Now Since We Know That the Perimeter Is 21 Feet We Have

1. Solve

2. Solve

When you solve you get , which does not check.

Answer: no solution

3. One positive number is five less than another. Their sum is 31. Find the numbers. To get any credit tin this question you solve an equation to determine the answer.

4. A picture frame has a total perimeter of 21 feet. The width is of the height. Find the dimensions of the picture frame.

First find the perimeter in terms of h.

Now since we know that the perimeter is 21 feet we have

Then Answer: Height = 6 ft, width = ft

5. A grocer mixes peanuts that cost $1.41 per pound and walnuts that cost $2.61 per pound to make 100 pounds of a mixture that costs $2.37 per pound. How much of each kind of nut is put into the mixture?

Use x pounds of peanuts and 100 x pounds of walnuts.

The idea is that the cost of x pounds of peanuts plus the cost of 100 x pounds of walnuts equals the cost of the 100 pounds of mixture.

Now solve

Make sure you answer the question!

Mix 20 pounds of peanuts and 80 pounds of walnuts.

6. To obtain the height of a tree (see figure), you measure the tree's shadow and find that it is x = 7 meters long. You also measure the shadow of a two-meter lamppost and find that it is 75 centimeters long. How tall in meters is the tree? (Round your answer to one decimal place.)

Units need to be consistent. Since the quaestion asks for the answer in meters use meters for the units. Since 1 m = 100 cm, 75 cmm =0.75 m. The idea is tha the two triangles are similar, meaning they have the same shape, in which case ratios of corresponding measurements are proportional. Suppose the tree is h meters tall.

The tree is 18.7 meters tall.

7. Simplify and write the result in standard form

8. Simplify and write the result in standard form

9. Simplify and write the result in standard form

10. Simplify and write the result in standard form

11. Solve by factoring

12. Solve by extracting square roots

First you have to have isolated on one side of the equation:

You now take the square root of each side and insert . Essentially you are using the property that if

You now solve for x.

When you get an answer of this form that does not involve a radical then you write the separate solutions:

13. Solve using the quadratic formula

14. Solve using the quadratic formula

15. Solve using the quadratic formula