A ride in an amusement park features a swinging ship suspended from a height of 50 feet. The motion of the ship can be modeled by the graph below, where x represents the time, in seconds, since the start of the ride, and f(x) represents the angle, in radians, that the center of the ship makes with respect to the equilibrium position.

Select all the correct answers.

Answer:

Angle 6x and Angle 5x + 10 are corresponding angle pair,

they are equal

so each angle = 6 × 10 = 60°

Answer:

x is 10

Step-by-step explanation:

draw a line AD to make triangle ABD (which will be a right triangle)

use Pythagorean theorem to find the length of AD

[tex]a^{2} +b^{2} =c^{2} \\6^{2} +8^{2} =c^{2} \\36+64=c^{2} \\100=c^{2} \\10=c[/tex]

Side AD is a radius of the circle, x is also a radius, so they are equal so x is 10

Answer:

Step-by-step explanation:

How much would the mortgage payment be on a $500K house? Assuming you have a 20% down payment ($100,000), your total mortgage on a $500,000 home would be $400,000. For a 30-year fixed mortgage with a 3.5% interest rate, you would be looking at a $1,796 monthly payment.

Answer: B'(-4, 1.5), C'(-2,-3), D'(1, 0)

Step-by-step explanation:

The coordinates of the vertices of triangle B'C'D' is B'(-4, 1.5), C(-2, 3) and D(1, 0)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in size of a figure. If a point A(x, y) is dilated by a factor k, the new point is at A'(kx, ky).

Given that Triangle BCD has vertices B(-8, 3), C(-4, 6), and D(2,0). If it is dilated by a factor of 0.5, the new point is at:

B'(-4, 1.5), C(-2, 3) and D(1, 0)

The coordinates of the vertices of triangle B'C'D' is B'(-4, 1.5), C(-2, 3) and D(1, 0)

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Answer:

Smaller number is 16 and larger number is 25

Step-by-step explanation:

[tex]x+y=41\\x=y-9\\\\(y-9)+y=41\\2y-9=41\\2y=50\\y=25\\\\x=25-9=16[/tex]

The smaller number is 16 and the larger number is 25

Answer:

30

Step-by-step explanation:

Answer:

30.

Step-by-step explanation:

2 x 3 x 5 = 30

Answer:

Answer:

u cant create any triangles because you have said that there are  three 45° angles

which is 45°, 45°, 45°

⇒ 135°

135≠180

every triangle is 180°

therefore no triangle

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Answer:

She did not add 5 to 30. ... Mona subtracted 5 where she should have divided 5.

Step-by-step explanation:

Answer:

B. She did not divide 30 by 5

Step-by-step explanation:

This is the only way to cancel out the 5 and get the variable alone

Answer:

3 roots

The graph crosses the x axis 3 times so there are 3 roots.

Step-by-step explanation:

This occurs when the number of $5 price increases is approximately 10.82 or 15.32.

The function given is P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. We are to identify the approximate value of the x-intercept and explain what the x-intercept means in terms of the problem scenario.

The x-intercept is a point where the graph of the function crosses the x-axis. At this point, the value of the function is zero.

We can find the x-intercept by setting P(x) = 0 and solving for x.0 = −6x2 + 156x + 1,0006x2 - 156x - 1000 = 0Dividing by 6, we get:x2 - 26x - 166.67 = 0Solving using the quadratic formula,

we get:x ≈ 10.82 or x ≈ 15.32So, the x-intercepts are approximately 10.82 and 15.32. In terms of the problem scenario, the x-intercept represents the point at which the company breaks even, i.e., the point at which the daily profit is zero.

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Answer:

Look Below

Step-by-step explanation:

1. A person would have to work 9 Hours to get 63$ for 7$ per hour.

2. Reese is 16 years old because if you do 34 - 18 = 16. Or you could do 16 + 18 = 34 to confirm it.

3. 10 - 4 = 6 Sean is 6 feet tall total because if you do a subtraction problem with the two variables you get 6.

4. I am not able to see the numbers on the right unfortunately so all you have to do for this one is to minus how much her brother has by 8 to get her amount.

Hope This Helps! Have A Good Day! Good Luck With Your Work!

Step-by-step explanation:

1. K = 13 (13+5=18)

2. X= 36 (36-12=24)

3. Y = 14 (17=3+14)

4. Z= 24(22=24-2)

5. A=7 (divide both sides by 4)

6. H=12 (12/6=2)

7. B= 10 (100=10*10)

8. Y=42 (6=42/7)

I'm pretty sure that this is correct.

9514 1404 393

Answer:

  720

Step-by-step explanation:

The LCM of these numbers will have every factor that is part of these numbers.

  16 = 2^4

  30 = 2 × 3 × 5

  36 = 2^2 × 3^2

So, the LCM will have factors of 2^4, 3^2, and 5:

  LCM(16, 30, 36) = 2^4 × 3^2 × 5 = 720

720 = 16×45 = 30×24 = 36×20

The least common multiple is 720.

Answer:

(4, -7) thats the largest maximum

Answer:32

Step-by-step explanation:

i think the answer will be 32 feet

Answer:LLLLLLLLLLLLLL

Step-by-step explanation:

LLLLLLLLLl

Answer:

4

Step-by-step explanation:

There are just 4

Answer:

Yes

Step-by-step explanation:

The left side  19  is less than the right side  20 , which means that the given statement is always true.

Answer:

n' = (-5,2)  k' = (-1,1)  t' = (-5,0)

Step-by-step explanation:

Answer:

6+4=10

7-6=1

6*6=36

1/3*6=2

Step-by-step explanation:

Plug in 6 for x and solve it.

yes, he is right all distance is the same from the origin point to any side of the circle same as radius which is half a line starts at any side of the circle and ends at the origin point.

Mason is correct.

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

A circle centered at the origin with a radius of 4 units can be represented by the equation:

x² + y² = r²

Substituting the coordinates of the point (4, 4), we have:

4² + 4² = r²

16 + 16 = r²

32 = r²

Taking the square root of both sides, we get:

r = 4√2

Therefore,

The circle centered at the origin with a radius of 4 units has an equation of x^2 + y^2 = 32.

Point (4, 4) satisfies this equation since:

4² + 4² = 32

16 + 16 = 32

32 = 32

Thus,

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

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Answer:

45,000 mL (Milliliters) = 45 L (Liters)

Explanation:

The word milliliters is made up of two words, "milli" and "liter"

"Milli" means a thousand, chiefly denoting a factor of one thousandth.

That means one milliliter is one thousandth of a liter

Answer:

.1

Step-by-step explanation:

Answer:

0.1

Step-by-step explanation

Answer:

66

Step-by-step explanation:

9514 1404 393

Answer:

  the maximum area that can be enclosed by the fencing

Step-by-step explanation:

If the width of the garden is w (in yards), then the length of the garden is (150-w) and the area is ...

  A(w) = w(150 -w) = -(w² -150w)

  A(w) = -(w² -150w +75²) +75²

  A(w) = -(w -75)² +5625

In this vertex form, the vertex is (75, 5625).

The graph of area versus width is a parabola that opens downward, so the vertex second coordinate is the maximum area that can be enclosed.