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adelina 88 [10]
3 years ago
14

PLEASE HELP. When solving the equation, what property was used to go from Step 2 to Step 3?

Mathematics
1 answer:
Vitek1552 [10]3 years ago
5 0

9514 1404 393

Answer:

  addition property of equality

Step-by-step explanation:

The addition property of equality is used to add 2x to both sides of the equation:

  -2x +2x -3 = x +2x -18 . . step 2 with 2x added

  -3 = 3x -18 . . . . . . . . . . . . step 3 (simplified)

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A card is chosen at random from a deck of 52 cards. What is the probability that a king or queen is chosen?
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The answer is B) 2/13.

An easy way to figure this out is to find what the unsimplified probability would be:

Since there are 8 kings and queens in total, the number is:

8/52

But, since these are both even numbers, they can be simplified.

1/4 x 8 = 2

1/4 x 52 = 13

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Since 13 is a prime number, the answer cannot be simplified anymore.

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3 years ago
a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form
lianna [129]

Answer:

The perimeter of the garden, in meters, is 24\sqrt{2}

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that d = 12, side s. So

s^2 + s^2 = 12^2

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s^2 = \frac{144}{2}

s^2 = 72

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Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

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3|3

1

So

72 = 2^{3}*3^{2}

So, in simplest radical form:

s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

P = 4s

In this question, since s = 6\sqrt{2}

P = 4s = 4*6\sqrt{2} = 24\sqrt{2}

The perimeter of the garden, in meters, is 24\sqrt{2}

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2 years ago
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