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3 years ago

PLEASE HELP FIND THE LENGTH OF RS.

Mathematics

2 answers:

Gwar [14]3 years ago

8 0

Answer:

Step-by-step explanation:

Distance between 2 points

$= \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} }$

☆ (x₁, y₁) is the first coordinate while (x₂, y₂) I'd the second coordinate.

Length of RS

$= \sqrt{ {[ - 1 -( - 4)] }^{2} + (9 - 1)^{2} } \\ = \sqrt{( - 1 + 4)^{2} + 8^{2} } \\ = \sqrt{ {3}^{2} + 64 } \\ = \sqrt{73} \\ = 8.54 \: (3 \: s.f.)$

Thus, RS is about 8.5 units.

Vesnalui [34]3 years ago

6 0

Answer:

I believe its A. 8.5

Step-by-step explanation:

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8 is to 32 as 1 is to

kati45 [8]

Answer:

1 is to 4

Step-by-step explanation:

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5 0

3 years ago

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Calculate the slope of the line that contains the points: (2, -3) and (6, -3)

Brilliant_brown [7]

Answer:

$\displaystyle m = 0$

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)
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Step-by-step explanation:

Step 1: Define

Identify

Point (2, -3)

Point (6, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]: $\displaystyle m = \frac{-3- -3}{6- 2}$
[Fraction] Subtract: $\displaystyle m = \frac{0}{4}$
[Fraction] Divide: $\displaystyle m = 0$

6 0

3 years ago

If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (H

vovikov84 [41]

Step-by-step explanation:

We will prove by contradiction. Assume that $2^n + 1$ is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that $p\mid n$ . Then, for some integer $k\geq 1$ ,

$n=p\times k.$

Therefore

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p.$

Here we will use the formula for the sum of odd powers, which states that, for $a,b\in \mathbb{R}$ and an odd positive number $n$ ,

$a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+b^{n-1})$

Applying this formula in 1) we obtain that

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Then, as $2^k+1>1$ we have that $2^n+1$ is not a prime number, which is a contradiction.

In conclusion, if $2^n+1$ is an odd prime, then n must be a power of 2.

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