Determine the slope of the curve y = -x² at the point (2,3).

Determine the rationalized value of the complex number:

What is the value:

Find the value of x and y in the following equations: 2x + 3y = 6 5y - 3x - 2 = 0

The sum of the interior angles of a polygon is 540°. Find the number of sides.

A lighthouse blinks five times in a minute. A neighboring lighthouse blinks 4 times in a minute. If they will blink simultaneously, how many seconds they will blink together again?

Mr. Leviste traveled 55 km in 4 hours by driving his car 40 kph and by walking 5 kph the remainder of his trip. What fraction of the distance did Mr. Leviste go by his car ?

Four committee is to be formed in a high school club of 8 sophomores and 5 freshmen, in how many ways they can be formed by choosing two from each group ?

An urn contains 7 red balls ans 3 white balls. What is the probability of getting 2 red balls and then a white ball ?

A card is to be dealt successively without any repitition from an ordinary deck of 52. What is the probability of getting a spade, diamond, a heart and a club?

Lamberto has 2 times as many racing horses than Sonny. If Lamberto gives 10 horses to Sonny, he has only half as many as racing horses than Sonny. How many racing horses do they have ?

A man weighing 70 kilograms jumps on a raft with and area of 4 m² that is floating on a fresh water lake. Find the rise of the raft.

√8 + 3√18 - 7√12 =

If 3× = 54; then 3^×+2 is equal to:

Answer the following question:

R pounds of cheese is fed to N people. If N + P people attend the party, how many pounds of cheese must buy to feed them in the same rate?

A telephone number has 7 digits. How many ways that the 1 digit will occur only once.

A cube is inscribe in a sphere with radius 6 in. What is the maximum volume of a cube?

What is the present worth of a $100 annuity starting at the end of the third year and continuing to the end of the fourth year, if the annual interest rate is 8 % ?

Going against the wind, a domestic plane can travel 5/8 of the distance, if can travel in one hour if is going with the wind. If the plane can fly 300 miles, per hour in calm wind, what is the velocity of the wind?

You deposit $1000 into a 9% account today. At the end of two years, you will deposit another $3000. In five years, you plan a $4000 purchase. How much is left in the account one year after the purchase?

How long is each side of regular hexagon with perimeter 18 ft ?

Find the value of x and y in the equation: 2x - y = 12 and 3x + y = 13

A line passes through ( 4 , 2 ) and ( 1 , 2 ). Find the slope of the line.

A rectangular 200 m is to contain 125 m² of flooring. If the length is to be five times its width, what should its dimension be ?

CPM factory employs 60 workers. If 4 out of every 5 workers are married, how many married workers are employed by the factory ?

The front wheel of a bicycle has a diameter of 50 cm, Approximately how many times has the front wheel turned if the bicycles has traveled 1 km ?

In a PSME meeting, Cofee and cake were served during the break. Of the 50 people who attended the meeting, 30 ate cake while 34 drink coffee. If there were 22 people who had both cake and coffee. how many had neither coffee nor cake ?

What is the diameter of a circle with the following equation: x² + y² - 6x + 4y - 12 = 0 ?

The directrix of the parabola is y - 5 = 0, and its focus is at (4 , -3). Find the length of its lactus rectum.

If f(x) = 2x² + 2, find the value of f(x+4).

If f(x) = 3x + 2 and g(f(x)) = x, then g(x) is equal to:

If John can paint a room in 30 minutes and Tom can paint it in 1 hour, how many minutes will it take them to paint the room if they work together?

A train can pass an average of 3 stations every 10 minutes. At this rate, how many stations will pass it in one hour ?

Find the number of ways two balls, four dolls, and six toy guns can be given to 12 children, if each child gets a toy.

An hour-long test has 60 problems. If a student completes 30 problems in 20 minutes, how many seconds does he have on an average for completing each of the remaining problems ?

The sum of two numbers is 10 and the sum of the squares of the numbers is 52. Find the product of the two numbers.

After 8:00 pm, a ride in a cab cost P25.00 plus P3.00 for every fifth of a kilometer traveled. If a passenger travel x kilometers, what is the cost of the pesos, as a function of x?

On a scaled map, a distance of 10 cm represents 5 km. If a street is 750 meters long, what is the length of the map, in centimeters?

If x is an integer, which of the following must be an odd integer?

The perimeter of a circular sector, whose central angle is 60⁰ is 14 feet. Find the radius of the circle.

A rectangular lot has a total area of 81,600 ft². The flooring at the center 300 ft × 200 ft is surrounded with a uniform width of grass. Find the length of uniform width.

A circle has a center of ( -3 , 1 ) and a radius of 4. Another circle which is tangent to this circles has a center of ( 4 , -4 ). What is the radius ?

At one side of a road is a pole 25 ft high fixed on top of a wall 15 ft high. On the other side of the road, at a point on the ground directly opposite, the flagstaff and the wall subtended equal angles. Find the width of the road.

Carpenter Pedro can make a cabinet in 5 working days alone. Carpenter Juan can do it in 10 days also working alone. How long will it take them to finish the same job working together?