Abigail is 54 inches tall. Which of the following is Abigail's height?

The ordered pair of a unit circle is represented as:

[tex](x,y) \to (\sin(\theta),\cos(\theta))[/tex]

The point where the terminal side of [tex]\tehta[/tex][tex]\theta[/tex] intersect with the unit circle is: 240

The given parameter can be represented as:

[tex](x,y) \to (-\frac{\sqrt 3}{2},-\frac{1}{2})[/tex]

This means that:

[tex]\sin(\theta) = -\frac{\sqrt 3}{2}[/tex]

[tex]\cos(\theta) = -\frac{1}{2}[/tex]

Let the angle between the x-axis and the terminal side be [tex]\alpha[/tex]

So, we have:

[tex]\theta = 180 + \alpha[/tex]

Using [tex]\cos(\theta) = -\frac{1}{2}[/tex]

The equation becomes

[tex]\cos(180 + \alpha) = -\frac{1}{2}[/tex]

Apply cosine formula

[tex]\cos(180)*\cos(\alpha) - \sin(180)*\sin(\alpha) = -\frac{1}{2}[/tex]

[tex]-1*\cos(\alpha) - 0*\sin(\alpha) = -\frac{1}{2}[/tex]

[tex]-1*\cos(\alpha)= -\frac{1}{2}[/tex]

Divide both sides by -1

[tex]\cos(\alpha)= \frac{1}{2}[/tex]

Take arccos of both sides

[tex]\alpha= \cos^{-1}(\frac{1}{2})[/tex]

[tex]\alpha= \cos^{-1}(0.5)[/tex]

[tex]\alpha= 60[/tex]

Recall that:

[tex]\theta = 180 + \alpha[/tex]

[tex]\theta = 180 +60[/tex]

[tex]\theta = 240[/tex]

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Given:

A figure of a triangle.

To find:

The value of g.

Solution:

Law of Cosines:

[tex]a^2=b^2+c^2-2bccosA[/tex]

Using the Law of Cosines for the given triangle, we get

[tex]g^2=8^2+7^2-2(8)(7)cos(65^\circ)[/tex]

[tex]g^2=64+49-112(0.4226)[/tex]

[tex]g^2=113-47.3312[/tex]

[tex]g^2=65.6688[/tex]

Taking square root on both sides.

[tex]g=\sqrt{65.6688}[/tex]

[tex]g=8.10363[/tex]

[tex]g\approx 8.10[/tex]

Therefore, the value of g is about 8.10 units.

Answer: 12.6 would be the answer

Step-by-step explanation:

Answer:

B) 6.3 m

Step-by-step explanation:

Answer i cant read it..

Step-by-step explanation:

Answer:

y = 18.4

Step-by-step explanation:

[tex]12^{2} + 14^{2} = y^{2}[/tex]

144 + 196 = [tex]y^{2}[/tex]

340 = [tex]y^{2}[/tex]

y = [tex]\sqrt{340}[/tex]

y = 18.4 (to 3 significant figures)

Answer:

22123

Step-by-step explanation:

→ Find the multiplier

3% decrease = 0.97

→ Multiply the population by the multiplier which is to the power of years

30000 × 0.97¹⁰ = 22122.7 = 22123

Answer:

The amount of steel used = 94.38 [tex]m^{2}[/tex]

Step-by-step explanation:

Height of the tank = 4.5 m.

Diameter of the tank = 4.2 m.

But,

radius = [tex]\frac{diameter}{2}[/tex]

           = [tex]\frac{4.2}{2}[/tex]

radius  = 2.1 m

Total surface area of a cylinder = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex][tex]r^{2}[/tex]

                                      = 2[tex]\pi[/tex]r(r + h)

                                      = 2 x [tex]\frac{22}{7}[/tex] x 2.1 (2.1 + 4.5)

                                      = 44 x 0.3 (6.6)

                                      = 87.12

Total surface area of a cylinder = 87.12 [tex]m^{2}[/tex]

Since [tex]\frac{1}{12}[/tex] of the steel was wasted, then;

[tex]\frac{1}{12}[/tex] x 87.12 = 7.26 [tex]m^{2}[/tex]

Actual area of steel sheet used = 87.12 + 7.26

                                                     = 94.38 [tex]m^{2}[/tex]

Thus, 94.38 [tex]m^{2}[/tex] of steel was used in making the tank.

Answer:

Distance travelled = 91.61 feet

Step-by-step explanation:

Given the following data;

Diameter, d = 35 inches

Number of revolutions = 10 Rev

To find the distance travelled by the bike;

First of all, we would determine the circumference of the bike's tire, which is circular in shape.

Circumference of circle = πd

Circumference of circle = 35π

Next, we multiply by the number of revolutions to get the distance travelled.

Distance travelled = 35π * 10

Distance travelled = 350π inches

But pie, π = 3.142

Distance travelled = 350 * 3.142

Distance travelled = 1099.7 inches.

In feet;

1 inches = 0.0833 feet

1099.7 inches = x feet

Cross-multiplying, we have;

x feet = 1099.7 * 0.0833

x feet = 91.61 feet

Distance travelled = 91.61 feet

Answer:

Step-by-step explanation:

Answer:

Each sandwich costs 4$.

Step-by-step explanation:

To find the answer we will divide 72$ by 18 and we get 4$.

The number of sandwiches and the total price of sandwiches are directly proportional.

Cost of 18 sandwiches = $72

Cost of 1 sandwich = $72/18

= $4

Hence the cost of 1 sandwich is $4.

Answer:

6

Step-by-step explanation:

Answer:

u use like 4/6=2/3=0.6

Answer:

(h+63)

Step-by-step explanation:

Given that,

Isabella has 63 hair bows.

Isabella's sister has h more hair bows than Isabella. It means,

Isabella's sister = h+63

h and 63 are added as Isabella's sister has h more hair bows than Isabella.

Hence, the expression would be (h+63).

Step-by-step explanation:

-6 / 24/3

= -6 x 3/24

= -18/24

= -6/8

= -3/4

Answer:

steps below

Step-by-step explanation:

x²/16 + y²/36= 1

x²/4² + y²/6²= 1

Eclipse center ed origin: standard formula  

²/radius of minor axis + y²/ radius of major axis =1

Vertices of major axis: (6 , 0) and (-6 , 0) ... horizontal

vertices of minor axis: (0 , 2) and (0 , -2)  ... vertical

Answer:

42

Step-by-step explanation:

A regular polygon with 42 sides where the length of each side is 2 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 42 sides. What are the interior angles and exterior angles?

If the length of each side is 2 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 42

Perimeter of a polygon with 42 sides = (side length) x 42 = 84 units

Area of a polygon with 42 sides = (n x Side2 x cot (Π/n))/4 = (n x 22 x cot (Π/42))/4 = 560.45 square units

Sum of the interior angles of a polygon with 42 sides =  (n-2) x 180 degrees =  (42-2) x 180 degrees = 7200 degrees

Interior Angle of a polygon with 42 sides = (n-2) x 180/n degrees = (42-2) x 180/42 degrees = 171.42 degrees

Exterior angle of a polygon with 42 sides = 180 - Interior Angle = 180 - 171.42 = 8.57 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/42) = 2 x cot 4 = 26.68 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/42) = 2 x cosec 4 degrees = 26.76 units

Symmetry Group = D42  42 rotational symmetries and 42 reflection symmetries. The "D" stands for di-hedral.

Answer:

the answer is the first one

Answer:

I'm sorry but I can't see it lol.. maybe try taking a clear pic ya know.

Answer:

y = [tex]\frac{1}{3}[/tex] x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 2 - 1 = - 3

y = [tex]\frac{1}{3}[/tex] x - 3 ← equation of line

Answer: 7000.

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

70000 ÷ 10% = 700000

Answer:

7

Step-by-step explanation:

26

Step-by-step explanation:

3x + 2x = 50 = 180

5x = 130

x = 26

Answer:

Look at the other question i answered it for you

Step-by-step explanation:

You can download answer here

tinyurl.com/wpazsebu

Answer:

48 drops of red food coloring

Step-by-step explanation:

32/8 = 4

SO she uses 4x as much yellow food coloring meaning you need to use 4x as much red food coloring.

4 x 12 = 48 so she needs to add 48 drops of red food coloring

Answer:

Mya will need 48 drops of red food coloring

Answer:

x(12y+4)

Step-by-step explanation:

Answer:

If you talking about how many blocks she needs to walk, the answer is simple: 5 + 2 = 7

But if you use blocks as a sort of lenght measurement system, it's

[tex] \sqrt{7 {}^{2} + 5 ^{2} } [/tex]