Shown in the figure is part of a design for a water slide. Find the total length of the slide to the nearest foot, if α = 25°, β = 31°, a = 35 ft, and b = 170 ft.

Answer:

Step-by-step explanation:

1. Newton's first law of motion: Also called the law of inertia, states that "An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force"

2. According to Newton's second law "the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a)", meaning that when the soccer player kicks a ball, a force is acting on the ball, therefore increasing it's acceleration. After the force is applied, the gravity and the resistance of air will be the ones in charge of stopping the ball.

3. a) Baseball: The ball changes direction and speed when it's hit with the bat.

b) Bowling: When the ball hits the pins, the change from being at rest to a higher velocity.

c) Wrestling: The wrestler exerts a force on the oponent increasing or decreasing it's velocity.

4. The jet airplane has more inertia. Inertia is the resistance of an object to move if at rest, or to change its velocity and it is proportional to the mass of the object. Therefore, the jet airplane being heavier than the car will have more inertia. It has to be clear that it is not due to the fact that is at rest that is the one with more inertia, but mostly related to the mass. If the example was with two cars, one at constant velocity and the other at rest, both with the same mass, the one with greater inertia will be the one moving.

5. No, forces do not always cause motion. They have to be greater than the forces that oppose movement, such as friction, air resistance or gravity.

Final answer:

To find the unit rate in miles per hour, divide the distance by the time. In this case, Jon travels at a unit rate of 2 miles per hour.

Explanation:

To find the unit rate in miles per hour, we need to convert the given information into the same units. Jon travels 1/2 mile in 1/4 hour, so we can simplify the fraction to 2/4, which is equal to 1/2. This means Jon travels 1/2 mile every 1/4 hour. To find the unit rate, we divide the distance (1/2 mile) by the time (1/4 hour).

1/2 mile ÷ 1/4 hour = 2 miles per hour

Therefore, the unit rate at which Jon travels is 2 miles per hour.

There are 12 number of multiple-choice questions are on the test.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that m, and the number of free-response questions, f, on the test.

m + f = 15.

Then multiply by -5

3m + 5f = 51

-----------------

-5m - 5f = - 75

3m + 5f = 51

Now add

-2m = - 24

m = -24/-2

m = 12

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To work out 49.2 x 10.3, you multiply the two numbers together.

To work out 49.2 x 10.3, you multiply the two numbers together.

Step 1: Multiply the whole numbers: 49 x 10 = 490

Step 2: Multiply the decimals: 0.2 x 0.3 = 0.06

Step 3: Add the results from step 1 and step 2: 490 + 0.06 = 490.06

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Answer:

There are many ways to do this calculation. Few are listed below.

1. Whenever we say percent, that means divided by hundred. And any number divided by 100 will result in putting a decimal to two places left. Like 20% will becomes [tex]\frac{20}{100}[/tex] = 0.20

And you can multiply the bill amount with 0.20 mentally.

2. You can also simply divide the total bill amount by 5, it will be equal to  20% of the total bill amount. Like if bill amount is $200.

[tex]\frac{200}{5}=40[/tex] and [tex]0.20\times200=40[/tex]. Both values are same.

Answer:

The simplified form of the provided fraction is [tex]\frac{226}{3}\%[/tex].

Step-by-step explanation:

Consider the provided fraction.

The provided fraction can be written as:

[tex]75\frac{1}{3}\%[/tex]

Convert the provided mixed number into a proper fraction.

Multiply the number 75 with 3 and add 1 to the obtained number.

[tex]75\frac{1}{3}\%[/tex]

[tex]\frac{(75\times 3+1)}{3}[/tex]

[tex]\frac{225+1}{3}\%[/tex]

[tex]\frac{226}{3}\%[/tex]

Hence, the simplified form of the provided fraction is [tex]\frac{226}{3}\%[/tex].

To convert 75 1/3 % to a fraction in simplest form, first change the mixed number to an improper fraction, then write it over 100, and finally simplify by dividing both numerator and denominator by their greatest common divisor.

To convert 75 1/3 % to a fraction in simplest form, start by understanding that a percent is a ratio whose denominator is 100. Therefore, 75 1/3 % can be expressed as the fraction 75 1/3 over 100.

First, convert the mixed number to an improper fraction. Multiply the whole number 75 by the denominator 3 and add the numerator 1:

Now, 75 1/3 as an improper fraction is 226/3. Write this as a fraction over 100:

226/3 % = (226/3) / 100 = 226/300

To simplify this fraction, we look for the greatest common divisor of 226 and 300, which is 2. Divide both the numerator and the denominator by 2 to get:

The fraction in simplest form is therefore 113/150.

The solution to the equation -7=-1+ x/3 is obtained by adding 1 to both sides, then multiplying both sides by 3 to solve for x. This yields x = -18.

To solve the equation -7=-1+ x/3, we can first isolate the x term using the addition and multiplication properties of equality.

Hence, the solution to the equation -7=-1+ x/3 is x=-18.

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Answer:

1.96

Step-by-step explanation: