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Gnom [1K]
2 years ago
8

In parallelogram EFGH, the measure of angle E is (2x + 3) and the measure of angle F is (3x – 33). What is the measure of angle

E?
36°
42°
87°
93​
Mathematics
2 answers:
sesenic [268]2 years ago
7 0

Answer:

87 deg

Step-by-step explanation:

torisob [31]2 years ago
5 0

Answer:

87 deg

Step-by-step explanation:

Angles E and F are internal and adjacent to one another, hence they both add up to 180 deg

(2x+3) + (3x-33) = 180

2x+3 + 3x-33 = 180

5x -30 = 180

5x = 180 + 30 = 210

x = 42 deg

Angle E = 2(42) + 3 = 87 deg

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Answer:

176

Step-by-step explanation:

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2 years ago
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Greg is designing a clock face. Using the center of the clock face as the origin, he keeps its diameter at 10 units. Match the p
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Find the markup and the cost of the following item. Round answers to the nearest cent.
scoray [572]

Answer:

1st question: M=22.62 while C=75.38

2nd question: M=.22 while C=1.97

Step-by-step explanation:

If a mirror costing x dollars is marked up 30%, then we have to find x such that 30%x+x is 98 dollars.

We are solving:

.3x+x=98

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1.3x=98

Divide both sides by 1.3:

x=75.38

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C=75.38

So M=22.62 while C=75.38.

If ream of paper cost x and is marked up 11%, then we have to find x such that 11%x+x is 2.19.

We are solving:

.11x+x=2.19

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M=2.19-1.97=.22

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8 0
2 years ago
The variable complex number z is given by z=1+cos 2θ+isin2θ,where θ takes all values in the interval −1/2π<θ<1/2π
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The given complex number is
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Part (i)
Let V = the modulus of z.
Then
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     = 1 + 2 cos(2θ) + cos²2θ + sin²2θ

Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)

Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because  -1/2π < θ < 1/2π,
V = 2 cosθ                          PROVEN

Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
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The denominator is
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Therefore
\frac{1}{z} = \frac{1}{2} -i \frac{sin2\theta}{2(1+cos2\theta)}

The real part of 1/ = 1/  (constant).
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Add all the numbers together and the difference is the answer which is 44%

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