To find what percent 37 is of 144, divide 37 by 144 and multiply by 100%:
\(\frac{37}{144}\) ≈ 0.26
0.26 × 100% = 26%.

If the sum of the real numbers a and b is 13, then a+b = 13. If the difference between a and b is 5, then |a−b| = 5. Think of the difference as the positive distance between a and b on the number line. Solve the first equation for a, as follows:
a + b = 13
a = 13 − b
Now, substitute 13−b for a in the second equation and solve for b:
|13 − b − b| = 5
|13 − 2b| = 5
| − 2b| = 8
| − b| = 4
b = 4
Now substitute b in the first equation to get a+4 = 13, so a = 9. If a = 9 and b = 4, ab = 36.

Since the triangle is isosceles, the base angles will have the same measure, x.

Since the sum of the angles in a triangle is 180°, 50 + 2x = 180, making x =\(\frac{(180 − 50)}{2}\)= \(\frac{132}{2}\), or 65°

Recall that in scientific notation 2.0 × 10² = 2.0 × 100 = 200 and 2.0 × 10⁻² = 2.0 × 0.01 = 0.02. To solve this problem, determine the decimal value of each answer choice by changing the scientific notation to decimals:
A. 0.02 × 10⁴ = 0.02 × 10,000 = 200
B. 0.2 × 10³ = 0.2 × 1000 = 200
C. 2.0 × 10⁻² = 2.0 × 0.01 = 0.02
D. 20.0 × 10² = 20.0 × 100 = 2000
E. 0.002 × 10⁵ = 0.002 × 100,000 = 200
Thus 2.0 ×10⁻² = 2.0×0.01 = 0.02 is the number that is least in value.

To solve this problem, first note that AB is the hypotenuse of a right triangle with legs AE and BE, then apply the Pythagorean Theorem. According to the figure, E is between A and D, which means that AD = AE + ED, or AE = AD − ED. It is given that AD = 16 and ED = 11, therefore AE = 16−11, or 5. Also according to the figure, you can reasonably assume that BE and CD have the same length, and since AE is congruent to CD, the segments BE and CD have a length of 5 as well. Thus, AB is the hypotenuse of a right triangle with legs of 5, making AB² = 5² + 5² = 25 + 25, or 50. Since AB² = 50, AB = \(\sqrt{50}\) = \(\sqrt{(50\times 2)}\) = \(\sqrt{25}\)√2, or 5√2.

To solve this problem, recall that when two numbers that consist of the same base and different exponents are multiplied together, you keep the base and add the exponents. Because multiplication is commutative, the expression 4a³ × 5a⁸ can be written as 4 × 5 × a⁸ × a³, or 20a⁸⁺³, which equals 20a¹¹. You can eliminate answer choice A, B, and C because they add the coefficients instead of multiplying them.

To solve this problem, substitute the value 250 for x in the expression 10(100x − 10, 000) + 100, as follows:
10(100(250) − 10,000) + 100 =
10(25,000 − 10,000) + 100 =
10(15,000) + 100 =
150,000 + 100 = 150,100.

To multiply these quantities, first group like terms:
2x² × 3x²y² × 5x²y = (2 × 3 × 5)(x²x²x²)(y²y).
To multiply the same base, add the exponents:
(2 × 3 × 5)(x²x²x²)(y²y) = 30x⁶y³.

If all CDs are equally priced and 8 CDs cost $76.00, then the cost of 1 CD is \(\frac{\$ 76.00}{8}\), or $9.50.

The positive factors of 32 include all of the positive integers that divide evenly into 32. Don’t get confused between positive integers (which include 1) and even integers.