Solve the equation. 5x + (2x + 40) = 180. What are the two angle measures of this supplementary angle?

Mathematics

1 answer:

satela [25.4K]3 years ago

5 0

It is 5 and 6 supplementary

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What is the simplified form of 12x/900x²y4z6?

zalisa [80]

Answer:

$360xy^2|xz^3|$

Step-by-step explanation:

Given expression:

$12x \sqrt{900x^2y^4z^6}$

$\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:$

$\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

Replace 900 with 30² :

$\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

$\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:$

$\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}$

$\implies 360x|x|\sqrt{y^4}\sqrt{z^6}$

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

$\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:$

$\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}$

Simplify:

$\implies 360xy^2|xz^3|$

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

7 0

1 year ago

Prove that the two circles shown below are similar.

s344n2d4d5 [400]

The circles B and D are similar since the radius of the former is as twice as the radius of the latter.

<h3>Are the two circles shown in the figure similar?</h3>

By geometry we know that circles are defined by only one characteristic: radius. If two circles are similar, then the radii must be <em>different</em>. After a quick look at the figure, we conclude that the radii are $r_{B} = 4$ and $r_{D} = 2$ . Hence, the circles B and D are similar since the radius of the former is as twice as the radius of the latter.