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zepelin [54]
2 years ago
11

How does the distributive property work

Mathematics
1 answer:
jonny [76]2 years ago
7 0

Explanation:

The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...

  a(b +c) = ab +ac

__

<h3>Groups and Multiples of Groups</h3>

The parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.

In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.

For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...

  3(f +2w + s + h) = 3f +6w +3s +3h

__

<h3>Eliminating Parentheses</h3>

Using the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. <em>The multiplier multiplies every member of the group</em>.

__

<h3>Adding Parentheses</h3>

The reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.

  3f +6w +3s +3h = 3(f +2w + s + h)

Often, we're asked to choose the multiplier to be the <em>greatest common factor (GCF) </em>of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be <em>a</em> common factor, not necessarily <em>the greatest</em> common factor.

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erma4kov [3.2K]

Answer:

m\angle XYW  = (155 - 20x)\degree

Step-by-step explanation:

m\angle XYZ= m\angle XYW +m\angle WYZ\\\\150\degree = m\angle XYW +(20x-5)\degree \\\\150\degree - (20x-5)\degree = m\angle XYW  \\\\(150 - 20x+5)\degree = m\angle XYW  \\\\(155 - 20x)\degree = m\angle XYW  \\\\m\angle XYW  = (155 - 20x)\degree \\\\

7 0
3 years ago
Can someone help solve
leva [86]

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For example:

\frac{x^2}{x^1} = x^{2-1} =x^1

\frac{x^5}{x^3} =x^{5-3} = x^2

8 0
3 years ago
The equation y=5+0.5x represents the cost of getting a car wash and using the vacuum for x minutes. What is the y-intercept?
adell [148]

5 is the y intercept.

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5 0
2 years ago
The hypotenuse of a right triangle is 50 millimeters long. One leg of the right triangle is 30 millimeters long. What is the len
alexandr1967 [171]
First. we use the Pythagorean theorem:
a {}^{2} +  b {}^{2} =  c {}^{2}
Add the numbers in
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start simplifying
{b}^{2}  = 1600
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So, the leg has a length of 40 mm.
6 0
3 years ago
The graph of the function f(x) = (x + 2)(x + 6) is shown
Vitek1552 [10]

Answer:

The function is negative for all real values of x where

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Step-by-step explanation:

f(x) = (x +2)(x + 6)

 x + 2 = 0    or   x + 6 = 0

x = -2     or x = -6

 After graphing the function is negative between -6 < x < -2

7 0
2 years ago
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