Pair Fiberglass
Radical Expressions. Solve these equations.?
I really need help with these:
Solve and check.
1. (sqrt of 2y + 7) + 4 = y
Pythagorean theorem.
Express your answer in simplified radical form.
2. A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulation comes in 40-cm wide rolls that are cut to fit between the rafters in the attic. if the roof is 7 m from peak to eave and the attic space is 3 m high at the peak, how long does each of the pieces of insulation
need to be? Round to the nearest tenth.
Find the distance between each pair of points.
3. (-3,0) and (4,0)
Use the Pythagorean theorem to determine the length of the line segment. Where appropriate, round to the nearest hundredth.
4. (3,2) and (1,-1)
Simplify by combining like terms.
5. x * sqrt of 18 - 3 * sqrt of 8x^2
Simplify each radical expression.
6. (sqrt of 3 + 5)(sqrt of 3 - 3)
Express your answer in simplified radical form.
7. 8^2 + x^2 = 12^2
Thanks for all of your help!
1) SQRT(2Y + 7) + 4 = Y
subtract 4 from both sides
SQRT(2Y + 7) = (Y - 4)
square the equation
2Y + 7 = (Y - 4) * (Y - 4) = Y^2 -8Y +16
subtract 2Y + 7 from both sides
0 = Y^2 - 10Y + 9
Use the binomial equation to finish.
2) The triangle gives us 1/2 the length of the roof. Draw a picture. /|\ The height of the roof (triangle) is 3m. The long side (hypotenuse) is 7m. Use the Pythagorean theorem to calculate the remaining side, S. (7-squared = s-squared plus 3-squared). Remember, S is only half the roof length!
3) Draw the two points on a graph if you are having trouble. You can count the distance since they are both on the X axis.
4) a) Draw two points on a graph and
.....b) use the two points for two corners of a right triangle. Start with point 2 and draw a line from 1,-1 to 3,-1. Then draw a line down from point 1 to meet with the first line. Now you have a right triangle, you can count the length of each side and calculate the hypotenuse using Pythagorean T.
5) X * SQRT(18) - 3 * SQRT(8x^2)
term 1 = SQRT(18)x
term 2 = 3 * SQRT(8x^2) = 3 * SQRT(8) * SQRT(x^2)
...........= 3 * SQRT(8) x
You should be able to calculate square roots and add to get an answer. If you are not supposed to calc square roots, then continue:
term 1 = SQRT(18)x = SQRT(9) * SQRT(2) * x = 3*SQRT(2)x
term 2 = 3 *SQRT(8)x = 3*SQRT(4)*SQRT(2)*x = 6*SQRT(2)x
term1 + term2 = 9*SQRT(2)x
6) Multiply each term in parenthesis A by each term in parenthesis B and combine:
SQRT(3) * SQRT(3) = 3
SQRT(3) * -3 = -3*SQRT(3)
5 * SQRT(3) = 5*SQRT(3)
5 * -3 = -15
Now combine:
3 + 2*SQRT(3) - 15
7) I'm not sure what they're asking for here. Sorry. I would just solve for X, but I don't think that's what they want.
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