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Adding polynomials

Add:     \[ (-9 + 3n^6 + 3n^5) + (2n^6 + 5n^5 + 6) \]

Number: 
To add these polynomials, you need to add the "like" terms. Here are the step-by-step solution:

=> (
9+3n6+3n5)+(2n6+5n5+6)

 9+3n6+3n5 + 2n6+5n5+6  (dropping the parentheses)

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

( 9+6) +(3n5 +5n5 ) + (2n6+3n6)

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


-3  + 8n5 + 5n6  (Answer)

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

A framed painting has overall dimensions of 32 inches by 29 inches. The area of the painting itself is 550 square inches. Find the width of the frame.
Duration: 
expired

A ball is dropped from a height of 36 feet

A 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)

Number: 

Using the formula:

d=21gt2


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

The sum of two numbers is 66. Two times the larger number minus the smaller number is 177. What are the numbers?

Number: 

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

A 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.

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