Mathematics, 25.03.2021 17:40 Ibnushuaibabutalhah

What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.

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Answer from: allykram7

$\displaystyle d = 5.7$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (2, 3)

Point (-2, 7)

Step 2: Identify

(2, 3) → x₁ = 2, y₁ = 3

(-2, 7) → x₂ = -2, y₂ = 7

Step 3: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(-2-2)^2+(7-3)^2}$ [Distance] [√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(-4)^2+(4)^2}$ [Distance] [√Radical] Evaluate exponents: $\displaystyle d = \sqrt{16+16}$ [Distance] [√Radical] Add: $\displaystyle d = \sqrt{32}$ [Distance] [√Radical] Simplify: $\displaystyle d = 4\sqrt{2}$ [Distance] Evaluate: $\displaystyle d = 5.65685$ [Distance] Round: $\displaystyle d = 5.7$

Answer from: Quest

Ithink the right answer could be 50%

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary....