Drag a statement or reason to each box to complete this proof.

Mathematics

1 answer:

ololo11 [35]4 years ago

5 0

Answers:

1) -3(x + 8) = -21

2) Division Property of Equality

3) x + 8 = 7

4) Subtraction Property of Equality

Reasoning:

You are already given the equation, so that will be #1 in the Given.

#2 shows both sides being divided by -3, so you will put the Division Property of Equality.

#3 shows the Division Property after it is carried out, so you will put the equation after the division is done.

#4 shows you are subtracting 8 from both sides, so put the Subtraction Property of Equality.

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The corners of a square are cut off two centimeters from each corner to form an octagon. If the octagon is 10 centimeters wide,

zvonat [6]

Answer:

92 cm²

Explanation:

The area of the octagon may be calculated as the difference of the area of the original square and the area of the four corners cut off.

1) Area of the square.

The original square's side length is the same wide of the formed octagon: 10 cm.

So, the area of such square is: (10 cm)² = 100 cm².

2) Area of the four corners cut off.

Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.

The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).

Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².

Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².

3) Area of the octagon:

Area of the square - area of the cut off triangles = 100 cm² - 8cm² = 92 cm².

And that is the answer: 92 cm².

4 0

3 years ago

1. Amanda tells you that because a variable is in the denominator, the equation three over x plus one over three equals five ove

Hunter-Best [27]

Answer: x = 6

Step-by-step explanation:

$\dfrac{3}{x}+\dfrac{1}{3}=\dfrac{5}{6}$

$(6x)\dfrac{3}{x}+(6x)\dfrac{1}{3}=(6x)\dfrac{5}{6}$ multiplied by common denominator

18 + 2x = 5x

-2x -2x

18 = 3x

÷3 ÷3

6 = x

Since "x" is in the denominator, the restriction is that x ≠ 0. If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.

Remember that "x" is just an unknown value. It is possible to add two fractions together and have their sum be a fraction.

For example: $\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}$ could be written as $\dfrac{1}{5} + \dfrac{2}{x} = \dfrac{3}{5}$ . When we solve it, we will get x = 5.