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2 years ago

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Segment GH is the diameter of a circle. If point K is located on the circle, which of the following could be the measure of angl

e GHK
A 59°
B 99°
C 123°
D 180°

2 answers:

Hoochie [10]2 years ago

6 0

I think the answer is A not sure

Oksana_A [137]2 years ago

6 0

Check the picture below

now, based on Thales theorem, the angle at K will always be 90°, that means, the other two angles, G and H, will always share the other 90°, since the sum of all internal angles is 180°, so, either G or H, will never be 90°, will always be less than 90°, always an acute angle

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Solve the trigonometric equation in the interval [0, 2π). Give the exact value, if possible; otherwise, round your answer to two

svp [43]

Answer:

θ∈{ $\frac{\pi }{8},\frac{5\pi }{8},\frac{9\pi }{8},\frac{13\pi }{8}$ }

Explanation:

The given equation is

$sin(2\theta )-cos(2\theta )=0$

$\Rightarrow sin(2\theta )=cos(2\theta )\\\\\therefore \frac{sin(2\theta )}{cos(2\theta )}=1\\\\tan(2\theta )=1\\\\\therefore 2\theta =n\pi +\frac{\pi}{4}\\\\\therefore \theta =\frac{n\pi }{2}+\frac{\pi }{8}$

Applying values on 'n' we obtain values of θ that beling to [0,2π)

For n=0, θ= $\frac{\pi }{8}$

For n=1, θ = $\frac{5\pi }{8}$

For n=2,θ = $\frac{9\pi }{8}$

For n=3,θ = $\frac{13\pi }{8}$

6 0

2 years ago

What’s the angle it’s looking for ?

Law Incorporation [45]

Given:

m(ar KN) = 2x + 151

m(ar LN) = 61°

m∠NMK = 2x + 45

To find:

m∠NMK

Solution:

By property of circle:

<em>If a tangent and a secant intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.</em>

$$\Rightarrow m\angle NMK=\frac{1}{2} (m \ ar(KN) - m\ arLN))$

$$\Rightarrow 2x+45=\frac{1}{2} (2x + 151-61)$

$$\Rightarrow 2x+45=\frac{1}{2} (2x + 90)$

Multiply by 2 on both sides, we get

$$\Rightarrow 2\times (2x+45)=2\times \frac{1}{2} (2x + 90)$

$$\Rightarrow 4x+90=2x + 90$

Subtract 90 from both sides.

$$\Rightarrow 4x+90-90=2x + 90-90$

$$\Rightarrow 4x=2x$

Subtract 2x from both sides.

$$\Rightarrow 4x-2x=2x-2x$

$$\Rightarrow 2x=0$

$$\Rightarrow x=0$

Substitute x= 0 in m∠NMK.

m∠NMK = 2x + 45

= 2(0) + 45

= 45

Therefore m∠NMK = 45.

8 0

2 years ago

A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, and the turkey special gives a pro

nikklg [1K]

Answer:

The constraints are as follows;

1) 2·x + 2·y ≤ 120

2) 3·x + 4·y ≤ 160

3) x = 2.30

4) y = 3.10

5) P = 2.3·x + 3.10

Step-by-step explanation:

The question is a word problem, with the analysis as follows;

The profit from the roast beef special per sandwich = $2.30

The profit from the turkey special per sandwich = $3.10

The number of slices of bread in the roast beef special = Two slices

The number of slices of cheese in the roast beef special = Three slices

The number of slices of bread in the turkey special = Two slices

The number of slices of cheese in the turkey special = Four slices

The number of slices of bread the deli has = 120 slices

The number of slices of cheese the deli has = 160 slices

Let 'x' and represent the number of roast beef special and 'y' represent the number of turkey special the deli makes, then we have the constraints as follows;

For the number of slices of bread used;

2·x + 2·y ≤ 120...(1)

For the number of slices of cheese used;

3·x + 4·y ≤ 160...(2)

x = 2.30

y = 3.10

The profit 'P' is given by the following equation

P = 2.3·x + 3.10.

5 0

2 years ago

The school cafeteria has 4 rows of tables each row has 22 seats. The school patio has 12 tables. Each table seats 4 students. Ho

o-na [289]

Answer:

Here the answer, dearie.

Step-by-step explanation:

$22 \times 4 = 88 \\ 12 \times 4 = 48 \\ 88 + 48 = 136$

So, 136 people can sit in cafeteria and the patio.

6 0

2 years ago

A bowl of flower seeds contains 5 petunia seeds and 15 begonia seeds. Riley calculated the probability that a random selected se

Vlad1618 [11]

Answer:

Riley divided the number of petunia seeds by the number of begonia seeds, getting $\frac {5}{15} = \frac {1}{3}$ . What you actually need to do to calculate the probability of selecting a petunia seed is divide the number of petunia seeds by the <em>total</em> number of seeds. 5 petunia seeds and 15 begonia seeds makes 20 total seeds, so you divide 5 petunia seeds by 20 total seeds to get $\frac {5}{20} = \frac {1}{4}$ .

7 0

2 years ago