What is the area in square centimeters of the triangle below?

Answer:

Step-by-step explanation:

Since this is a 30-60-90 triangle, we need the Pythagorean triple for such a triangle. the side length across from the 30 degree angle is labeled as x, the side across from the 60 degree angle is x√3, and the hypotenuse is 2x. Since we know the side length of the side across from the 60 degree angle, we use that identity and solve for x:

[tex]x\sqrt{3}=18[/tex] and

[tex]x=\frac{18}{\sqrt{3} }[/tex] and rationalizing the denominator,

[tex]x=\frac{18}{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }=\frac{18\sqrt{3} }{3}=6\sqrt{3}[/tex]

This is the side length of the side across from the 30 degree angle. In order to find the hypotenuse, we have to multiply this value by 2 to get

12√3, the third choice down.

Answer:

The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.

Therefore, we have the following equation:

[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]

The Pythagorean identity  comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

, where  is the hypotenuse of the triangle and  and  are two legs of the triangle.

Therefore, we have the following equation:

Answer:

2.) 56

Step-by-step explanation:

(5 x 4) ÷ 2 = 10

10 x 4 = 40

4 x 4 = 16

40 + 16 = 56

Answer:

Amount A get = 2,575

Total amount = 5,150

Step-by-step explanation:

Given:

Ratio between A,B and C = 10:6:4

Assume;

Common ration is 'a'

So,

Amount A get = 10a

Amount B get = 6a

Amount C get = 4a

So,

Amount B get - Amount C get = 515

6a - 4a = 515

2a = 515

a = 257.5

Total amount = 10a + 6a + 4a

Total amount = 20a

Total amount = 20(257.5)

Total amount = 5,150

Amount A get = 10a

Amount A get = 10(257.5)

Amount A get = 2,575

Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:

[tex]5-8=-3[/tex]

[tex]2-5=-3[/tex]

[tex]-1-2=-3[/tex]

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:

[tex]f(n)=a+(n-1)d[/tex], for [tex]n\geq 1[/tex]

Where, a is the first term and d is the common difference.

Putting [tex]a=8,d=-3[/tex], we get

[tex]f(n)=8+(n-1)(-3)[/tex]

[tex]f(n)=8-3(n-1)[/tex]

[tex]f(n)=-3(n-1)+8[/tex], for [tex]n\geq 1[/tex]

Therefore, the correct option is A.

Answer:

B: as they enter a music store

Step-by-step explanation:

b is in a music store where you find people who enjoy music, but have diverse tastes.

in a classical choir recital, your results will be biased because a majority of the people there enjoy classical choir music the most.

Answer:

48

Step-by-step explanation:

The blank would be 48 because 3 times 4 is 12. 12 times 4 is 48. And 48 times 4 would be 192

Answer:

84/3=28

Alex earns $28 a week mowing lawns.

Answer:

He earns 28 dollars per week mowing lawns

Step-by-step explanation:

Wow Alex should get a higher paying job lol

Answer:

See explanation

Step-by-step explanation:

The question is incomplete; So, I will solve the question generally.

Assume the following;

[tex]l \to length[/tex]

[tex]w \to width[/tex]

[tex]h \to height[/tex]

Since the water level must be 2 inches below the tank height, the water height is:

[tex]H \to h - 2[/tex]

So, the water volume is:

[tex]Volume = l * w * H[/tex]

[tex]Volume = l * w * (h - 2)[/tex]

Hence, the expression is:

[tex]Volume = l * w * (h - 2)[/tex]

Assume that:

[tex]l = 5; w = 10; h = 8[/tex]

The volume becomes:

[tex]Volume = 5 * 10 * (8 - 2)[/tex]

[tex]Volume = 5 * 10 * 6[/tex]

[tex]Volume = 300[/tex] cubic units

Answer:

(0, 3)

Step-by-step explanation:

y= 3 when x=0

Answer:

d= 8.3 units

➴➵➶➴➵➶➴➵➶

[tex]Given:[/tex]

[tex]L=7[/tex]

[tex]B=4[/tex]

[tex]H=2[/tex]

[tex]d=\sqrt{L^2+B^2+H^2}[/tex]

[tex]d=\sqrt{7^2+4^2+2^2}[/tex]

[tex]d=\sqrt{49+16+4}[/tex]

[tex]d=\sqrt{69}[/tex]

[tex]d=8.3~units[/tex] ✔︎

•❅────✧❅✦❅✧────❅•

hope it helps...

have a great day!!!

Answer:

you have 48

Step-by-step explanation:

15x2=30

9x2=18

18+30=48

Answe545r:

45454

Step-by-step explanation:

Answer: [tex]6x^2-2x+4[/tex]

Step-by-step explanation:

Given

The length of a rectangle is given by

[tex]l=2x^2-5x+5[/tex]

and the breadth is given by

[tex]w=x^2+4x-3[/tex]

Perimeter is the sum of the sides of rectangle

[tex]\therefore \text{Perimeter P= }2(2x^2-5x+5+x^2+4x-3)\\\Rightarrow P=2(3x^2-5x+4x+5-3)\\\Rightarrow P=2(3x^2-x+2)\\\Rightarrow P=6x^2-2x+4[/tex]

Thus, the perimeter is given by [tex]6x^2-2x+4[/tex].

Answer:

4pi or 12.57

Step-by-step explanation:

Area = pi * radius^2

Area = pi * 2^2

Area = pi * 4

Area = 4pi or 12.57

Answer:

y=25x+150

Step-by-step explanation:

The slope is 25 and the y-intercept is 150.

Hope this helps.

Answer:

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation on interval of [0,2π)

[tex] \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} [/tex]

remember that,

[tex] \displaystyle \cos(t) = \cos(2\pi - t) [/tex]

so the equation has two solutions

[tex] \begin{cases} \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} \\ \cos \left(2\pi - (2 \theta + \frac{\pi}{3} )\right ) = \frac{ \sqrt{3} }{2} \end{cases}[/tex]

take inverse trig both sides which yields:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ 2\pi - 2 \theta - \frac{\pi}{3} = \frac{\pi}{6} \end{cases}[/tex]

simplify the second equation:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} \end{cases}[/tex]

add period of 2kπ:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} + 2k\pi\end{cases} [/tex]

By making theta subject of the equation we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} - k\pi\end{cases} [/tex]

since [tex]k\in\mathbb{Z}[/tex] we get:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} + k\pi\end{cases} [/tex]

as we want to Solve the trigonometric equation on the interval of [0,2π) we get

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + \pi \\ \theta = \frac{3\pi}{4} + \pi\end{cases} [/tex]

by simplifying we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{23\pi}{12} \\ \theta = \frac{7\pi}{4} \end{cases} [/tex]

and we are done!

hence,

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]

Answer:

nfdsBFS>BFBms?FBsbn

Step-by-step explanation:vkhgv

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Answer: X=6  Y=4

x+y= 10

6+4=10

 x-y=2

6-4=2

Answer:

x=6

y=4

Step-by-step explanation:

Use an elimination method:

add equation 1 and 2 together.

2x = 12

divide both side by 2

x = 12/2

x = 6

use equal 1,

x + y = 10

y = 10 - x

y = 10 - 6

y = 4

Answer: X is do it yourself and y is do it yourself X is do it yourself and y is do it yourself

Step-by-step explanation:

Lolol

Answer:

7 hours

Step-by-step explanation:

Rental cost :

Fixed pay = $20

Hourly cost = 2.65

To obtain the minimum rental hour, we work with the least amount that can be spent ;

For tourist that can spend more than $37 but less than $65

Total cost of rental :

20 + 2.65h ; h = number of hours

When total cost > 37

20 + 2.65h > 37

2.65h > 37 - 20

2.65h > 17

h > 6.415

Hence, the minimum whole hour of bicycke rental is 7 hours

Answer:  4.3 cm

Step-by-step explanation:

Leroy's rectangle's width is 7.6 cm in length and the length of the triangle is 11.9 cm.

The length is therefore longer than the width and the difference is:

= Length - Width

= 11.9 - 7.6

= 4.3 cm

You add half of the coefficient of x and square it.

What you do on one side,you must do it on the other.

Answer:

96 squared units

Step-by-step explanation:

Please find attached the diagram used in answering this question

The surface area is equal to the area of each shape

Area of a triangle = Area of a triangle = 1/2 x ( base x height)

1/2 x 2 x 3= 3

there are 4 triangles, area of both triangles = 3x4 = 12

Area of rectangle = length x width

Area of middle rectangle = 6 x 7 = 42

Area of two side rectangles = (3 +3) x 7 = 42

surface area = 42 + 42 + 12 = 96

Answer:

32 just multiply by four

Answer:

NO = 10

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle, then it is half the length of the third side, that is

18 - 2x = [tex]\frac{1}{2}[/tex] (9x - 16) ( multiply both sides by 2 to clear the fraction )

36 - 4x = 9x - 16 ( add 4x to both sides )

36 = 13x - 16 ( add 16 to both sides )

52 = 13x ( divide both sides by 13 )

4 = x

Then

NO = 18 - 2x = 18 - 2(4) = 18 - 8 = 10