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3 years ago

Simplify the expression below.

Mathematics

1 answer:

Novay_Z [31]3 years ago

5 0

Answer:

$\displaystyle 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{7^2 - 13}{24 - 18}$

Step 2: Evaluate

[Fraction] Exponents: $\displaystyle \frac{49 - 13}{24 - 18}$
[Fraction] Subtract: $\displaystyle \frac{36}{6}$
[Fraction] Divide: $\displaystyle 6$

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baherus [9]

Answer: see proof below

Step-by-step explanation:

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

$\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}$

Proof LHS → RHS:

LHS cos 165

Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

⇒ 2 cos² 165 = cos 330 + 1

Given: $2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1$

$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

Divide by 2: $\cos^2 165 = \dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}$

Square root: $\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}$

Scratchwork: $\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2$

$\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}$

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

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3 years ago

Determine the sign of the some of negative 8 + 11

AVprozaik [17]

Answer:

positive 3

Step-by-step explanation:

-8 + 11 is 3. the other way you can think of it is by subtracting 8 from 11.

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PilotLPTM [1.2K]

Answer:

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Step-by-step explanation:

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boyakko [2]

One answer could be 6:8

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Vladimir79 [104]

Answer:

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xy+x+y^2+4y+3

Which is an equivalent expression after applying the distributive property.

As we can see we have an one of the variables squared, so we obtain an Parabolic Cillinder

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3 years ago

Simplify the expression below. ​

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