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EleoNora [17]
1 year ago
5

Alexa uses the binomial theorem to correctly expand (x+2)^4. which is one of the terms in alexa's answer?

Mathematics
2 answers:
sammy [17]1 year ago
8 0
^0 ...............1
^1..............1  1
^2............1  2  1 
^3...........1 3  3  1
^4..........1 4 6  4  1

(x+2)^4 = 1(x)^4(2)^0 + 4(x)^3(2)^1 + 6(x)^2(2)^2 + 4(x)^1(2)^3 + 1(x)^0(2)4
             = x^{4} + 8 x^{3} + 24 x^{2} + 32x + 16
Aloiza [94]1 year ago
6 0
The first term is x^4.
The second term is  8x^3
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2 years ago
What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minu
lisov135 [29]

Answer:

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

Step-by-step explanation:

Given:

(2x + 5) / (x² - 3x) - (3x + 5) / (x³ - 9x) - (x + 1) / x² - 9

Factor the denominators

(2x + 5) / x(x - 3) - (3x + 5) / x(x - 3)(x + 3) - (x + 1) / (x - 3)(x + 3)

Lowest common multiple of the 3 fractions is x(x - 3)(x + 3)

= (2x+5)(x+3) - (3x + 5) - (x + 1)x / x(x - 3)(x + 3)

= (2x²+6x+5x+15) - (3x + 5) - (x² + x) / x(x - 3)(x + 3)

= 2x² + 11x + 15 - 3x - 5 - x² - x / x(x - 3)(x + 3)

= x² + 7x + 10 / x(x - 3)(x + 3)

Solve the numerator.

Solve the quadratic expression by finding two numbers whose product is 10 and sum is 7

The numbers are 5 and 2

= x² + 5x + 2x + 10 / x(x - 3)(x + 3)

= x(x + 5) + 2(x + 5) / x(x - 3)(x + 3)

= (x + 5)(x + 2) / x(x - 3)(x + 3)

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

Recall,

x(x - 3)(x + 3) is a factor of x³ - 8x

A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction

(x + 5)(x + 2) / x³ - 9x

B. StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction

(x + 5)(x + 4) / x³ - 9x

C. StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction

2x + 11 / x³ - 12x - 9

D. StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction

3(x + 2) / x² - 3x

3 0
1 year ago
In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014,
DochEvi [55]

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

7 0
2 years ago
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8_murik_8 [283]
We can solve this equation by using the Square Root Method.
First, take the square root of each side of the equation:
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Then add 8 to both sides.
x=20

The original lawn was d. 20 feet by 20 feet.
5 0
2 years ago
Read 2 more answers
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