Everything is in the picture please help me.

Answer:

[tex]x = 18[/tex]

[tex]y = 6\sqrt{3}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.  

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:

Cosine Ratio

[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

Sine Ratio

[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

Consider the angle of θ=30°, then we can write:

[tex]\displaystyle \cos 30^\circ=\frac{x}{12\sqrt{3}}[/tex]

Solving for x:

[tex]x=12\sqrt{3}\cos 30^\circ[/tex]

Since:

[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]

Then:

[tex]x=12\sqrt{3}\cdot \frac{\sqrt{3}}{2}[/tex]

[tex]x = 18[/tex]

Now apply the sine:

[tex]\displaystyle \sin 30^\circ=\frac{y}{12\sqrt{3}}[/tex]

Solving for y:

[tex]y=12\sqrt{3}\sin 30^\circ[/tex]

Since:

[tex]\sin 30^\circ=\frac{1}{2}[/tex]

Then:

[tex]y=12\sqrt{3}\cdot \frac{1}{2}[/tex]

[tex]y = 6\sqrt{3}[/tex]

Answer:

[tex]x = 18[/tex]

[tex]y = 6\sqrt{3}[/tex]

Answer:

1.125 m squared

Step-by-step explanation:

Answer:

37/50

Step-by-step explanation:

because 37% is out of 100

Answer:

37/50

Step-by-step explanation:

as 37% means 37/100, when 37 is divided by a smaller number such as 50, the result will be greater.

Answer:

$2,854.2

Step-by-step explanation:

For Sebastian

It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month.

1 year = 12 months

10 years = x

Cross Multiply

x = 10 × 12 = 120 months

He pays $296.66 monthly

Hence, the total amount he paid in 10 years =

$296.66 × 120

= $35,599.2

The loan he took was $30,000.

Hence, the interest Sebastian paid on his loan = $35,599.2 - $30,000

= $5,599.2

For Jana

Jana paid off a loan for the same

amount at the same interest rate in 5 years by paying $545.75 per month.

1 year = 12 months

5 years = x

Cross Multiply

x = 10 × 5 = 60 months

He pays $545.75 monthly

Hence, the total amount he paid in 5 years =

$545.75 × 60

= $32,745

The loan she took was $30,000.

Hence, the interest Sebastian paid on his loan = $32,745 - $30,000

= $2,745

How much more did Sebastian pay in interest than Jana?

This is calculated as:

The interest Sebastian paid - The Interest Jana paid

= $5,599.2 - $2,745

= $2,854.2

Therefore, Sebastian paid $2,854.2 more than Jana

Answer: 7 waffles

Step-by-step explanation: trust me pls. you have a total of 120 minutes. 7 waffles takes you 105 minutes, and the remaining 15 minutes can be spent on 3 cookies.

Hey there!

The vertical angles in the diagram shown are 2 and 3, and 1 and 4, because they are formed by 2 intersecting lines and are across from eachother.

Hope it helps and have a good day!

Answer:

(x+7) (x^2+3)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping. Hope this helps!

Answer:

-3

Step-by-step explanation:

3x-8x=17-2

3x-8x=15

-5x=15

-x=15/5

-x=3

x=-3

Answer:

Step-by-step explanation:

if you serve all the pie to 8 guests.. then they would each get 1/8.. if you were able to cut it exactly the same.. but..  we all know that there is always one piece that is bigger and we all want that piece  :P  b/c pumpkin pie is good

1/8

1/4

1/2

respectively for each of the questions

Answer:

BC = 104

Step-by-step explanation:

By the SAS postulate, ΔBDA and ΔBDC are congruent, meaning that each of the corresponding sides are equal in length.

BD = BD

AD = CD

BA = BC

If we know BA = 21x - 1 and BC = 9x + 59, then we can set them equal to each other and solve for "x".

BA = BC

21x - 1 = 9x + 59

21x = 9x + 60                     Added 1 to both sides

12x = 60                             Subtracted 9x from both sides

x = 60/12                            Divided both sides by 12

x = 5                                   Reduced fraction, solved for "x"

To find BC, substitute x = 5 into the equation for BC.

BC = 9x + 59

BC = 9(5) + 59                    Substituted "x" for 5

BC = 45 + 59                      Multiplied 9 and 5

BC = 104                            Added, solved for BC

∴ BC = 104

Answer:

Step-by-step explanation:

[tex]hope \: it \: helps[/tex]

Answer:

= $963.65

Step-by-step explanation:

Value of stock = value of the stock at the time it was bought x ( 1 + average rate of increase)^number of years

$675 x [1 + (12 + 3/5% ) ]^3 =

$675 x ( 1 + 0.126)^3 = $963.65

Answer:

∠VUW

Step-by-step explanation:

A triangle is a three sided polygon with three angles. Types of triangles are obtuse, scalene, isosceles, equilateral and so on.

In triangle VUW, since VU = WU, hence it is an isosceles triangle. In an isosceles triangle, two sides of the triangle are equal.

The size of an angle depends on its opposite side, the higher the opposite side the higher the angle. Since In triangle VUW, VU = 9, WU = 9, VW = 5. Since VW is the smallest side, the angle opposite to VW is the smallest angle.

Hence the smallest angle = ∠VUW

The cost of having a car towed 14 miles is $103.

To express Linda's towing cost, C, in terms of miles towed, x, we can use the given information that Little Town Auto charges a flat fee of $75 plus $2 per mile towed.

The function for the towing cost, C, can be written as:

C(x) = 75 + 2x

Where x represents the number of miles towed.

To find the cost of having a car towed 14 miles, we substitute x = 14 into the function:

C(14) = 75 + 2(14)

C(14) = 75 + 28

C(14) = 103

Therefore, the cost of having a car towed 14 miles is $103.

To know more about cost click here :

https://brainly.com/question/31665993

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Answer:

Length of ladder =L =15

Distance from wall = D =9

Height on wall = H =??

Pythagoras equation L*L = D*D + H*H

15×15= (9×9) + H×H

225-81 = 144 =HxH

H= 12 feet.

I am right or wrong

please check

Answer: 17

Step-by-step explanation: thx

Answer: 9 using pemdas

Step-by-step explanation: parenthesis, expressions, multiplication, division, addition, subtraction.

Answer:

40/3

Step-by-step explanation:

4x -20 = 10x -100 (Distributive Property)

4x -10x = -100 +20 (I swith the numbers so all of them are similar)

-6x= -80 (Divide -6 on both sides)

And you will get 40/3 or 13.3333..

Answer:

x = 40/3

Step-by-step explanation:

4(x-5)=10(x-10)

=> 4x - 20 = 10x - 100

=> 4x - 10x = - 100 + 20

=> -6x = -80

=> x = 80/6

=> x = 40/3

Answer:

1) 43/10

3) p = kt/v

4) C

1. The distance (d) from the center of the seesaw varies inversely as the weight (w) of a person.

[tex]\rm d\times w = constant[/tex]

JB who weighs 50 kg sits 3 feet from the fulcrum.

Distance of JP from the fulcrum in order to  balance with JB if he weighs 35 kg?

[tex]\rm JB \times 3 = JP \times 35 \\50\times 3 = JP \times 35 \\JP = 4.28\; feet[/tex]

So JP must sit at a distance of about 4.28 feet from the fulcrum

2. The number of pages (p) that Ethan reads varies directly as the number of hours (1) he is  reading.

A. write the variation equation

 let the number of pages read by Ethan be p

let the number of hours he is reading be  h

According to the given situation

[tex]\rm p \; \alpha\; h \\So \; equation\; is \; p = ch[/tex]

B . According to the given condition

[tex]\rm 21 = c \times 14\\c = 3/2 = 1.5[/tex]

hence the constant of proportionality c = 1.5  

So let us consider he reads p' pages in 21 minutes

[tex]\rm p' = 1.5 \times 21 = \bold{31.5\; pages}[/tex]

3. The pressure of the gas is directly proportional to the temperature and inversely proportional to  its volume.

A. Write the variation equation.

Let P = Pressure , V = Volume and T = Temperature

The equation is

[tex]\rm P \; \alpha \; \dfrac{T}{V}........(3.1)[/tex]

B. What will happen to the pressure if the volume is reduced to half and the temperature is doubled?

Since the temperature is doubled and volume is halved  so putting 2T and  and volume V/2 in equation (3.1) we get

[tex]\rm P \; \alpha \; \dfrac{4T}{V}[/tex]

So the values of new pressure become 4 times the value.

4. Given the equation y = k ma, where k is the constant of variation, which of the following

statements are TRUE or FALSE.

A. y and r varies directly.  

B.y and q are directly proportional

C.y and pq2 varies jointly

D. p and r are inversely proportional

E. y and p varies directly.​

It seems that Question 4  has an ambiguity since the equation y = k ma

does not signifies any of the option

For more information please refer to the link  given below

https://brainly.com/question/17948320

Answer:

Tens

Step-by-step explanation:

The 5 in 51 should be above the nine

Answer:

B.

Step-by-step explanation:

2,495 ÷ 48 is 51.97

the tens is the largest place value so thats where you would start

Answer:

-4

Step-by-step explanation:

7-4=3

3-4=-1

-1-4=-5

Answer: the answer is 12

Step-by-step explanation:

2x+6 =4x-12

-2x=-18

x=9

3(9)-15

27-15

12

Answer:

Yes

Step-by-step explanation:

3(3x+1) = 9x+3

2x+3+7x = 9x+3

Answer:

80

Step-by-step explanation:

Answer:

4x-3y=8

Simplifies to x=3/4y+2

2x+5y=-9

Simplifies to -5/2y+-9/2

Answer:   6

Step-by-step explanation:

30÷5=6

Answer:

4 more students

Step-by-step explanation:

10% of 40 is 4, since the membership went up by 10% it is clear that there are 4 more students that joined the chess club.

Answer:

10/100*40

=4 more students joined the club

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

3x2+9x+4=0

For this equation: a=3, b=9, c=4

3x2+9x+4=0

Step 1: Use quadratic formula with a=3, b=9, c=4.

x=−b±√b2−4ac/2a

x=−(9)±√(9)2−4(3)(4)/2(3)

x=−9±√33/6