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3 years ago

One complementary angle is half as large as the second angle. What is the measure of each angle

Mathematics

1 answer:

Brut [27]3 years ago

7 0

Answer:

30° and 60°

Step-by-step explanation:

Complementary angles sum to 90°

let 1 angle be x then the other angle is 0.5x ( half as large ), then

x + 0.5x = 90

1.5x = 90 ( divide both sides by 1.5 )

x = 60

Hence angles are x = 60° and 0.5x = 30°

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PLEASE I NEED HELP NOW!!! IF CORRECT I WILL GIVE BRAINLIEST!!

Ira Lisetskai [31]

Answer:

- 4 4/5 *C

Step-by-step explanation:

12:00-6:00 is 6hrs

7/10*6 = 42/10 = 4 1/5

1 - 4 1/5 = - 4 4/5

4 0

3 years ago

Simplify the expression. Rewrite using only positive exponents.

Dvinal [7]

The simplified form of the given expression is $x^{18}a^{3}b^{3}$ .

The given expression is $(\frac{x^{4}a^{2}b^{3} }{x^{-2}ab^{2}} )^{3}$ .

We need to simplify the given expression.

<h3>What are the basic laws of exponents?</h3>

The basic laws of exponents are as follows:

$a^{m} \times b^{m} =(ab)^{m}$

$a^{m} \div b^{m} =(\frac{a}{b} )^{m}$

$a^{m} \times a^{n} =(a)^{m+n}$

$a^{m} \div a^{n} =(a)^{m-n}$

Now, $(\frac{x^{6}a^{2}b^{3} }{ab^{2}} )^{3}=(\frac{x^{18}a^{6}b^{9} }{a^{3}b^{6}} )$

$=x^{18}a^{3}b^{3}$

Therefore, the simplified form of the given expression is $x^{18}a^{3}b^{3}$ .

To learn more about the exponents visit:

brainly.com/question/26296886.

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4 0

2 years ago

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the

kolbaska11 [484]

Answer:

Volume of cylinder = $\pi r^2h$

Step-by-step explanation:

Given : A cylinder fits inside a square prism.

To find : The volume of cylinder

Solution : Refer the attached graph.

Area of circle = $\pi r^2$

Area of square = $s^2$

Side of square = diameter of circle= $D^2$

Diameter = 2r

∴ Area of square= $2r^2=4r^2$

$\frac{Area of circle}{Area of Square}=\frac{\pi r^2}{4r^2}=\frac{\pi}{4}$

Area of circle is $\frac{\pi }{4}$ of area of square.

Volume is always = area × height

Volume of prism = Area of square × h = $4r^2h$

Volume of cylinder = Area of circle × h = $\pi r^2h$

Now, rate

$\frac{Volume of cylinder}{Volume of prism}=\frac{\pi r^2h}{4r^2h}=\frac{\pi}{4}$

⇒Volume of cylinder is $\frac{\pi }{4}$ of Volume of prism.

Volume of Cylinder = $\frac{\pi }{4}\times Volume of prism$

Volume of cylinder = $\frac{\pi }{4}\times 4r^2h$

Volume of cylinder = $\pi r^2h$

6 0

3 years ago

Read 2 more answers

Evaluate [(51 + 3) − 3²] ÷ 9 ⋅ 2.

sashaice [31]

[(51 + 3) - 3^2]/9 * 2
[ 54 - 3^2] / 9 * 2
[ 54 - 9 ] / 9 * 2
[45] / 9 * 2
5 * 2 = 10

3 0

4 years ago

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboa

Aliun [14]

Given the dartboard of diameter $20in$ , divided into 20 congruent sectors,

The central angle is $18^\circ$

The fraction of a circle taken up by one sector is $\frac{1}{20}$

The area of one sector is $15.7in^2$ to the nearest tenth

The area of a circle is given by the formula

$A=\pi r^2$

A sector of a circle is a fraction of a circle. The fraction is given by $\frac{\theta}{360^\circ}$ . Where $\theta$ is the angle subtended by the sector at the center of the circle.

The formula for computing the area of a sector, given the angle at the center is

$A_s=\dfrac{\theta}{360^\circ}\times \pi r^2$

<h3>Given information</h3>

We given a circle (the dartboard) with diameter of $20in$ , divided into 20 equal(or, congruent) sectors

<h3>Part I: Finding the central angle</h3>

To find the central angle, divide $360^\circ$ by the number of sectors. Let $\alpha$ denote the central angle, then

$\alpha=\dfrac{360^\circ}{20}\\\\\alpha=18^\circ$

<h3>Part II: Find the fraction of the circle that one sector takes</h3>

The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by $360^\circ$ . The angle has already been computed in Part I (the central angle, $\alpha$ ). The fraction is

$f=\dfrac{\alpha}{360^\circ}\\\\f=\dfrac{18^\circ}{360^\circ}=\dfrac{1}{20}$

<h3>Part III: Find the area of one sector to the nearest tenth</h3>

The area of one sector can be gotten by multiplying the fraction gotten from Part II, with the area formula. That is

$A_s=f\times \pi r^2\\=\dfrac{1}{20}\times3.14\times\left(\dfrac{20}{2}\right)^2\\\\=\dfrac{1}{20}\times3.14\times10^2=15.7in^2$

Learn more about sectors of a circle brainly.com/question/3432053

8 0

3 years ago