The terminal side of angle θ intersects the unit circle in the first quadrant at x=2/5. What are the exact values of sinθ and cosθ?

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

Answer: I say 4/3 the fraction so your answer is D

Explanation: Because its white cars to blue cars the problem is whats equivalent to the ratio 40 to 30, 4:1 is not the same as 40 to 30 neither

is 1:4 or 3 to 4 So its D. :)

Table is attached below-

1) 1 m² = 10.75 tiles

2) 10 m² = 107.5 tiles

3) 9.3 m² of tiles = 100 tiles

4) a m² = 10.5a tiles

We have been given that

Every square meter of ceiling requires 10.75 tiles.

we have find missing values in the table.

We know,

1 square meter of ceiling =  10.75 tiles.      ...(i)

1. Therefore, the number of tiles corresponding to 1 square meter of         ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

2. Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

(1/10.75) square meter of ceiling = 1 tile.

Multiply both sides by 100.

(100/10.75) square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

3. Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling =  a×10.75 tiles.

a square meter of ceiling =  10.75a tiles.

4. Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.

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Answer:

the action of inflating something or the condition of being inflated.

"the inflation of a balloon"

ASTRONOMY

(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.

2.

ECONOMICS

a general increase in prices and fall in the purchasing value of money.

"policies aimed at controlling inflation"

In the given diagram, the value of x is 16

From the question, we are to determine the value of x

In the given diagram, we can observe that (6x + 20)° and 4x° form a linear pair,

Thus, we can write that

(6x + 20)° + 4x° = 180°

Now, we will solve for x

(6x + 20)° + 4x° = 180°

6x + 20 + 4x = 180

10x = 180 - 20

10x = 160

x = 160/10

x = 16

Hence, the value of x is 16

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Joe earned $140 for working 20 hours

To determine the value of a single unit from a specified multiple, use the unitary technique. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Joe worked 14 hours  and earned = $119

Joe worked for 1 hour and earned = $ 119/ 14

Joe worked for 20 hours and earned = $ 119/ 14 x 20

                                                                 = 4140

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Using the Pythagorean Theorem, it is found that the length of AB is of 8.54 units, considering that BC = 3 and that AC = 8.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this triangle, we have that:

Hence the length of AB is given as follows:

h² = 3² + 8²

h² = 73

h = sqrt(73)

h = 8.54 units.

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Answer:

Domain: [-20, 20]

Range: [-30, 5]

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

Answer:

Well the IMC 2014 is

IMC 2014 + hMc

Answer:

[tex]=-6w^2-31w-35[/tex]

Step-by-step explanation:

Apply Foil.
[tex]\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=-6w^2-31w-35[/tex]

Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

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Answer:

$42.00

Step-by-step explanation:

Let x  = the original cost of the sweatshirt

x - .15x = 35.70  We don't know the original cost so we will call it x.  I know that we are taking 15 off of this number to get the sale's price.  15% means per 100, so as a fraction this would be 15/100.  To make this a decimal, I would divide 15 by 100 to get .15

x - .15x = 35.70  Combine the like terms

.85x = 35.70  This is say that 85% if the original price is the sale price of 35.70

Divide both sides of the equation by .85 and we get x = 42.00

Check:

42 - .15(42) = 35.70

42 - 6.30 = 35.70

Answer:

Step-by-step explanation:

(2*9/5d*9)-(1*5/9d*5)

18/45d-5/45d

13/45d

Answer:

28

Step-by-step explanation:

-28 + 28 = 0

Answer:

3

Step-by-step explanation:

32 - 20 = 12

12/4 = 3

This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.

Answer:

$675.00

Step-by-step explanation: The chart says it all

Answer:

36in

Step-by-step explanation:

A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.

FINAL ANSWER: 36in

Answer: x^2-4

Step-by-step explanation: I can only assume that is the answer given the limited prompt. Please comment and let me know if that is the desired answer or if you need more help. (X = a number ^2 = squared -4 = 4 is subtracted)

The polynomial expression for the area of the room is f(x) = x^2 + 16x + 48.

Here, we are given that the side of the length of the rug = x

Now, the square rug is placed on the rectangular room such that on 2 sides the uncovered floor is 6 meters.

This means that the length of the 2 opposite sides of the rectangle will be (x + 6 + 6) = (x + 12)

Similarly, there is 2 feet of uncovered floor on the other 2 sides, which means that the length of other two opposite sides is- (x + 2 + 2) = (x + 4)

Kindly refer to the diagram below for a better clarity of how we found out the sides.

Now, the area of a rectangle = Length × Breadth

Thus, area of the room = (x + 12) (x + 4)

= x^2 + 4x + 12x + 48

= x^2 + 16x + 48

Thus, the polynomial expression for the area of the room is f(x) = x^2 + 16x + 48

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The total spent amount on water is $220

The total area is 37.5=75/2

The number of lots is 75/2/3/4=50 nos

Total rent is 50×50=2500

So 3/5 will go to david 2500×3/5=1500

2/5 will go to john 2500×2/5=1000

So 60% Renters choose 100 gallons

Total renters is 50

60% renters is 50×60%=30 nos

40% renters choose 70 gallons

40% of 50 is 20 nos

The tank fills twice

100×30+70×20=4400 to be filled

Per gallon cost is $0.05

So the total cost is 4400×0.5=$220

So they spent $220 on water

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The solution for the given system of equations is (3,5) and (-4,12).

Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.

⇒x+y=8; let's assume this equation as A

⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B

From equation A

⇒y=8-x

From equation B

⇒y=[tex]x^{2}[/tex]-4

Equating both the values of y

⇒8-x=[tex]x^{2}[/tex]-4

⇒[tex]x^{2}[/tex]-8-4+x=0

⇒[tex]x^{2}[/tex]-12+x=0

{solving quadratic equation}

⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}

⇒[tex]x^{2}[/tex]+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0

Therefore, the value's of x=3,-4

⇒if x=3

From  equation A

⇒y=8-3=5

For x=3 ; y=5

⇒if x=-4

From  equation A

⇒y=8-(-4)=12

For x=-4 ; y=12

Therefore,The solution for the given system of equations is (3,5) and (-4,12).

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Answer:

-3/7

Step-by-step explanation:

[tex]-3\frac{1}{7} / 7 \frac{2}{6}[/tex]

[tex]-3 \frac{1}{7} = \frac{-22}{7}[/tex]

[tex]7\frac{2}{6} = 7\frac{1}{3} = \frac{22}{3}[/tex]

[tex]\frac{\frac{-22}{7} }{\frac{22}{3} }[/tex][tex]= \frac{-22}{7} * \frac{3}{22} = \frac{-3}{7}[/tex]

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Answer:

x = 1

Step-by-step explanation:

2 x [tex]x[/tex] = 10

10 > -10

9 x [tex]x[/tex] = 9

9 < 18

Answer:

Given d = 75, respectively,

135

Step-by-step explanation:

[tex]2\left(75\right) = 2 \cdot 75\\= 150\\\\\sqrt[3]{-45\left(75\right)}\\\left(75\right)=75\\\sqrt[3]{-45\cdot \:75}\\45\cdot \:75=3375\\\sqrt[3]{-3375}\\\sqrt[3]{-3375}=-\sqrt[3]{3375}\\-\sqrt[3]{3375}\\-\sqrt[3]{15^3}\\\sqrt[3]{15^3}=15\\=15\\\\=150-15\\=135[/tex]

Answer:

x = -2

Step-by-step explanation:

-12 = 1/2(6x - 12)  Multiply everything inside the parentheses by 1/2

-12 =1/2(6x) - (1/2)(12)

-12 = 3x - 6  Add 6 to both sides of the equation

-6 = 3x  Divide both sides by 3

-2 = x

Check:

Plug -2 in for x and see if statement is true

-12 = 1/2(6x - 12)

-12 = 1/2[(6)(-2) - 12]  Simplify inside the brackets

-12 = 1/2(-12 -12)

-12 = 1/2 (-24)

-12 = -12

The value of  dy/dx at x = 1 is  mathematically given as

dy/dx=5-1.8898i

This is further explained below.

Generally, Given that cost y of producing x gallons ag an implicit evaluation

y^2-10 x y=200

Differentiate the above equation as

[tex]\begin{aligned}&2 y y^{\prime}-10 y-10 x y^{\prime}=0 \\&y^{\prime}(2 y-10 x)=10 y \\&y^{\prime}=\frac{10 y}{2 y-70 x}=\frac{5 y}{y-5 x}\end{aligned}[/tex]

when x=1, substitute in the given equation to get y value

y^2-10 y=200

or

y=5+13.2288i

y=5−13.2288i

y represents the cost and hence cannot be negative Hence practical solution for y is y=5+13.2288i substitute in the ' y ' equation to get [tex]$\frac{d y}{d x}$ at $x=1$[/tex]

when x=13 y=5+13.2288i

Hence

d y/d x at x=1 will be

dy/dx[tex]=\frac{5(5+13.2288i)}{5+13.2288i-5}[/tex]

[tex]dy/dx=\frac{25+66.144}{13.2288i}[/tex]

dy/dx=5-1.8898i

In conclusion, the value of  dy/dx at x = 1 i

dy/dx=5-1.8898i

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Answer:

78.99

Step-by-step explanation:

Rounding to the 2nd decimal place the number 78.987625

Write down everything upto and including the 2nd decimal: 78.98

Check out the next digit. If >= 5, then increase the 2nd decimal digit above by 1, if not leave it as is.

For 78.987625 the digit next to the 2 decimal digit is 7 so we increase 78.98 to 78.99