Solve for x. PLEASE SHOW WORK AND HELP

Given:

[tex](\sin x)^2+(\cos x)^2=1[/tex]

[tex]\cos \theta = \dfrac{4\sqrt{2}}{7}[/tex]

To find:

The value of [tex]\sin \theta[/tex].

Solution:

We have,

[tex]\cos \theta = \dfrac{4\sqrt{2}}{7}[/tex]

Putting this value in the Pythagorean identity, we get

[tex](\sin \theta)^2+(\cos \theta)^2=1[/tex]

[tex](\sin \theta)^2+\left(\dfrac{4\sqrt{2}}{7}\right)^2=1[/tex]

[tex](\sin \theta)^2+\dfrac{16(2)}{49}=1[/tex]

[tex](\sin \theta)^2+\dfrac{32}{49}=1[/tex]

[tex](\sin \theta)^2=1-\dfrac{32}{49}[/tex]

[tex](\sin \theta)^2=\dfrac{49-32}{49}[/tex]

[tex](\sin \theta)^2=\dfrac{17}{49}[/tex]

Taking square root on both sides, we get

[tex]\sin \theta=\pm \sqrt{\dfrac{17}{49}}[/tex]

[tex]\sin \theta=\pm \dfrac{\sqrt{17}}{7}[/tex]

The given value of [tex]\sin \theta[/tex] is positive. So, [tex]\sin \theta= \dfrac{\sqrt{17}}{7}[/tex].

Therefore, the value of value [tex]\sin \theta[/tex] is [tex]\sin \theta= \dfrac{\sqrt{17}}{7}[/tex].

Answer:

3 boxes

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4) volume =288

5) 4=r

Step-by-step explanation:

Question 4

volume=length*width*height

volume= 3*8*12

volume=288

question 5

V=pie r^2*h

144pie=pie r^2 *9

144/9=r^2

16=r^2

4=r

Answer:

D

Step-by-step explanation:

As,

-10 is always greater than -13

Hence, -13 < -10

Answer:

[tex]k=\dfrac{5}{4}[/tex]

Step-by-step explanation:

Given that,

y varies directly as x. It means,

y = kx

Where

k is the constant of variation

or

[tex]k=\dfrac{y}{x}\\\\k=\dfrac{5}{4}[/tex]

So, the constant of variation is [tex]\dfrac{5}{4}[/tex].

Answer:

A 1/2

Step-by-step explanation:

(2, -1.5) & (4, -0.5)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-0.5 - (-1.5)) / (4 - 2)

Simplify the parentheses.

= (-0.5 + 1.5) / (2)

= 1 / 2

Simplify the fraction.

1/2

This is your slope.

Hope this helps!

The simplification of the expression given us the value of 6.5

A number line is a visual representation of the real numbers, which are used to describe quantities that can be any value, including fractions and decimals. A number line is typically represented as a straight line with numbers increasing from left to right.

We are required to carry out a simplification of -4- 2 1/2

this is given as

-4 - 2.5

= -6.5

We are to find where this point lies in the number line.

This lies between - 6 and - 7 on the number line that we have here

Read more on the number line here:https://brainly.com/question/25230781

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Answer:

C: 1

this answer is c because the line is one the Y intercept of 1

Answer:

9 buses

12 cars

(Step-by-step explanation:

x=bus x+y=21 --> y=-x+21

30x+4y=318 --> y= -30x/4 + 318/4

y=car

x= 9

y=12

:) hope this help

Answer:

9

Step-by-step explanation:

Answer: 18 quarts for Part a

9 gallons for part b

Step-by-step explanation:

Answer:

Part A: 18

Part B: 4 1/2

Step-by-step explanation:

Part A:

He needs to triple his recipe by 3, so 12 x 3. So you get 36. The question was how many quarts does he need. So 36 divided by 2 is 18. So 18 quarts is needed!

Part B: We need to find out how many gallons he needs, we already know that he has 18 quart. There are 4 quarts in a gallon. So 18 divided by 4 is 4 1/2.

Good Luck And Hope this helps!

Yours Truely, TheAnimeCatUwU

Answer:

she can get 11.5 but you have to round down so 11 roses and the vase

Step-by-step explanation:

Step-by-step explanation:

We can set up an average equation in the form, where x is the last score in the fourth quarter:

[tex]\frac{85 + 88 + 92 + x}{4} = 90[/tex]

[tex]85 + 88+92 + x =360\\\\x = 95[/tex]

She needs at least a 95 on the last quarter to average 90 in all four quarters.

100 = 10^2

1000 = 10^3

10000 = 10^4

0.1 = 10^(-1)

0.01 = 10^(-2)

0.001 = 10^(-3)

Now,

100 × 0.1 = 10^2 × 10^(-1)

= 10

Step-by-step explanation:

For every page that Liam reads, Amir reads five, so if Liam read 12 pages, then Amir read 12 * 5 = 60 pages

Answer:

C: (12,4)

Step-by-step explanation:

We can find the slope of the line with "rise over run"

The pattern is 1 unit up, 3 units to the right

By following this pattern from point (9,3),

we go 1 unit up on the y axis, moving (9,3) to (9,4)

Next we move 3 units right on the x-axis,

moving (9,4) to (12,4)

Answer is (12,4)

Answer:

Let's work this out.

n - 3 / n + 3

n / n + 6

In order to avoid it cancelling out, we only cancelled out one side.

2n = 6

n = 3

Answer:

※※※※※※※※※※※※※※※※※

Hi! The answer to your question is [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Use the Distance Formula to determine the distance between two points.

- Brooklynn Deka

❣❣

Answer:

1498.78125 i used calculator

Step-by-step explanation:

Answer:

the answer would be A because that makes a straight line.

Answer:

x = 1/2 and y=6x, so 8x/2y = 8(1/2)/2(6*1/2) = 4/6 = 2/3

Step-by-step explanation:

Answer:

[tex]Area = 96[/tex]

Step-by-step explanation:

Given

[tex]x = 9[/tex]   [tex]y =3[/tex]    [tex]h = 8[/tex]

See attachment for rhombus

Required

Determine the area

From the attached rhombus:

We have

(1) Triangle

[tex]Base = x;\ \ Height = h[/tex]

The area is:

[tex]Area = 0.5 * Base * Height[/tex]

[tex]A_1= 0.5 * x*h[/tex]

[tex]A_1 = 0.5 * 9 *8[/tex]

[tex]A_1 = 36[/tex]

(2) Triangle

[tex]Base = y;\ \ Height = h[/tex]

The area is:

[tex]Area = 0.5 * Base * Height[/tex]

[tex]A_2 =0.5 * y * h[/tex]

[tex]A_2 =0.5 * 3 * 8[/tex]

[tex]A_2 =12[/tex]

(3) Rectangle

[tex]Area = Length * Width[/tex]

[tex]Length =h; Width = x - y[/tex]

because all sides are equal, so the remaining side is x - y

So:

[tex]A_3 = h * (x - y)[/tex]

[tex]A_3 = 8 * (9 - 3)[/tex]

[tex]A_3 = 8 * 6[/tex]

[tex]A_3 = 48[/tex]

So, the area is:

[tex]Area = A_1 + A_2 + A_3[/tex]

[tex]Area = 36 + 12 + 48[/tex]

[tex]Area = 96[/tex]

Answer: area 72

Step-by-step explanation:

Answer:

1. possibly congruent

2. possibly congruent

3. congruent

4. similar

Step-by-step explanation:

It is impossible to tell for the first two.  In order to be congruent they must have the measurements (lengthes& angles)  for all coordinating sides and angles.  Since we don't have that info we can only guess and since the look exactly the same we can guess they are congruent.

The third one being on the graph we can tell these are congruent.

the fourth one is obviously not congruent because the side lengths are different.  We are guesing that the coordinating angles are congruent    

the question did not give enough information to properly answer the questions with confidence

Answer:

152

Step-by-step explanation:

Answer:

-64

Step-by-step explanation:

we should put -2 for j and -1 for k,

Answer:

the answer is 64

Answer:

The third number line where x = -2, 2

Step-by-step explanation:

The solution is, the number line represents the solutions is given below.

here, we have,

given equation is,

25x + 200 > 1,200

Subtract 200 from each side

25x + 200-200 > 1,200-200

25x> 1000

Divide by 25

25x/25 >1000/25

x>40

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Answer:

the wall is 66 inches long

Step-by-step explanation:

hope this helps :)

Answer:

C. 44 cm, 30cm, and 16 cm

Step-by-step explanation:

Sana nakatulong