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3 years ago

(4x-10) Use the diagram above to determine the mCE The mCE-

Mathematics

1 answer:

BabaBlast [244]3 years ago

3 0

Answer: Arc CE measures 62 units

Step-by-step explanation: What we have in the question is a circle with two secants ABC and ADE. The two secants have been extended such that two arcs have been formed which are, major arc CE (that is, 4x - 10) and minor arc BD (that is 26).

When you have a circle with two intersecting secants, the angle x (that is angle CAE) is derived as half of the difference of the two intercepted arcs. That is;

Angle x = 1/2 [CE - BD)

Angle x = 1/2 [ (4x - 10) - 26]

Angle x = 1/2(4x - 36)

Cross multiply and we now have

2x = 4x - 36

Collect like terms and we now have

36 = 4x - 2x

36 = 2x

Divide both sides by 2

18 = x

Having calculated x as 18, where arc CE equals 4x - 10, then substitute for the value of x.

CE = 4(18) - 10

CE = 72 - 10

CE = 62

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Answer:

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3/4(2x+5)=5(x+12)

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2 years ago

Is 1/3 greater or less than 1/2

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3 years ago

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3 years ago

For which value of theta is sine theta = negative 1?

Ivan

Answer:

1) 270 degrees

2) pi/4 rad

Step-by-step explanation:

1.) For which value of theta is sine theta = negative 1?

Given

sintheta = -1

theta = arcsin(-1)

theta = -90degrees

Since sin is negative in the third and 4th quadrant

In the third quadrant, theta = 180 + 90 = 270degrees

In the fourth quadrant, theta = 360 - 90 = 270 degrees

Hence the required value of theta is 270degrees

2) Given the radius of the circle to be 1, the y axis value will also be 1 units

Opposite = 1

adjacent = 1

hyp = √1²+1²

hyp = √2

sin theta = opp/hyp

sin theta = 1/√2

theta = arccsin(1/√2)

theta = 45 degrees

Express in radians

45 degrees = pi/4 radians

Hence the required angle in the first quadrant is pi/4 rad

4 0

3 years ago

Read 2 more answers

PLZZZ HELP NOOOOWWW!!!

maw [93]

Hello!

You can use the Pythagorean Theorem

$a^{2} + b^{2} = c^{2}$

C is the hypotenuse which is the line across the diameter
a and b are the other sides

You have to find the bottom side of the triangle

9 - 6 = 3

Put in the values you know

$9^{2} + 3^{2} = c^{2}$

Square the numbers

$81 + 9 = c^{2}$

Add

$90 = c^{2}$

take the square root of both sides

$\sqrt{90} = c$

The answer is $C) \sqrt{90}$

Hope this helps!

4 0

3 years ago