Find the circumference and the area of a circle with radius .
Use the value for , and do not round your answers. Be sure to include the correct units in your answers.

Applying the cosine ratio of trigonometry, the exact value of cos(-60°) which equals cos (π/3) is: C. 1/2.

In trigonometry, the vaue of the cosine ratio is the cosine of the reference angle which equals the ratio of the adjcent side over the hypotenuse.

To get the exact value of cos(-60°), convert 60 to radians.

π radian = 180

60° = (π/3) radians

Note: cos (-θ) = cos θ

Therefore, cos (-π/3) = cos (π/3)

cos (π/3) = 1/2

The exact value of cos(-60°) = 1/2 (option C).

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Answer:

The value of x = 3.5 or -4

Step-by-step explanation:

=> 2x² = 28 – x

=> 2x²+ x - 28 = 0

=> 2x² + 8x - 7x - 28 = 0

=> 2x ( x + 4 ) - 7 ( x + 4 ) = 0

=> (2x - 7 ) ( x + 4 )

=> x = 7/2 = 3.5 or x = -4

Answer:

x = –4 or x = 3.5

Step-by-step explanation:

[tex]2x^{2}=28-x\Longleftrightarrow 2x^{2}+x-28=0[/tex]

                    [tex]\Longleftrightarrow 2x^{2}-7x+8x-28=0[/tex]

                    [tex]\Longleftrightarrow x(2x-7)+4(2x-7)=0[/tex]

                    [tex]\Longleftrightarrow (2x-7)(x+4)=0 \ \ \ \ \text{factor out} \left( 2x-7\right)[/tex]

                    [tex]\Longleftrightarrow 2x-7=0 \ \ or\ x+4=0\ \ \ \ \text{(zero product rule)}[/tex]              

                    [tex]\Longleftrightarrow x=\frac{7}{2} \ \ or\ x=-4[/tex]

Recall: SOHCAHTOA

Sin M = Opp/Hyp

Reference angle = M

Opp = 3√/21

Hyp = 15

Sin M = (3-√21)/15

Sin M = √21/5

Cos M = Adj/Hyp

Reference angle = M

Adj = 6

Hyp = 15

Cos M = 6/15

Cos M = 2/5

Tan M = Opp/Adj

Reference angle = M

Opp = 3√21

Adj = 6

Tan M = (3√21)/6

Tan M = √21/2

:Therefore: Sin M = √21/5

Cos M = 2/5

Tan M = √21/2

Answer:

[tex]\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}[/tex]

[tex]\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}[/tex]

The solution is Option A.

The value of x is given from proportion and x = 10 1/2 or x = 10.5

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the first rectangle be A

The dimensions of the rectangle A = 4 by 3

Let the second rectangle be B

The dimensions of the rectangle B = 14 by x

The two rectangles A and B are similar , so

Now , the proportion equation will be

3 / 4 = x / 14

Multiply by 14 on both sides of the equation , we get

x = ( 14 × 3 ) / 4

x = 42/4

x = 10.5

The value of x = 10 1/2

Therefore , the value of x is 10 1/2

Hence , the value of x of the rectangle is 10 1/2

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Answer:

Guessing you want me to figure out what your cost should have been. On it!

Step-by-step explanation:

130 * .15 = 19.5

130 - 19.5 = $110.5

That should be the new cost.

The price of the thing after applying 15% discount is $110.50.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The price at which thing is purchased = $130.

Since, The salesperson forgot to give a discount of 15%.

The discounted price = 130 x 15 %

= 130 x 15/100

= 1950/100

= $19.5

The price after discount = 130 - 19.5 = 110.5

The required price after discount is $110.5.

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Step-by-step explanation:

-y is the same as writing -1y. if we forget about the y’s, -1 + 2 = 1. so -1y + 2y = 1y, or just y to be simpler :)

i hope this helps :)

[tex]-y+2y=2y-y=(2-1)y=y[/tex]

It is positive because the coefficient is positive.

Answer:

x=26

Step-by-step explanation:

Since they are complementary

2x+38⁰=90⁰

2x=90⁰-38⁰

2x=52⁰

x=26⁰

I hope it helped you

Answer:

Step-by-step explanation:

This is self-explanatory, We just need to find the value of x by doing this:

Brainliest please. I didn't get one on this account.

Check the picture below.

so notice the top part of the picture

if we move the "4" and "17" sides  close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.

notice the bottom part of the picture

if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line.  So whatever the red side is, must be less than 21.

The area of the lot with a shape of a parallelogram if its base measures 20 meters and the distance given is 160m².

Area of a parallelogram will be:

= Base × Height

= 20 × 8

= 160m²

The area of the triangular landscape that has a base of 24 meters and a height of 12 meters will be:

= 1/2 × base × height

= 1/2 × 24 × 12

= 144m²

The area of the trapezium will be:

= 1/2 × (a + b) × h

= 1/2 × (16 + 30) × 10

= 1/2 × 46 × 10

= 230m²

The area of the rectangular banner has a length of 5 meters and a width of 3 meters will be:

= Length × Width

= 5 × 3

= 15m²

The area of a soccer ground square in shape with a side of 8 meters will be:

= 8 × 8

= 64m²

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The logic network to control the lights on the staircase; has been designed as seen below.

The truth table for the required response of the question is;

SWITCH A        SWITCH B         SWITCH C            Y

0(OFF)               0(OFF)               0(OFF)               0(OFF)

0(OFF)               1(ON)                  1(ON)                 1(ON)

1(ON)                  0(OFF)               1(ON)                 1(ON)

1(ON)                  1(ON)                  0(OFF)              1(ON)

1(ON)                  1(ON)                  1(ON)                0(OFF)

The expression for the output Y in SOP form will be;

A ⊕ B ⊕ C = A⁻B⁻C + AB⁻C⁻ + A⁻BC⁻

That's the output expression for the XOR gate.

Thus, we can conclude that in the staircase wiring, higher output is obtained when two out of three of the inputs are different.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$\stackrel{12000~~ + ~~1200}{13200}\\ P=\textit{original amount deposited}\dotfill &\$12000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1.8 \end{cases}[/tex]

[tex]13200=12000\left(1+\frac{~\frac{r}{100}~}{1}\right)^{1\cdot 1.8}\implies \cfrac{13200}{12000}=\left( 1+\cfrac{r}{100} \right)^{1.8} \\\\\\ \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{1.8}\implies \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \\\\\\ \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\left[ \left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \right]^{\frac{5}{9}}\implies \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\cfrac{100+r}{100}[/tex]

[tex]\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=\cfrac{100+r}{100}\implies 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=100+r \\\\\\ 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}-100 = r\implies 5.44\approx r[/tex]

Answer:

B  at least 103 flights are on time. :)

Step-by-step explanation:

First we need to turn the percentage into a decimal :)

131 x 0.80 = 104.8

The answer should be B  at least 103 flights are on time.

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

No

Step-by-step explanation:

Plugging in n=0 into the equation gets us:

7(0) = 7

0 = 7

This says that 0 = 7 which is not true

Median:

The median in this set is the 5th term.

Therefore the median in this set is 23.

Answer:

length times width equals area LxW=Area

Step-by-step explanation:

so,

4 times 4= 26 yards

1=4 square yards

then 26X4 = 104 square yards

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=-3x-1

Answer:

178

Step-by-step explanation:

Perimeter = distance all the way around the outside of a 2D shape

Missing vertical length = 45 - 14 - 17 = 14

Missing horiztonal length = 44 - 8 - 29 = 7

⇒ perimeter = 45 + 8 + 17 + 29 + (45 - 14 - 17) + (44 - 8 - 29) + 14 + 44

                     = 45 + 8 + 17 + 29 + 14 + 7 + 14 + 44

                     = 178

Answer:

First finding the perimeter of rectangle

Step-by-step explanation:

Which is 2(17+8)=2(25)=50

Now finding the perimeter of next rectangle

Which is 2(45+29) = 2 (74) =148

Now finding the perimeter of next rectangle

Which is 2(44+14)=2(58)=116

Adding them up we get 116 + 50 +148=314

178 is the correct answer however

I do not why 178 is correct

Answer:

1/3

Step-by-step explanation:

Answer:

1/6  

Step-by-step explanation:

2/3-1/2 =     find the denominator 3×2=6

4/6-3/6 =     rewrite with a denominator of 6

(4-3)/6 = 1/6     subtract numerators

Answer:

22 ounces is more

Step-by-step explanation:

1 pound is equal to 16 ounces

Answer:

1 pound

Step-by-step explanation:

1pound=16oz 22oz= 1.375pound

Draw a box between the first quartile; third quartile

Answer:

42qt

Step-by-step explanation:

First, multiply 2 x 3 x 7

2 x 3 = 6

6 x 7 = 42

Second, q x t

Qt

Third, put together

42qt

Answer:

k = 15

Step-by-step explanation:

k + 45 = 60

k = 60 - 45

k = 15

Answer:

3

Step-by-step explanation:

3 to get to 15, multiply by 3, same for other sides.

Answer:

C

Step-by-step explanation:

9 divided by 3 is 3, 15 divided by 5 is 3, and 12 divided by 4 is 3. it all adds up to three

Answer:

E

Step-by-step explanation:

if the x value or y value is 0 the equation is undefined

When tangent TA is parallel to KM, it can be proved that KS = MS since they're congruent.

It should be noted that when the tangent line TA is parallel to chord KM, it simply means that segment KS and MS are congruent.

Therefore, since they're congruent, SKM and SMK are equal. By the theorem of inscribed angle, we will have:

SKM = 1/2m(MS)

SKM = 1/2m(KS).

Since SKM = SMK

1/2m(MS) = 1/2m(KS).

MS = KS

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Answer:

b = 25 degrees

c = 81 degrees

d = 64 degrees

Answer:

18 inches is equal to 46 CM rounding or 45.72 CM without rounding.

Please mark brainliest if this helped you :)

Step-by-step explanation:

Answer:

lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex] ⇒ Answer D is correct

Step-by-step explanation:

First, let us find the area of the semi-circle.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Given that,

diameter of the semi-circle is ⇒ l

∴ radius ⇒ l / 2

Let us find it now.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Area =  [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Secondly, let us find the area of the rectangle.

Area = length × width

Given that,

length ⇒ l

width ⇒ w

Let us find it now.

Area = length × width

Area = l ×w

Area = lw

And now let us find the total area.

Total area =  Area of the rectangle + Area of the semi - circle

Tota area = lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Answer:

It will take 7 weeks for Sophie to catch up to Pete. Both of them will each have completed 48 missions.

Step-by-step explanation:

27 + 3x = 13 + 5x

27 + 3x - 3x = 13 + 5x - 3x

27 = 13 + 2x

27 - 13 = 13 + 2x - 13

14 = 2x

x = 7

27 + 3x

27 + 3(7)

27 + 21

48

13 + 5x

13 + 5(7)

13 + 35

48

Answer:

[tex] \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} [/tex]

Step-by-step explanation:

I hope I helped you! :)