# basic algebra questions

1. Factor:

x^3y + 2x^2y^2 + xy^3

2. Solve the equation:

2h^2 - h - 3 = 0

3. Solve the equation.

2w (4w + 1) = 1

4. Solve the equation.

M^3 + 2m^2 - 3m = 0

5. Solve the equation.

1/18 h^2 - ½ h + 1 = 0

6. Rectangular stage. One side of the rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the side?

7. Avoiding a collision. A car is travelling on a road that is perpendicular to a railroad truck. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing.

8. winter wheat. While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kms, then what is the area of each field?

9. Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 + r)^2 = 27,000.

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#### Solution Summary

Basic algebra questions are solved, such as simplifying expressions, factoring, and solving equations.

Solving Basic Algebra Questions

1) The spread of a virus in an isolated community is modeled by N(t)=1100/1+49e^-0.3t, where N(t) is the number of people infected after t days.

a) Approximately how many people will be infected in 16 days?

___________

b) How long until 900 people have been infected? Round to the nearest day.

_________days

2) Solve for x: 2^5x-4=3^7x+4

Round to the nearest 0.001.

x=________

3) The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of organic matter can be used to determine the age of the organic matter. Archaeologists discovered a linen wrapping from an ancient scroll had lost 24.2% of its carbon-14.

a) If the model A=Ce^kt is used to model the amount of carbon-14 present at time t, determine the value of k. Round to five decimal places.

k=_________

b) Use the model to estimate how old the linen wrapping was when it was found. Round to the nearest year.

__________years.