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atroni [7]
3 years ago
11

In the diagram shown, /Il m, m

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

Answer:

  29°

Step-by-step explanation:

Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

  m∠1 = m∠8

  3x+25 = 4x-17

  42 = m . . . . . . . . add 17-3x

Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...

  m∠2 = 180° -151° = 29°

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Factorise this equation: 4x²-2x-5
Karolina [17]

Answer:

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3 years ago
If
baherus [9]

Answer:  see proof below

<u>Step-by-step explanation:</u>

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
Clare knows that Priya has a bunch of nickels and dimes in her pocket and 2 points
Maurinko [17]

Answer:

5x + 10y = 125

Step-by-step explanation:

Let :

Number of nickel = x

Number of dime = y

Nickel = 5 cent

Dime = 10 cent

Total value = $1.25

Total value should be converted to cent since both dime and nickel are both in cent

= $1.25 * 100 = 125 cents

Therefore,

5x + 10y = 125 cents

4 0
3 years ago
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