What is the slope of the line shown below?

Mathematics

1 answer:

Anton [14]3 years ago

8 0

Answer:

Slope = 3

Step-by-step explanation:

2 - 8 = -6

2 - 4 = -2

Slope = 3

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How does the Binomial Theorem’s use Pascal’s triangle to expand binomials raised to positive integer powers?

MrMuchimi

Answer:

There are ways for quickly multiply out a binomial that's being raised by an exponent. Like

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = (a + b)(a + b)2 = (a + b)(a2 + 2ab + b2) = a3 + 3a2b + 3ab2 + b3

and so on and so on

but there was this mathematician named Blaise Pascal and he found a numerical pattern, called Pascal's Triangle, for quickly expanding a binomial like the ones from earlier. It looks like this

1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

5 1 5 10 10 5 1

Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle.

Hope this helps!

5 0

3 years ago

A rectangular swimming pool measures 7.5 m by 4.5 m. It is completely surrounded by a fence parallel to each edge of the pool an

Illusion [34]

The total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.

<h3>What is rectangle?</h3>

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A rectangular swimming pool measures 7.5 m by 4.5 m.

It is completely surrounded by a fence parallel to each edge of the pool and at a distance of 3 m from each edge of the pool.

The total length of the fence = 2(7.5+3×2 + 4.5+3×2)

The total length of the fence = 2(7.5+6 + 4.5+6)

The total length of the fence = 2(24)

The total length of the fence = 48 m

Thus, the total length of the fence is 48 m if the rectangular swimming pool measures 7.5 m by 4.5 m.

Learn more about the rectangle here: