of 100 and 120 is 600.

The LCM of 5 and 120 is 120.

LCM of 5 and 100 is 100.

Step-by-step explanation:

I think this is the answer . If it is not sorry .

Answer:

see below

Step-by-step explanation:

Part 1:

(512) ^ 1/3

-------------------

(2197) ^ 1/3

8

-----

13

The scale factor is 8:13

Part 2

The ratios of the areas is related by scale factor squared

8^2

-----

13^2

64      

------  

169

Part 3

64       960

------  = ----------------

169     SA larger

Using cross products

64 * SA = 169 * 960

64 SA = 162240

Divide each side by 64

64 SA/ 64 = 162240 / 64

SA = 2535

2535 cm^2

Answer:

8? not sure tho....

Step-by-step explanation:

Answer:

10 ft, 20ft and 25 ft.

Step-by-step explanation:

10 ft, 20ft and 25 ft.

This will make a triangle as 25 < (10 + 20).

Answer:

Solution given:

one side of a triangle must be less than the sum of two other side .

by making these sense:

3<10+20

10<20+3

20<10+3not true

these three side are not possible.

again

10<20+25

20<25+10

25<20+10

these three side are true so

required side are:

Side 1:10

Side 2:25

Side 3:20

Answer:

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )  

Blade D : H(θ) = 75 + 50 sin( θ + 270° )

Step-by-step explanation:

Given data :

Diameter of blade = 50 m

overall height = 125 m

The four blades : Blade A , Blade B, Blade C, Blade D  all moves in same direction hence they make 90° to each other.

Lets assume The blades are standing at  θ with the horizontal

The four equation  modelling the heights :

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )  

Blade D : H(θ) = 75 + 50 sin( θ + 270° )

Answer:

Which subject is this . please tell

Answer:

see explanation

Step-by-step explanation:

1

(a)

Calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁  = (8, 3) and (x₂, y₂ ) = (10, 7)

m = [tex]\frac{7-3}{10-8}[/tex] = [tex]\frac{4}{2}[/tex] = 2

(b)

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

(c)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 3) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of perpendicular line

--------------------------------------------------------------------------

2

(a)

with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (4, 4)

m = [tex]\frac{4-5}{4-3}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1

(b)

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1

(c)

y = x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = 3 + c ⇒ c = 5 - 3 = 2

y = x + 2 ← equation of perpendicular line

Answer:

x=7/3

Step-by-step explanation:

8 ^ (x - 1 ) = 16

We need to rewrite 8 as 2^3  and 16 as 2^4

2^3 ^ (x - 1 ) = 2^4

We know that a^b^c = a^(b*c)

2^(3(x-1)) = 2^4

The bases are the same so the exponents are the same

3(x-1) = 4

Distribute

3x-3 = 4

Add 3 to each side

3x-3+3 = 4+3

3x = 7

Divide by 3

3x/3 = 7/3

x=7/3

Answer:

14

Step-by-step explanation:

7*4*1/2=14

Multiply each payout by the corresponding probability and take the total:

E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95

The expected value = 3.92

"It describes the average of a discrete set of variables based on their associated probabilities."

[tex]E(x)=\Sigma[ xP(x)][/tex]

Multiply each value of the random variable by its probability and add the products.

For given question,

We have been given a payout probability distribution.

We need to find the expected value of the winnings.

First we multiply each value of the random variable by its probability .

0 × 0.5 = 0

5 × 0.2 = 1

8 × 0.15 = 1.2

10 × 0.1 = 1

15 × 0.05 = 0.75

Now, we find the sum of above products.

0 + 1 + 1.2 + 1 + 0.75 = 3.95

By using the formula of expected value,

[tex]\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92[/tex]

Therefore, the expected value = 3.92

Learn more about the expected value here:

https://brainly.com/question/18523098

#SPJ3

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

50% as a fraction would be 1/2

Answer:

B

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]

Then

cosA = sinC → B

Answer:

Range: {1, -1, 0}

Step-by-step explanation:

Just subtract 2 from each number :)

Answer:

7

Step-by-step explanation:

when multiplying powers with the same base, add the powers

Answer:

a²×a⁵

a²⁺⁵

a⁷

OAmalOHopeO

Answer:

Step-by-step explanation:

The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:

                          original                 new

length

width

And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:

                           original                  new

length                       L

width                       2L

Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.

The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:

                            original                        new

length                      L                       100%L + 50%L

width                       2L

The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:

                             original                       new

length                        L                     100%L + 50%L

width                        2L                  100%(2L) - 20%(2L)

And now we'll simplify that "new" column:

                              original                         new

length                        L                         150%L = 1.5L

width                         2L               80%(2L) = 160%L = 1.6L

Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:

248 = 2(1.5L) + 2(1.6L) and

248 = 3L + 3.2L and

248 = 6.2L so

L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)

Answer:

0.75 → 0.5 → 1/3(0.33) → 1/4(0.25)

Answer:

Choice A

Step-by-step explanation:

An arithmetic sequence is one which has an incremental change.

for our answer, our change is +5

Answer:

(C) 2x^3 - 3x^2 - 35x + 36

Step-by-step explanation:

First multiply 2x by x^2 + 3x - 4:

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

2x^3 + 6x^2 - 8x

Next multiply -9 by x^2 + 3x - 4:

(-9)(x^2 + 3x - 4)

-9x^2 - 27x +36

Now add the two polynomials by adding like terms:

(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)

2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36

2x^3 - 3x^2 - 35x + 36

Hope this helps (●'◡'●)

Answer: 64°

Step-by-step explanation:

Answer:

x = 64°

Step-by-step explanation:

Since the triangle is isosceles, the base angles are congruent, that is

∠ R = ∠ Q = 32° , then

vertex angle = 180° - (32 + 32)° = 180° - 64° = 116°

∠ NSR = 116° ( vertically opposite angle )

∠ MNS and ∠ NSR are same- side interior angles and sum to 180° , then

x = 180° - 116° = 64°

Answer:

Step-by-step explanation:

Sample space of die 1 = {1,2,2,3,3,4}

Sample space of die 2 = {1,3,4,5,6,8}.

The highest value that we get by rolling die 1 is 4 and die 2 is 8, which give the sum 12. So, we cannot have any other combinations other than this , as the highest value itself gives 12.

Rolling a sum of 12 with the dice = {(4,8) }

Probability = 1/36

Answer:

see explanation

Step-by-step explanation:

Using the identities

cotA = [tex]\frac{1}{tanA}[/tex]

cot²A = cosec²A - 1

tan²A = sec²A - 1

Consider the left side

(cotA + tanA)² ← expand using FOIL

= cot²A + 2cotAtanA + tan²A

= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1

= cosec²A - 1 + 2 + sec²A - 1

= sec²A + cosec²A - 2 + 2

= sec²A + cosec²A

= right side, thus proven

Answer: Reflection

Step-by-step explanation: Please mark brainliest

Answer:

I think this is the ans

Step-by-step explanation:

ab+c=0

(p+q)(p-q)=0

p Square-q Square =0

0=p Square-q Square

Answer:

74

Step-by-step explanation:

4(2) raise to power 4 - 2(7) raise to power 2 +40

4(16) - 2(49) +40

64-98+40

64- 138

74

Answer:

2

Step-by-step explanation:

is the value of k

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer: 33x=27 2x-1

33 x=3 3(2x-1)

as base are same so powers are equal

3x=3(2x-1)

3x=6x-3

3x-6x=-3

-3x=-3

x=1

Answer:

all I know is sin square A +cos square A =1

Answer:

Step-by-step explanation:

That 3 sitting outside there in that little "box" thing is a root/solution/zero of the polynomial. The numbers underneath the line are the coefficients of the depressed polynomial, which means that the polynomial is 1 degree lower than the degree with which we started. If we started with an x-squared, this degree is a single x, better known as linear (a line). Anyway, (x - 3) is a zero of the polynomial, which also means that it's a factor. So A applies. x = 3 is a root, so C applies. And F also because the depressed polynomial, the remainder, is 2x + 4.