Sterling ✨

For the following problem, the slope and one point on a line is given. Use the point-slope form to find the equation of that line. (Write your answer in slope-intercept form.)

(−1,−8), m = 3

Thank you!

A Ferris wheel has a circumference of 592 feet. If a trip around takes 45 seconds, find the average speed in miles per hour. Round to the nearest tenth.

The average speed of the Ferris wheel is miles per hour.

thank you!

A crystal ball with a diameter of 6 inches is being packaged for shipment. If the crystal ball is placed inside a circular cylinder with radius 3 inches and height 6 inches, how much volume will need to be filled with padding? (The volume of a sphere with radius r is 4/3πr3, and the volume of a right circular cylinder with radius r and height is πr2h.) Use "pi" for π.

If you invest $8000 into an account with an annual interest rate of r compounded annually, the amount of money you have in the account after one year is:

A=8000+8000r

Write this formula again with the right side in factored form.

Find the amount of money in this account at the end of one year if the interest rate is 19%.

There will be $ in his count at the end of year one.

The width and length of a rectangle are given by two consecutive integers. Write an expression for the area of the rectangle. Use x for the variable.

The product of two consecutive integers is 30. Find the two integers.

The smaller of the two integers is , and the larger of the two is .

Or the smaller is and the larger is

Suppose you have two squares, one of which is larger than the other. Suppose further that the side of the larger square is twice as long as the side of the smaller square. If the length of the side of the smaller square is 13 miles, give the area of each square.

The area of smaller square is mi².

The area of larger square is mi².

How many of the smaller squares will it take to cover the larger square? smaller squares will cover the larger square.

Mr. Wilson invested money in two accounts. His total investment was $30,000. If one account pays 6% in interest and the other pays 8% in interest, how much does he have in each account if he earned a total of $1,920 in interest in 1 year?

He invested $ in the 6% account and $ in the 8% account.

thank you!

Temperature Change: In a chemistry class, a thermometer is placed in a beaker of hot water. The initial temperature of the water is 160 °F. After 9 minutes the water has cooled to 106 °F. If the water temperature drops at a constant rate, by how much does the water temperature change each minute? (Round your answer to a tenth of a degree.)

Answer = The temperature dropped °F per minute.

Evaluate the following expressions when a is −3 and b is 5

a^2+2ab+b^2

thank you!

You own 405 shares of stock A and 780 shares of stock B. During one week, A increases by $3.05 per share, while B loses $1.24 per share. How much did the value of your investment change?

thank you!

How long will it take for $1,000 to be worth $3,500 at 7% interest, compounded continuously

Solve the following equation for x:

log3x=3

Write the expression as a single logarithm:

1/5logx−5logy−5logz=log

A gun fires a bullet almost straight up from the edge of a 140-foot cliff. If the bullet leaves the gun with a speed of 556 feet per second, its height at time t is given by h(t)=−16t2+556t+140, measured from the ground below the cliff.

When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)

The bullet will land after seconds.

How long will it take for $1,000 to be worth $3,000 at 7% interest, compounded continuously?

part 1: How long will it take for $1,200 to double if it is invested at 8% annual interest compounded 4 times a year? Enter in exact calculations or round to 3 decimal places.

part 2: how long will it take if the interest is compounded continuously?

thank you!

Solve for t : |6−4/7t|+7=9

The corporate profits for various U.S. industries vary from year to year. An approximate model for profits of U.S. "communications companies" during a given year between 1990 and 1997 is given by

P=−3400|x−5.5|+36000

where P is the annual profits (in millions of dollars) and x is the number of years after 1990. Use the model to determine the years in which profits of "communication companies" were $31.5 billion ($31,500 million).

In the years and the communication companies had profits of $31.5 billion.

thank you!

The fuel efficiency (mpg rating) for cars has been increasing steadily since 1980. The formula for a car's fuel efficiency for a given year between 1980 and 1996 is

E=0.36x+15.9

where E is miles per gallon and x is the number of years after 1980.

a. In what years was the average fuel efficiency for cars less than 17 mpg (in interval form)?

b. In what years was the average fuel efficiency for cars more than 20 mpg (in interval form)?

thank you!

Write the ratio as a fraction to lowest terms.

30 to 6

A person riding a Ferris Wheel travels once around the wheel, a distance of 172 feet, in 30 seconds. What is the average speed of the rider in feet per second? Round to the nearest tenth.

thank you!

For the following problem, y varies directly as x.

If y = 12 when x = 16, find x when y is 15.

1. For the following problem, y varies directly as the square of x.

If y = −50 when x = 5, find y when x is 8.

2. For the following problem, y varies inversely with x.

If y = 4 when x = 1, find y when x is 6.

3. For the following problem, y varies inversely as the square of x.

If y = 48 when x = 2, find y when x is 4.

4. The current I in an electric circuit varies inversely with the resistance R. If a current of 50 amperes is produced by a resistance of 6 ohms, what current will be produced by a resistance of 2 ohms?

*These are proportions problems..*

A map is drawn so that every 3.1 inches on the map corresponds to an actual distance of 100 miles. If the actual distance between the two cities is 400 miles, how far apart are they on the map?

A solution contains 72 milliliters of HCl and 104 milliliters of water. If another solution is to have the same concentration of HCl in water but is to contain 65 milliliters of water, how much HCl must it contain?

A basketball player makes 9 of 15 free throws in the first week of the season. If she shoots with the same accuracy for the next week, how many of the 10 free throws she attempts will she make?

If 4/9 is added to five times the reciprocal of a number, the result is 1. Find the number.

A boat travels 28 miles up the river in the same amount of time it takes to travel 40 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water?

A water faucet can fill a sink in 7 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?

thank you!

One number is 5 times another. Write an expression for the sum of their reciprocals. Then simplify the expression. (Use x for the variable.)

Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains a variable.

2/y+5+4/y−2= −2/y2+3y−10

thank you!

A Ferris wheel has a circumference of 592 feet. If a trip around takes 45 seconds, find the average speed in miles per hour. Round to the nearest tenth.

Write the ratio as a fraction to lowest terms.

30 to 6

A person riding a Ferris Wheel travels once around the wheel, a distance of 172 feet, in 30 seconds. What is the average speed of the rider in feet per second? Round to the nearest tenth.

Thank you!

The product of two consecutive integers is 30. Find the two integers.

The smaller of the two integers is , and the larger of the two is .

Or the smaller is and the larger is .

he length of a rectangle is 1 inches more than the width. The area is 6 square inches. Find the dimensions.

The length of the rectangle is inches, while the width is inches.

A company can manufacture x hundred items for a total cost of C=600+1100x−100x2. Find x if the total cost is $3,000.

A gun fires a bullet almost straight up from the edge of a 140-foot cliff. If the bullet leaves the gun with a speed of 556 feet per second, its height at time t is given by h(t)=−16t2+556t+140, measured from the ground below the cliff.

When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)

The bullet will land after seconds.

thank you!