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4 years ago

In the above figure (not drawn to scale), Find ∠AEC.

Mathematics

2 answers:

n200080 [17]4 years ago

7 0

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

$m\angle AEC=\frac{110^o+40^o}{2}$

$m\angle AEC=\frac{150^o}{2}$

$m\angle AEC=75^o$

Therefore, measure of angle AEC is 75 degrees and option C is the correct choice.

Alex777 [14]4 years ago

7 0

Answer : C. 75°

Given : arc length AC=110, CB=20, AD=190, and BD=40

We need to find ∠AEC

The below is the formula for measure of an angle formed by two chords

∠AEC = $\frac{1}{2} ( arc AC + arcBD)$

We know arc AC = 110 and arc BD = 40

So ∠AEC = $\frac{1}{2} ( 110 + 40)$

= $\frac{150}{2} = 75$

∠AEC = 75 degrees

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The 10th term of an a.p is -27 and the 5th term is -12 .find the first term?

horsena [70]

Step-by-step explanation:

$a_{10} = - 27... (Given) \\\\\therefore a + 9d = - 27...... (1)\\\\a_{5} = - 12... (Given) \\\\\therefore a + 4d = - 12.......(2)\\\\$

Subtracting equation (2) from equation (1)

$a + 9d-( a + 4d )= - 27-(-12)\\\\\therefore a +9d - a-4d = - 27+12\\\\\therefore 5d = - 15\\\\\therefore d = \frac {- 15}{5}\\\\\huge \orange {\boxed {\therefore d = -3}} \\\\$

Substituting d = - 3 in equation (1), we find:

$a + 9\times (-3)= - 27\\\\\therefore a - 27 = - 27\\\\\therefore a = 27- 27\\\\\huge \red {\boxed {\therefore a = 0}}\\\\$

Hence, first term is zero.

3 0

3 years ago

20 points to whoever gets the correct answer uwu

S_A_V [24]

Answer:

Angle EFG = 104 degrees

Angle GFH = 76 degrees

Step-by-step explanation:

Angle EFG and Angle GFH are a linear pair, which means that they add up to 180 degrees.

Angle EFG = 4n + 20 and Angle GFH = 2n + 34, so 4n + 20 + 2n + 34 = 180.

We can then combine like terms, getting 6n + 54 = 180.

Then, we can subtract both sides by 54, getting 6n = 126.

Lastly, we can divide both sides by 6, getting n = 21.

EDIT - solve for EFG and GFH:

Angle EFG = 4n + 20 = 4(21) + 20 = 104 degrees

Angle GFH = 2n + 34 = 2(21) + 34 = 76 degrees

8 0

3 years ago

Read 2 more answers

Select all order pairs that satisfy the function y = -2x + 5

Viktor [21]

It would be (2,1)
y=-2*2+5
y=-4+5
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3 years ago

If f(x)=1/9x-2 , what is f–1(x)?

Anna71 [15]

Lets get started :)

f(x) = $\frac{1}{9}x$ - 2
y = $\frac{1}{9}x$ - 2
This is the original equation, and now we have to find the inverse.

When finding the inverse, just flip the variables, x as y and y as x

f ⁻¹(x)
↓
x = $\frac{1}{9}y$ - 2
We have to isolate y as it is our f ⁻¹(x)

Take 2 to the other side { When you see subtraction, you do addition }
x + 2 = $\frac{1}{9} y$

Take 9 to the other side { When you see division, you do multiplication }
9 ( x + 2 ) = y
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3 years ago

If PQ=8 and Q lies at -13 where could P be located?

choli [55]

Answer:

In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).

Step-by-step explanation:

There is really no need to use any quadratics or roots.

( Consider the same problem on the plain number line first. )

How do you find the number between 2 and 5 which is twice as far from 2 as from 5?

You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get

4=2+23(5−2)

It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then

R=P+23(Q−P)

so in your case we get

R=(0,−1)+23(3,3)=(2,1)

Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)

Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get

s=a+b=2b+b=3b

⇔b=13s⇒a=23s

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3 years ago