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2 years ago

What is the prime factorization of 140? A 2^2×3×7 B. 2^3×7 C. 4×5×7 D. 2^2×5×7

Mathematics

1 answer:

Andreyy892 years ago

7 0

Answer:

Step-by-step explanation:

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olga_2 [115]

Answer:

$x=8$

Step-by-step explanation:

Given

$AB||CD$

$\angle ABC = 5x + 50$

$\angle BCD = 7x + 34$

Required

Find x

If $AB||CD$ i.e. If AB is parallel to CD, then

$\angle ABC = \angle BCD$

Substitute values for ABC and BCD

$5x + 50 = 7x + 34$

Collect Like Terms

$5x - 7x = -50 + 34$

$-2x = -16$

Multiply through by $-\frac{1}{2}$

$-\frac{1}{2} * -2x = -16 * -\frac{1}{2}$

$\frac{1}{2} * 2x = 16 * \frac{1}{2}$

$\frac{2x}{2} = \frac{16}{2}$

$x = \frac{16}{2}$

$x=8$

3 0

2 years ago

Find the distance between the

Dovator [93]

Answer:

$\displaystyle d = \sqrt{29}$

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:

*Note:

The distance formula is derived from the Pythagorean Theorem.

Step 1: Define

Identify

Point (5, 10)

Point (10, 12)

Step 2: Find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{5^2 + 2^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{25 + 4}$
[√Radical] Add: $\displaystyle d = \sqrt{29}$