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3 years ago

-50 added to three times an unknown number equals -11? What is the solution to the sentence shown?

Mathematics

1 answer:

docker41 [41]3 years ago

5 0

Answer:

Step-by-step explanation:

-11= 3x-50

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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 $\checkmark$

4 0

3 years ago

What is 6 x 2 without using 12 for the answer?

marusya05 [52]

Answer: the answer is 12

Step-by-step explanation:

6 0

3 years ago

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Help with this please, picture above ^

Irina18 [472]

Answer:

y = -3x -2

Step-by-step explanation:

parallel lines have same slope

line d: slope (m) = -3

y intercept (b) = -2

equation y = mx + b y = -3x -2

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3 years ago

ANSWER IN THE COMMENTS SECTION

ryzh [129]

Answer:

Step-by-step explanation:

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3 years ago

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Hey there! I would like some help please :) Thanks!

Alchen [17]

AC is a common side, ∠ACD = ∠ACB and CD = BC ⇒ ΔACD and ΔABC are congruent (SAS definition).

Congruent triangles have exactly the same three angles, so ∠D = ∠B.

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3 years ago