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3 years ago

Given : cos(θ)= -4/5 | sin x = -12/13 Evaluate: cos(θ + x)

Mathematics

1 answer:

artcher [175]3 years ago

8 0

cos (θ + x) is 16/65

Step-by-step explanation:

Step 1:

Given cos θ = -4/5, find sin θ.

cos θ = adjacent side/hypotenuse = -4/5

The opposite side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Opposite side² = Hypotenuse² - Adjacent Side²

= 5² - (-4)² = 25 - 16 = 9

∴ Opposite Side = 3

⇒ sin θ = opposite side/hypotenuse = 3/5

Step 2:

Given sin x = -12/13, find cos x.

sin x = opposite side/hypotenuse = -12/13

The adjacent side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Adjacent side² = Hypotenuse² - Adjacent Side²

= 13² - (-12)² = 169 - 144 = 25

∴ Adjacent Side = 5

⇒ cos x = adjacent side/hypotenuse = 5/13

Step 3:

Find cos (θ + x).

cos (θ + x) = cos θ cos x - sin θ sin x

= -4/5 × 5/13 - 3/5 × -12/13

= -20/65 + 36/65 = 16/65

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1. What is a perfect square? 2. What is the square root of 4x²? 3. What is the square root of 25? 4. Factor 4x² + 20x + 25.

Ulleksa [173]

Answer:

Step-by-step explanation:

1) A perfect square is a whole number which is a product of a smaller whole number and itself. Examples of perfect squares are

4(2 × 2)

9(3 × 3)

16(4 × 4)

25(5 × 5)

36(6 × 6)

2) Square root of 4x² is 2x(product of square root of 4 and square root of x²)

3) square of 25 is 5

4) 4x² + 20x + 25

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 4

b = 20

c = 25

Therefore,

x = [- 20 ± √(20² - 4 × 4 × 25)]/2 × 4

x = [- 20 ± √(400 - 400)]/8

x = [- 20 ± 0]/8

x = - 20/8

x = - 2.5

3 0

3 years ago

If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.

harina [27]

Answer:

Step-by-step explanation:

When we simplify we get $z(6xy+21x+2y+7)+30xy+105x+10y=812.$

Then we continue to factor to get: $(z+5)(6xy+21x+2y+7)&=847.$

We then see that we can factor $(6xy+21x+2y+7)$ into $(z+5)(3x+1)(2y+7)&=847.$

we then do the prime factorization of 847, which i think is, $7*11*11$ . we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.

It has to be a positive, non-negative integer, right?

We also see that 3x+1=11 so we see that x=10/3 (which wont work).

So 3x+1=7, so x=2.

So 11 has to be in another term. It has to be in 2y+7=11 so y=2

for the last term we get z+5=11 so z=6

2+2+6=10

Hope this helps and if you want please consider giving me brainliest. :)

8 0

3 years ago

Can you draw an isosceles triangle with only one 80 degree angle?

aev [14]

Answer:

The triangle is 50,50 80

Step-by-step explanation:

The three angles of a triangle equal 180 degrees

We only want one 80 degree angle. That means the other two angles have to be the same, since it is an isosceles triangle. Call the other angle x

x+x+80 = 180

2x+80 =180

Subtract 80 from each side

2x+80-80=180-80

2x =100

Divide by 2

2x/2=100/2

x = 50

Each of the other angles in the triangle would have to equal 50 degrees

The triangle is 50,50 80

6 0

3 years ago

HELP!<br> I’ll give brainliest if u get it right

Tomtit [17]

Answer:

its 36 gallons

Step-by-step explanation:

6 0

3 years ago

Robert borrowed $750 from his parents. He promised to repay the loan by giving his parents at least $67 from his paycheck each w

Luda [366]

To answer this question we can propose the following equation:

$d=750 -x(67)$

Where:

x is the number of weeks elapsed.

d is the debt depending on the weeks.

Robert promised to pay at least $ 67 each week.

Therefore, after 5 weeks the debt of rober should be:

$d\leq750-5*67$

$d\leq415$

Then scenario A) is possible because $150$ .

After 6 weeks:

$d\leq750-6*67$

$d\leq348$

Then scenario B) is possible because $200$ .

After 7 weeks

$d\leq750-7*67$

$d\leq281$

Then scenario C) is possible because $250$ .

After 8 weeks

$d\leq750-8*67$

$d\leq214$

So scenario D) is NOT possible because $300>214$

Finally the correct answer is option D.

3 0

3 years ago