# Adding polynomials

Submitted by francisrwd on Fri, 03/15/2013 - 00:00Add: \[ (-9 + 3n^6 + 3n^5) + (2n^6 + 5n^5 + 6) \]

=> (−9+3n6+3n5)+(2n6+5n5+6)

−9+6 +3n5 +5n5 + 2n6+3n6(grouping like terms)

( −9+6) +(3n5 +5n5 ) + (2n6+3n6)

(-3 ) + (8n5) + (5n6) (combining LIKE terms)

**-3 + 8n5 +**

**5n**

**6**(Answer)

# A framed painting has overall dimensions of 32 inches by 29 inches

Submitted by enrico on Thu, 03/14/2013 - 11:52# A ball is dropped from a height of 36 feet

Submitted by dondilaboy on Thu, 03/14/2013 - 02:56A ball is dropped from a height of 36 feet. The quadratic equation:

\[d = \frac {1}{2}gt^2 \]

is used to culate the distance $\mathbf{d}$ the ball has fallen after $\mathbf{t}$ seconds. The constant $\mathbf{g}$ is the acceleration of gravity, 9.8 m/s2. How long does it take the ball to hit the ground? (in this problem, as in problem 3, we’re ignoring air resistance)

Using the formula:

With the given g = 9.8 m/s^2, we will convert it to ft/s^2.

9.8 m x 3.28084 ft / 1 m

9.8 m = 32.1522 ft

Therefore, g = 32.1522 ft/s^2

Using the formula:

# The sum of two numbers is 66

Submitted by Guest on Sun, 03/10/2013 - 02:11The sum of two numbers is 66. Two times the larger number minus the smaller number is 177. What are the numbers?

The sum of two numbers is 66. We can represent the numbers as follows:

x = the bigger number

y = the smaller number

Thus,

x + y = 66 (Eq1)

Two times the larger number minus the smaller number is 117. Thus, we derives equations:

2x - y = 117 (Eq2)

Solving for y in Eq2 gives:

2x - y = 117

2x - 117 = y (Eq3)

Substituting Eq3 in Eq1 gives:

x + y = 66

x + (2x - 117) = 66

x + 2x - 117 = 66

3x - 117 = 66

3x = 66 + 117

3x = 183

x = 183/3

x = 61

Therefore, the bigger number is 61.

To solve for y, substitute 61 in Eq1, giving:

x + y = 66

61 + y = 66

y = 66 - 61

y = 5

Therefore, the smaller number is 5.

CHECK:

Eq1: x + y = 66

61 + 5 = 66

66 = 66

Eq2: 2x - y = 117

2(61) - 5 = 117

117 = 117

# A woman invested $25,000 in two business ventures

Submitted by Guest on Tue, 03/05/2013 - 22:10A woman invested $25,000 in two business ventures. Last year she made a profit of 15 percent from the first venture but lost 5 percent from the second venture. If last year’s income from the two investments was equivalent to a return of percent on the entire amount invested, how much had she invested in each venture.