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3 years ago

Angle C is an inscribed angle of circle P. Angle C measures (-x + 8) degrees and arc AB measures (12x) degrees. Find x

Mathematics

2 answers:

Bas_tet [7]3 years ago

5 0

Answer:

<h2>The variable is 8/7.</h2>

Step-by-step explanation:

Givens

$\angle C = -x+8\\arcAB=12x$

To solve this problem, we need to use the Inscribed Angle Theorem which states that an angle inscribed in a circle is half of the subtended arc.

Based on this theorem, we have

$\angle C=\frac{1}{2}arcAB$

Replacing each expression

$-x+8=\frac{1}{2}(12x)\\ -x=6x-8\\8=x+6x\\7x=8\\x=\frac{8}{7}$

Therefore, the variable is 8/7.

harina [27]3 years ago

4 0

The rule for this is that the measure in degrees of the inscribed angle is half the measure of the arc in degrees. If angle C measures 8-x and arc AB measures 12x, then the formula to solve for x would be

$8-x=\frac{1}{2}(12x)$ . Simplifying a bit gives us that 8 - x = 6x. Add x to both sides and we have 8 = 7x and x = 8/7.

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Mr. Thomas spent $1,600 of his savings on a television set and 2/5 of the remainder on a refrigerator. He had 1/3 of his origina

Katena32 [7]

Answer:

The amount spent on the refrigerator is $ 800 .

Step-by-step explanation:

Given as :

The amount spent on television = $ 1600

Le The total amount in the account = $ A

so, The amount left in account after spent on television = $ A - $ 1600

The amount spent on refrigerator = $\frac{2}{5}$ × ( A - 1600 )

The amount left in his saving account = $\frac{1}{3}$ × A

Now, According to question

A - ( 1600 + $\frac{2}{5}$ × ( A - 1600 ) ) = $\frac{1}{3}$ × A

Or, A - $\frac{1}{3}$ × A = 1600 + $\frac{2}{5}$ × ( A - 1600 )

Or, $\frac{2}{3}$ × A = 1600 + $\frac{2}{5}$ × A - $\frac{2}{5}$ × 1600

or, $\frac{2}{3}$ × A - $\frac{2}{5}$ × A = 1600 - 640

Or, $\frac{10 - 6 }{15}$ × A = 960

or, $\frac{4}{15}$ × A = 960

∴ A = $\frac{960\times 15}{4}$

I.e A = 3600

So, The amount in the saving account is $3600

∵ , The amount spent on refrigerator = $\frac{2}{5}$ × ( 3600 - 1600 )

Or, The amount spent on refrigerator = $\frac{2}{5}$ × 2000

I.e The amount spent on refrigerator = $ 800

Hence The amount spent on the refrigerator is $ 800 . Answer

4 0

3 years ago

Write the slope-intercept form of the equation.<br><br> 5x – y = 10

Rashid [163]

Answer:

y=5x-10

Step-by-step explanation:

5x - y = 10

-y = -5x + 10

y = 5x -10

4 0

2 years ago

Read 2 more answers

Save Work out the size of angle AED.<br> b) Work out x

Mamont248 [21]

Answer:

x = 10°

Step-by-step explanation:

a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"

Therefore, in cyclic quadrilateral ABDE,

m∠ABD + m∠AED = 180°

110° + m∠AED = 180°

m∠AED = 180° - 110°

= 70°

b). AD = ED [Given]

m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]

m∠EAD = m∠AED = 70°

By triangle sum theorem in ΔABD,

m∠BAD + m∠ABD + m∠ADB = 180°

m∠BAD + 110° + 40° = 180°

m∠BAD = 180 - 150

= 30°

m∠AEB = m∠AED + m∠DAB [By angles addition postulate]

m∠AEB = 70° + 30°

= 100°

By triangle sum theorem in the large triangle,

x° + m∠AEB + m∠EAB = 180°

x° + 100° + 70° = 180°

x = 180 - 170

x = 10°

8 0

2 years ago

I need help with 1 AND b, please explain!

Thepotemich [5.8K]

First answer is 27
Multiply -3 with -1
Then multiply it to the 3rd power.

2nd answer is 1 / 1296
First add the expoinents
-12 +8 = -4

Then you would need to do the equation
6^-4 x 6^0
And this would equal 1/1296

Please mark Brainliest :)

4 0

3 years ago

Read 2 more answers

Solve the following inequality: 10 - 2x ≥ 12.

enot [183]

Answer:

x<(with a line underneath)-1

Step-by-step explanation:

10-2x>(with a line underneath)12

-10 -10

-2x>(with a line underneath)2

/-2 /-2

x<(with a line underneath)-1

7 0

3 years ago