Triangle NOP is similar to triangle QRS. Find the measure of side RS. Round your answer to the nearest tenth.

Answer:

m∠CAB = 66°

m∠CAD = 24°

Step-by-step explanation:

m∠CAB

The given parameters are;

The measure of arc m[tex]\widehat{ADC}[/tex] = 228°

The diameter of the given circle = [tex]\overline{AD}[/tex]

The tangent to the circle = [tex]\underset{AB}{\leftrightarrow}[/tex]

The measure of m∠CAB and m∠CAD = Required

By the tangent and chord circle theorem, we have;

m∠CAB = (1/2) × m[tex]\widehat{AC}[/tex]

However, we have;

m[tex]\widehat{AC}[/tex] + m[tex]\widehat{ADC}[/tex] = 360° the sum of angles at the center of a circle is 360°

∴ m[tex]\widehat{AC}[/tex] = 360° - m[tex]\widehat{ADC}[/tex]

Which gives;

m[tex]\widehat{AC}[/tex] = 360° - 228° = 132°

m[tex]\widehat{AC}[/tex] = 132°

Therefore;

m∠CAB = (1/2) × 132° = 66°

m∠CAB = 66°

m∠CAD

Given that  [tex]\overline{AD}[/tex] is the diameter of the given circle, we have

The tangent, [tex]\underset{AB}{\leftrightarrow}[/tex], is perpendicular to the radius of the circle, and therefore [tex]\underset{AB}{\leftrightarrow}[/tex] is also perpendicular to the diameter of the circle

∴ m∠DAB = 90° which is the measure of the angle formed by two perpendicular lines

By angle addition property, we have;

m∠DAB = m∠CAB + m∠CAD

∴ m∠CAD =  m∠DAB - m∠CAB

By substitution, we have;

m∠CAD = 90° - 66° = 24°

m∠CAD = 24°

Answer:The expression that can be used to convert 100 USD to Japanese Yen is 100 USD = 100/Y Japanese Yen.

Step-by-step explanation:

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

Answer:

x=20,y=34

Step-by-step explanation:

x+14=2x-6 (vertically opposite angles)

x-2x = -6-14

-x = -20

x=20

x+14=y (corresponding angles)

20+14=y

y=34

Answer:

x = 20, y = 34

Step-by-step explanation:

(2x - 6) and (x + 14) are vertical angles and are congruent, then

2x - 6 = x + 14 ( subtract x from both sides )

x - 6 = 14 ( add 6 to both sides )

x = 20

Then

2x - 6 = 2(20) - 6 = 40 - 6 = 34

y and (2x - 6) are alternate angles and are congruent , so

y = 34

Answer:

hi, the answer is Nu5000

250×20=5000

Answer:

L = 31.5 w = (4/7)31.5 = 18 p = 2 * 31.5 + 2 * 18 A = 31.5 * 18

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i

Simplifying the radical

[tex]\sqrt{-80}[/tex]

= [tex]\sqrt{16(5)(-1)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex]

= 4 × [tex]\sqrt{5}[/tex] × i

= 4i[tex]\sqrt{5}[/tex]

Then

6 + [tex]\sqrt{-80}[/tex]

= 6 + 4i[tex]\sqrt{5}[/tex]

Answer:

x = 46°

Step-by-step explanation:

64° + 70° + x = 180°

x = 180° - 64° - 70°

x = 46°

Answer:

True is the correct answer

Answer:

I believe the answer is true

Answer:

3 marbles

Step-by-step explanation:

and they have died inside too

Answer:

3x - y/2

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

The slope of this equation is 5/2

Answer: A , 4x - 5y = 5

Step-by-step explanation:

i just did it , duhhh

Answer:

a

Step-by-step explanation:

Answer:

225Pi (in terms of Pi)

Or

706.5cm

Step-by-step explanation:

Area = Pi * radius^2

Radius is half of the diameter, so it is 15.

Area = Pi*15^2

Which is:

225Pi

Or

706.5

Answer:

The area of the circle is

[tex]225\pi[/tex]

Step-by-step explanation:

The diameter equals 30 cm, so the radio equals 15 cm.

The formula of the circle area is

[tex]\pi \times {r}^{2} [/tex]

Then,

[tex]\pi \times {15}^{2} = 225\pi[/tex]

Answer:

The required probability is 0.462.

Step-by-step explanation:

Probability to play the song = 6/7

Probability not to play the song = 1 - 6/7 = 1/7

Required probability  

= Probability to play 5 days x probability not to play 1 one + Probability to play 6 days

[tex]=\left (\frac{6}{7} \right ) ^5\times \frac{1}{7} + \left (\frac{6}{7} \right ) ^6\\\\= \frac{6^5 +6^6}{7^6}\\\\=0.462[/tex]

Answer:

second option

Step-by-step explanation:

y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)

2y = 180 - 38

y = 142/2

y = 71 degree

Answer:

71 degrees

Step-by-step explanation:

Hi there!

All the interior angles of a triangle add up to 180 degrees.

Knowing this, we can construct the following equation:

[tex]180=y+y+38\\180=2y+38[/tex]

Subtract 38 from both sides

[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]

I hope this helps!

Answer:

The answer is E.

Step-by-step explanation:

A quadrilateral that has only one pair of parallel sides is called a Trapezoid.

Answer:

-80

Step-by-step explanation:

So basically what we need to do is find the value of x that satisfies the equation.

When I mean satisfy, I basically mean a value of x that makes one side of the equals sign equal to the other side of the equals sign.

So in this case, we need -6 = -6.

To find this lets solve the equaion step by step:

-6=x/8+4

So first off, you always want to get the variable on one side, and the number on the other.

This means you want to subtract the 4 from both sides, leaving x/8:

-6=x/8+4

-4       -4

-10=x/8

Whenever x is not 1x, you have to divide or multiply to get it equal to 1x.

If this is a bit confusing, here is an example:

100=10x

We need 1x, but above is 10x. The reason why we want 1x is because it is the lowest ratio, and most accurate x value.

You can think of it like a 1 dollar bill. Its easier and better to use than per say a 3 dollar bill.

So in the example above you would divide by 10, since 10x/10 would equal 1x.

Remember the rule however, that what you do on one side you must do on the other. This emans you would divide both sides by 10:

100/10 =10x/10

=

10=1x

We have in our equation:

-10=x/8

Our x is lower than 1. It x/8. Whenever we have a value of x greater than 1, we divide, like we did in the example. However here, it is below x. So we multiply.

In this case we multiply by 8, since its x/8:

-10 * 8 = x/8 * 8

=

-80=x

So x is equal to -80.

I hope you understand it better now :D

Step-by-step explanation:

(4/3)–1 = 3/4 and (1/4)–1 = 4/1

now we have,

(3/4 - 4)–1 = (-13/4)–1

= -4/13

Step-by-step explanation:

pleae mark as brain list please give me some thanks please

Answer:

i wish i could tell you

Step-by-step explanation:

Answer:

(3, 0)

Step-by-step explanation:

A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.

The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:

[tex]4p(y-k)=(x-h)^2[/tex]

The directrix is at y = k - p, and focus is at (h, k + p).

Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:

[tex]-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\[/tex]

Comparing with the standard form:

The center = (h, k) = (3, 4)

Also, -16 = 4p

p = -4

Directrix is at y = k - p = 4 - (-4) = 8

Directrix is at y = 8

The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)

The focus is at (3, 0)

Answer:

270kg!

Step-by-step explanation:

Answer:

The answer would be A

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

Percent error = (actual - estimated) / actual x 100

(240 - 228) / 240 x 100 = 5%

Answer:

The goal to reduce the amount of energy used to provide products and services; saving the earth vibes.

Answer:

2.5

Step-by-step explanation:

Answer:

2 1/2

Step-by-step explanation:

5/8 ÷ 1/4

Copy dot flip

5/8 * 4/1

Rewriting

5/1 * 4/8

5/1 * 1/2

5/2

Writing as a mixed number

2 1/2