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2 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]2 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]2 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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Answer:

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Step-by-step explanation:

This is a arithmetic progression problem with the formula;

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We are told that In 1999 Daniel was 146 cm tall. He grew to be 176 cm by the year 2006.

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I need help putting this in corresponding factored form. I got two wrong but I’m not sure how to do it and show my work.

Anna11 [10]

Answer:

x^2-16 goes with (x+4)(x-4)

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Step-by-step explanation:

The first one you got wrong is known as a difference of squares.

To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.

So x^2-16=(x-4)(x+4) or (x+4)(x-4).

Let's check (x+4)(x-4) using foil!

First: x(x)=x^2

Outer: x(-4)=-4x

Inner: 4(x)=4x

Last: 4(-4)=-16

----------------------Add

x^2-16

Bingo! (x+4)(x-4) definitely corresponds to x^2-16.

Here are more examples of factoring a difference of squares:

Example 1: x^2-25 = (x+5)(x-5)

Example 2: x^2-81 = (x+9)(x-9)

Example 3: x^2-100 =(x+10)(x-10)

Onward to the next problem:

x^2+10x+16

When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.

Those numbers would be 8 and 2

because 8(2)=16 and 8+2=10.

So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).

Here is another example of when the leading coefficient of a quadratic is 1:

Example 1: x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.

Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.

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