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1 year ago

The 3rd term of (a-b)4 is

Mathematics

1 answer:

fgiga [73]1 year ago

4 0

The third term of the expansion is 6a^2b^2

<h3>How to determine the third term of the expansion?</h3>

The binomial term is given as

(a - b)^4

The r-th term of the expansion is calculated using

r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)

So, we have

3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)

Evaluate the sum and the difference

3rd term = C(4, 2) * (a)^2 * (-b)^2

Evaluate the exponents

3rd term = C(4, 2) * a^2b^2

Evaluate the combination expression

3rd term = 6 * a^2b^2

Evaluate the product

3rd term = 6a^2b^2

Hence, the third term of the expansion is 6a^2b^2

Read more about binomial expansion at

brainly.com/question/13602562

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Evaluate [3+(8-2)]x5

photoshop1234 [79]

Answer:

Step-by-step explanation:

Subtract the numbers

(3+(8-2)). x5

[3+6)]. x5

Add the numbers

[3+6]. x5

[9]. x5

8 0

3 years ago

1. Delia purchased a new car for $23,350. This make and model straight line depreciates to zero after 13 years.

frosja888 [35]

Answer:

a. y-intercept = 23350 and x-intercept = 13

b. $m = -\frac{23350}{13}$

c. $y = -\frac{23350}{13}x + 23350$

Step-by-step explanation:

Given

$Years = 13$

$Total\ depreciation = \$23350$

Solving (a): The x and y intercepts

The y intercept is the initial depreciation value

i.e. when x = 0

This value is the value of the car when it was initially purchased.

Hence, the y-intercept = 23350

The x intercept is the year it takes to finish depreciating

i.e. when y = 0

From the question, we understand that it takes 13 years for the car to totally get depreciated.

Hence, the x-intercept = 13

Solving (b): The slope

The slope (m) is the rate of depreciation per year

This is calculated by dividing the total depreciation by the duration.

So:

$m = \frac{23350}{13}$

Because it is depreciation, it means the slope represents a deduction.

So,

$m = -\frac{23350}{13}$

Solving (c): The straight line equation

The general format of an equation is:

$y = mx + b$

Where

$m = slope$

$b = y\ intercept$

In (a), we have that:

$y\ intercept = 23350$

In (b), we have that:

$Slope\ (m) = -\frac{23350}{13}$

Substitute these values in $y = mx + b$

$y = -\frac{23350}{13}x + 23350$

<em>Hence, the depreciation equation is: </em> $y = -\frac{23350}{13}x + 23350$ <em></em>

8 0

3 years ago

A car has a full tank with 13 and 1/2 gallon of gas .Over the course of two days the amount of gas decreased by 6.25 write and e

aleksklad [387]

Answer: 7.25 gallons

Step-by-step explanation:

Convert 13¹/₂ to a whole number with a decimal:

= 1/2 = 0.5

= 13.5 gallons of gas

If the gas reduces by 6.25 gallons, the amount of gas remaining will be:

= Starting amount - Amount reduced by

= 13.5 - 6.25

= 7.25 gallons

6 0

3 years ago

Find the value of each expression.<br> -5 -9 -13

Andrei [34K]

Answer:

-27

Step-by-step explanation:

-5-9=-14

-14-13=-27

3 0

3 years ago

The area of triangles and trapezoid

evablogger [386]

Shapes? We need to know how they look like in order to solve

7 0

3 years ago