Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.

Answer:

cos theta = -1/ 2

Step-by-step explanation:

sin theta = -sqrt(3)/2

Drawing a triangle

We know sin theta = opp/hyp

We can determine the adj side using the Pythagorean theorem

a^2 + b^2 = c^2

adj^2 + (-sqrt(3))^2 = 2^2

adj^2 +3 = 4

adj^2 = 4-3

adj ^2 =1

Taking the square root of each side

adj = 1

We know that since it is in the third quadrant the adj side is negative

adj = -1

cos theta = adj / hyp

cos theta = -1/ 2

Answer:

Solution given:

Sin[tex]\theta_{1}=\frac{-\sqrt{3}}{2}[/tex]

[tex]\frac{opposite}{hypotenuse}=\frac{-\sqrt{3}}{2}[/tex]

equating corresponding value

opposite=-[tex]\sqrt{3}[/tex]

hypoyenuse=2

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

2²=-[tex]\sqrt{3²}[/tex]+x²

4=3+x²

x²=4-3

x=[tex]\sqrt{1}=1[/tex]

x=-1

In third quadrant

Cos angle is negative

Cos[tex]\theta_{1}=\frac{-adjacent}{hypotenuse}[/tex]

Answer:

y=65x      and      8455 there yall go

Step-by-step explanation:

Answer:

Step-by-step explanation:

Diameter (D)= 42cm

Circumference = (pie)D= (22/7)*D=(22/7)*42 = 132cm

1 circumference = 1 revolution

1 revolution = 132cm = 1.32m

for covering 5.28km no. of revolution = 5.28*1000/1.32 = 4000

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

Step-by-step explanation:

The dimensions as a pair, appear twice for each combination.

SA = 2* 16 * 8 + 2 * 16 * 6 + 2*8* 6

That's because when you look at the figure, there are 2 places each face is positioned.

SA = 256 + 192 + 96

SA = 544

Answer:

x=2.24

Step-by-step explanation:

To do this problem, you must find the scale factor. Using two corresponding sides you can find it.

Using 2.4 and 3:

2.4 / 3 = 0.8

Scale factor: 0.8

Now find x:

2.8 × 0.8 = 2.24

x = 2.24

Hope this helped.

Answer:

11,968

Step-by-step explanation:

I'm not sure, but I think its 11,968

8xy + 3xy + x

= 11xy + x

= x(11y +1)

Answer:

u should use a ruler and multiplied

Step-by-step explanation:

I dont know the step by step sorry

Answer:

A=2(wl+hl+hw)

A=2(6ft×7ft+6ft×7ft+6ft×6ft)

A=2(42ft²+42ft²+36ft²)

A=2(120ft²)

A=240ft²

Step-by-step explanation:

Answer:

y=(4-2x)/3

Step-by-step explanation:

3y= 4-2x

y= (4-2x)/3

Answer:

829.6

Step-by-step explanation:

Volume = sh

= (5+12) x 6.1 / 2 x 16

= 12 x 6.1/2 x 16

= 17 x 6.1 x 8

= 829.6 mi^3

Answered by Gauthmath

Answer:

To determine which number is greater, 0.5 or 0.14, you must determine which of the two has a higher ratio with respect to a whole number. Thus, since 0.5 is equal to 1/2 and 0.14 is equal to 7/50, 0.5 is the greater number.

Answer:

44 +14i

Step-by-step explanation:

(5 + i)(9 + i)

FOIL

first 5*9 = 45

inner: 9i

outer :5i

last: i*i = i^2 = -1

Add togheter

45 + 9i+5i -1

Combine like terms

44 +14i

Answer:

see below

Step-by-step explanation:

Function 1

Find the slope

m = ( y2-y1)/ (x2-x1)

   = (-5 -3) /(3 - -1)

   = ( -5-3)/(3+1)

   = -8/4

   = -2

Function 2

Using the points (0,4) and (-1,0)

m = ( y2-y1)/ (x2-x1)

m = ( 0-4)/(-1-0)

   = -4/-1

    = 4

The function with the greater rate of change is function 2

#Function 1

Slope=

#Function 2

Slope

Function 2 has greater rate of change

Answer:

pandn

Step-by-step explanation:

jsubeuodoqok1kwnebhxhhw

emdndiiwjwkd

d

ddnjd

Answer:

5070

Step-by-step explanation:

Total = P(1+rt) =5000(1+0.007*2) =5070

If the question is asking about the amount of interest earnt, its 70

Answer:

0.1667 = 16.67% probability that they are both black.

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

5 + 4 = 9 balls, which means that [tex]N = 9[/tex]

4 are black, which means that [tex]k = 4[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

What is the probability that they are both black?

This is P(X = 2). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,9,2,4) = \frac{C_{4,2}*C_{5,0}}{C_{9,2}} = 0.1667[/tex]

0.1667 = 16.67% probability that they are both black.

Answer:

Volume: 52 Units Squared

Surface Area: 94 units.

Step-by-step explanation:

The volume is relatively simple to find. Just subtract the original volume by the 2x2x2 cube's volume. The original volume is 60. The cube's volume is 2x2x2 which is 8. 60-8=52.

The surface area is harder to find. Try to envision the corner of the rectangle being cut out. We see that each side of the cube has a surface area of 2x2 which is 4. In the picture, we see that three sides of the rectangle has been partially removed. But since each side of the cube has an equal surface area, it is safe to minus 3 of the sides that has been partially removed by 3. However, since that it is the corner, the "dent" that the cube made in the rectangle also needed to be counted. As we said, each of the sides of a cube has a surface area of 4, so since that the dent has 3 sides, we see that the surface area of the dent is 4x3 which is 12. Now we need to count the unaffected sides of the rectangle. There are three of them. Just multiply the edges to find the surface area of each side. Add all of the values up: 11+16+12+8+15+12+20=94 units.

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125

Let

ATQ

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]

Now

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]

Answer:

Step-by-step explanation:

a.)

[tex]14*2^x[/tex]

b.)

[tex]14*2^7=1792[/tex]

Answer:

3/10

Step-by-step explanation:

3 red, 4 green, and 3 yellow balls = 10 balls

P(red) = number of red balls / total balls

           = 3/10

Answer:

0.5

Step-by-step explanation:

k = y/x

k = 0.5/1

k = 0.5

Answer:

x=9 ⇒AC=24

Step-by-step explanation:

vì DE//B C⇒ΔABC  Tương ung ti tỉ lệ vớiv  ΔADE

⇒DB/AB=EC/AC

⇒AC=(EC.AB)/DB

⇒AC=24

Answer:

profit= sp-cp

loss %= loss ×100%/cp

=(cp-sp) ×100%/cp

= (1-sp)×100%/cp

Answer:

It already shows the answers.

Step-by-step explanation:

I'm pretty sure you already submitted. The ones with check marks are correct and the ones with x marks are incorrect.

Answer:

(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

From trigonometric identities, we have;

1 + cot²θ = cosec²θ

On the Left Hand Side of the equation, we get;

cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)

On the Right Hand Side of the equation, we have;

√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)

∴ √(cosec²θ - 1) = cot(θ)

By transitive property of equality, therefore;

cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³

(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))

∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))

(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(sinA - cosecA)²  = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A

(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A

∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A

Where;

sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A  - 2  - 2 + cosec²A + sec²A

sin²A + cos²A  - 2  - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A

1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3

Where;

cosec²A = cot²A + 1

sec²A = tan²A + 1

∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation

∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Squaring the Right Hand Side of the equation, we get;

(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA

sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA

∴ (sinA - cosA)² =  1 - 2·sinA·cosA

Taking the square root of both sides gives;

√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

By symmetric property of equality, we have;

[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Step-by-step explanation: