Use angles shown to make other angles

Answer:

  50√3 ≈ 86.6 m

Step-by-step explanation:

The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.

The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...

  Sin = Opposite/Hypotenuse

  sin(60°) = (kite height)/(100 m)

  kite height = (100 m)·sin(60°) = (100 m)(√3)/2

  kite height = 50√3 m ≈ 86.6 m

Answer:

48∛9 ft²

Step-by-step explanation:

The length (L) and width (W) are given by:

[tex]L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}[/tex]

Since this is a rectangular region, the area is given by:

[tex]A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2[/tex]

The answer can be further simplified by factoring as follows:

[tex]A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2[/tex]

The exact area is its simplest form is 48∛9 ft²

Answer:

The equation of a line y = ax + b passes point (-8, -33) and point (0, -1) can be formulated by:

(Note: we do not need all of 4 points, 2 points are enough)

-33 = a x (-8) + b

  -1 = a x 0 + b

From 2nd equation, we have:

b = -1

From 1st equation, we have:

b - 8 x a = -33

=> -1 - 8 x a = -33

=> 8 x a = 32

=> a = 4

=>  The equation of line: y = 4a - 1

Hope this helps!

:)

Answer:

7.5h + 10b > $150

Step-by-step explanation:

h represents the amount of hours Lynn works as a hostess for a restaurant, and she gets $7.50 per hour. $7.50h is how much money she gets per hour. b represents the amount of hours Lynn spends working as a babysitter, and she gets $10 per hour. $10b is how much money she gets from babysitting per hour. The total amount of money she gets this week must be more than $150. So the answer is 7.5h + 10b > $150. Hope this helped!

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

84 meters

Step-by-step explanation:

5 x 6 = 30 hypotenuse side not shown

3 x 4 ÷ 2 x 2 = 12 red (both ends)

3 x 6 = 18 green side

6 x 4 = 24 blue side

Answer:

A.

Step-by-step explanation:

The equation of circle is :

(x−a)² + (y−b)² = r²

So the equation is

(x-3)² + (y-(-2))² = (6)²

Where center = (a,b) = (3,-2) and

Radius = r = 6

Answer:

x = 2 π n_1 + π/2 for n_1 element Z

or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z

Step-by-step explanation:

Solve for x:

-3 + sin(x) + 2 sin^2(x) = 0

The left hand side factors into a product with two terms:

(sin(x) - 1) (2 sin(x) + 3) = 0

Split into two equations:

sin(x) - 1 = 0 or 2 sin(x) + 3 = 0

Add 1 to both sides:

sin(x) = 1 or 2 sin(x) + 3 = 0

Take the inverse sine of both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) + 3 = 0

Subtract 3 from both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) = -3

Divide both sides by 2:

x = 2 π n_1 + π/2 for n_1 element Z

or sin(x) = -3/2

Take the inverse sine of both sides:

Answer:  x = 2 π n_1 + π/2 for n_1 element Z

or x = π + sin^(-1)(3/2) + 2 π n_2 for n_2 element Z or x = 2 π n_3 - sin^(-1)(3/2) for n_3 element Z

48%

Step-by-step explanation:

add the ratio together which is 25

pick the ratio of boy

divide 12 by 25 and multiply 100

12/25×100= 48%

Answer:

48%

Step-by-step explanation:

b/g=12/13

so b/12=g/13=k

b=12k

g=13k

so b+g=25k so k=b+g/25

b=12*(b+g)/25=12*4*(b+g)/25*4=48(b+g)/100

so 48%  are boys

Answer:

84

Step-by-step explanation:

We simply plug in 1.75 for x into y = 48x, and when we do so we get y = 48 * 1.75 = 84 cups of coffee. Hope this helps!

Answer:

B) 84

Step-by-step explanation:

48 times x is the cups of coffee sold in x hours.

if x = 1.75, then you times 48 by 1.75

48 x 1.75 = 84

Answer:

SOS

Step-by-step explanation:

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Answer:

Length of arc: 6π

Step-by-step explanation:

~ Let us answer this question in terms of π, remaining so ~

1. Assume that this is a complete circle, for the moment being. The chord with length of 12 units would act as the diameter, and using that information we could determine the circumference of this complete circle...which will help us in the future. Apply the formula π * d as such: π * 12 ⇒ 12π to get the circumference as 12π.

2. Knowing that the length of the complete circle's circumference is 12π, this arc is part of a semicircle, meaning that it's value would be half of that of the complete circle's circumference, or in other words: 12π/2 ⇒ Answer ~ Length of arc: 6π

Answer:Length of arc: 6π

Step-by-step explanation:

Answer:

The converse of the Pythagorean Theorem states that: If the square of the longest side of the triangle is equal to the sum of the squares of the other two sides of the triangle, then the triangle is a right triangle.

Step-by-step explanation:

Answer:

A tangent to a circle is a straight line which touches the circle at only one point.

Step-by-step explanation:

This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

Same slopes, different constant, so parallel lines.

Answer: ... parallel because their slopes are equal.  Last choice.

Answer:

D

Step-by-step explanation:

Yes, lines l and k are parallel since they are having equal slopes

Answer:

Step-by-step explanation:

[tex]A = lw \nl\frac{\dA}{\dt}[/tex] =[tex]\frac{\dA}{\text{d}l}\frac{\text{d}l}{\dt} + \frac{\dA}{\text{d}w}\frac{\text{d}w}{\dt}[/tex] =[tex]w\frac{\text{d}l}{\dt} + l\frac{\text{d}w}{\dt}[/tex] [tex]\nll = 20 \text{ cm}[/tex] \;\; [tex]\frac{\text{d}l}{\dt} = 8 \text{ cm/s}[/tex] \;\;w = 10 \text{ cm}, \;\;  [tex]]\frac{\text{d}w}{\dt} = 3 \text{ cm/s}[/tex] [tex]\nl\frac{\dA}{\dt} =(  10 \text{ cm} )( 8 \text{ cm/s} ) + (  20 \text{ cm} )( 3 \text{ cm/s} )  =140 \text{ cm}^2\!\text{/s} [/tex]

Given :

To find :-

Solution :-

As we know that :-

To find the rate :-

Differenciate :-

Substitute :-

Step-by-step explanation:

Use double and triple angle identities:

sin(2x) + cos(3x)

2 sin x cos x + 4 cos³x − 3 cos x

Answer:

3 possible outcomes

Step-by-step explanation

1) R R

2) R G

3) G G

Answer:

I think of a number  "4"

4+1 = 5

then 5+5 or (5X2) = 10

Step-by-step explanation:

Hope this helped :)

Answer:

  12 1/2

Step-by-step explanation:

Multiply the equation by the inverse of the coefficient of a.

  5 = (2/5)a

  5(5/2) = (2/5)(5/2)a

  25/2 = a

  12 1/2 = a . . . . written as a mixed number

The solution is 12 1/2.

Answer:

12 1/2

Step-by-step explanation:

Discount = [tex]\frac{15}{100}[/tex] x 75

               = [tex]\frac{1125}{100}[/tex]

               = $11.25

Answer:

He spends $540

Step-by-step explanation:

literally just 45 multiplied by 12

Answer:

green triangle

Step-by-step explanation:

The green triangle has an area of

A = 1/2 bh

A = 1/2 (15) * 19

A =142.5 ft^2

The blue triangle has an area of

A = 1/2 bh

A = 1/2(16.1) (16.4)

A =132.02 ft^2

The green triangle has a greater area

Answer:

5/8 * 2 * pi *r

Step-by-step explanation:

First find the circumference of the circle

C = 2 * pi *r

Then multiply it by the fraction  of the circle  ( arc length) you wish to find

5/8 * 2 * pi *r

Answer:

-19/4

Step-by-step explanation:

-1/2 + x =-21/4

x=-21/4+1/2

x=-21/4+2/4

x=-19/4

Answer:

Step-by-step explanation:

Given the following data :

(Weight, miles per gallon) (x, y) = 3648, 19), (1638, 47), (1727, 09), (2535, 50), (1832, 86), (2029, 22), (2336, 54), (1725, 33), (2534, 27), (1838, 09), (1733, 72)

Using the least square regression calculator  :

y = -0.00941x + 59.07

B) slope = -0.00941

The slope 'm' of the graphical relationship is -0.009406

Intercept = 59.07 ( where the regression line crosses the x-axis)

C.) Using the regression equation:

y = -0.00941(3600) + 59.07

y = 25.194 gallons (above)

D.) No, because other factors also contribute to gas mileage such as cylinders, Displacement, mdoel e. T. C

Answer:

Remember that logarithms are inverse of exponentials. That means the result of the logarithm is equal to the exponent of a power with the same base.

[tex]log_{10} (10)=1[/tex]

Notice that the result is one beacuse [tex]10^{1}=10[/tex]

[tex]log_{10}(10000)=4[/tex]

Because [tex]10^{4}=10000[/tex]

[tex]log_{10}(?) =7 \implies 10^{7} =10000000[/tex]

So, [tex]log_{10}(10000000)=7[/tex]

I would say to thim that [tex]x[/tex] and [tex]y[/tex] are variables of the logarithm, which be solved by imagine the logarithm as an exponential like

[tex]log_{10} (x)=y \implies 10^{y}=x[/tex]

In other words, the [tex]y[/tex] is the exponent and the [tex]x[/tex] is the result of the exponential.