Why does sin54°≈0.809≈cos36° in a right triangle?

A
54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and the adjacent leg of 36° are the same leg in the triangle.

B
54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the adjacent leg and the hypotenuse and cos36° is the ratio of the opposite leg and the hypotenuse. In this triangle, the adjacent leg of 54° and the opposite leg of 36° are the same leg in the triangle.

C
54° and 36° are supplementary in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and adjacent leg of 36° are the same leg in the triangle.

D
54° and 36° are supplementary in the same right triangle. sin54° is the ratio of the adjacent leg and the hypotenuse and cos36° is the ratio of the opposite leg and the hypotenuse. In this triangle, the adjacent leg of 54° and opposite leg of 36° are the same leg in the triangle.

Answer:

22.) y = -1/7x + 8/7 23.) y = 2x -3 (x is the slope.)

Step-by-step explanation

22.) Divided each side by 7. Subtract 1/7x from each side to get the eqaution.

23.) Divided each side by 3. Add y to each side. then subtract 9 from each side to get the equation.

Answer:

4

Step-by-step explanation:

You would complete the square by dividing the b value by 2, and then squaring it. In this case, the b value is -4. You would divide -4 by 2 and get -2. Now, you would square -2, and you would get 4.

Answer:

25) B obtuse scalene

26) A acute isosceles

27) A acute isosceles

28) D obtuse isosceles

29) D right scalene

30) C obtuse isosceles

31) C obtuse scalene

32) C acute scalene

Step-by-step explanation:

A scalene triangle has sides of no equal measures (no side has the same length as another). An isosceles triangle has two sides of the same length. An equilateral triangle has three sides that all have the same lengths.

An acute triangle has all three angles that each measure less than 90°. An obtuse triangle has one angle that measures greater than 90°. A right angle has one angle that measures exactly 90°.

Hope this helps :)

Answer:

30

Step-by-step explanation:

5*2*3 - 2*0 = 30 - 0 = 30

Simplify the expression.

Exact Form:

10/9

Decimal Form:

1.¯1

Mixed Number Form:

1/1/9

Answer:

It would be 1⅑

Step-by-step explanation:

First we turn the fractions into improper fractions.

4 7/9 would now be 43/9

3 2/3 would not be 11/3

Now, we have to make them have the same “bottom number”

3x11=33, 3x3=9

Now our equation is..

43/9 - 33/9 = 10/9

When we turn it into a simplified fraction, it would be 1⅑  

0.14285714285

Calculator ;)

Answer:

[tex](-3,-2)[/tex]

Step-by-step explanation:

First, you need to get one like term in each equation the same in order to eliminate. To do less damage to the equation, we'll use the x terms.

To get the x terms the same, multiply both equations by the opposite x term:

[tex]-3(2x+5y)=-3(-16)\\\\2(-3x+7y)=2(-5)[/tex]

Simplify by multiplying. Use the distributive property for the left side (remember, two negatives make a positive and a negative multiplied by a positive will always be negative):

[tex]-3(2x)-3(5y)=-3(-16)\\\\2(-3x)+2(7y)=2(-15)\\\\\\-6x-15y=48\\\\-6x+14y=-10[/tex]

Now subtract all like terms. The x terms cancel out:

[tex]-6x-(-6x)=0\\\\-15y-14y=-29y\\\\48-(-10)=58\\\\-29y=58[/tex]

Now solve the new equation for y. Isolate the variable by using inverse operations. The term can be seen as -29×y. In order to isolate the variable, use division (opposite of multiplication). Divide both sides by 29:

[tex]\frac{-29y}{29} =\frac{58}{29} \\\\-1y=2[/tex]

Make the variable positive. Multiply both sides by -1:

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

The value of y is -2. Insert this value into either original equation:

[tex]2x+5(-2)=-16[/tex]

Solve for x. Simplify multiplication:

[tex]2x-10=-16[/tex]

Use inverse operations to get like terms on the same side of the equation. Add 10 to both sides (addition is the opposite of subtraction) to cancel out the -10 on the left:

[tex]2x-10+10=-16+10\\\\2x=-6[/tex]

Isolate the variable using inverse operations. The x term can be seen as 2×x. Division is the opposite of multiplication, so divide both sides by 2:

[tex]\frac{2x}{2}=\frac{-6}{2} \\\\x=-3[/tex]

The value of x is -3. Therefore, the solution to the system is:

[tex](-3_{x},-2_{y})[/tex]

:Done

Answer: (x + 2) • (x - 1) • (2x - 3)

Step-by-step explanation:

Answer:

If the pictures are relevant:

Step-by-step explanation:

Measure the sides, or look for the best fit image

Answer:

3 : 1

Step-by-step explanation:

Given that :

Total Marbles in bag = 44

Color of marbles in bag : red, green

Number of red marbles = 11

The ratio of green to red marbles :

Number of green marbles :

(Total marbles in bag - number of red marbles)

(44 - 11) = 33 green marbles

Hence, ratio of green to red Marbles:

Number of green marbles : number of red marbles

33 : 11

3 : 1

Answer:

The correct answer is 2:1.

Step-by-step explanation:

I did the K12 assignment and is said this was the right answer.  

Answer:

Your answer would be (7, -9)

Answer:246

Step-by-step explanation:

Answer:

Step-by-step explanation:

Take the two equations and equal them together (2.35 + 0.25x = 1.75 + 0.40x) 2. isolate x onto one side by canceling out (2.35 (- 1.75) + 0.25x (.25x) = 1.75 (-1.75) + 0.40x (.25x) ) 3. get what X equal (x=4) 4. plug the new value of x (4) into ONE of the equations (2.35 + 0.25(4) ) 5. get your answer (3.35)

Answer:

45.52

Step-by-step explanation:

Answer: 12 1/2

Step-by-step explanation: It is 12 1/2 because you have to multiply 4 times 8 1/2 and you'll get 12 1/2

Thats how you do It and make sure to subscirbe to GamerPlayzSupreme2 BYE!!

Answer:

The parents sell 48 pretzels.

Step-by-step explanation:

Let a be the number of bags of popcorn sold, and b the number of pretzels sold.

2.5a + 2b = 336

a = 2b

2.5a + a = 336

3.5a = 336

a = 96

b = 48

Answer:

7x+4y+1

Don’t low if you wanted it simplified

Answer:

3x + 4y + 5

Step-by-step explanation:

3(x + y) + 2 • 2 + (1 + y)

3x + 3y + 2 • 2 + (1 + y)

3x + 4y + 4 + 1

3x + 4y + 5

9514 1404 393

Answer:

  [tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]

Step-by-step explanation:

If we place the bottom center at the origin and make the sides of the triangle 2 units, then the right side can be described by the equation ...

  y = √3(1 -x)

and the terminal side of the angle α can be described by ...

  y = tan(α)·x

We want the height of the shaded area, which is the y-coordinate of the point of intersection of these two lines.

  y = √3(1 -y/tan(α)) . . . . substituting for x

  y = √3·tan(α)/(√3 +tan(α)) . . . . solved for y

Since we have defined the base of the shaded area to be 1, the shaded area is half this value, or ...

  A(α) = (√3/2)tan(α)/(√3 +tan(α))

Further manipulation can put this in the form ...

  A(α) = (√3/4)sin(α)/sin(α+π/3) . . . . for α ≤ π/2, side length 2

__

For α > π/2, we need to subtract the area A(π-α) from the area of the whole triangle. This gives an area (after some rearranging) of ...

  A(α) = √3(1 -sin(α)/(4·sin(α-π/3))) . . . . for α > π/2, side length 2

__

The problem statement defines the triangle as having a side length of 'a', so the final area formula will be a factor of (a/2)² times the above expressions. That is ...

  [tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]

_____

The graph (second attachment) shows the area as a function of α (in degrees) for a unit triangle. There are inflection points in the curve at 30°, 90°, and 150°

because you have to flip the thing

Answer:

Un experimento determinista es aquel cuyo resultado se puede predecir con certeza de antemano, como combinar hidrógeno y oxígeno o sumar dos números como 2 3. Un experimento aleatorio es aquel cuyo resultado se determina por azar.

Step-by-step explanation:

what is a deterministic experiment

A deterministic experiment is one whose outcome may be predicted with certainty beforehand, such as combining Hydrogen and Oxygen, or adding two numbers such as 2 3. A random experiment is one whose outcome is determined by chance.

Answer:

x = 7.5 cm

Step-by-step explanation:

ΔBCA ~ ΔECD ⇒ the corresponding sides are proportional.

[tex]\frac{AC}{DC}[/tex] = [tex]\frac{AB}{DE}[/tex]

AC = 4 + 6 = 10 cm

[tex]\frac{10}{6}[/tex] = [tex]\frac{x+5}{x}[/tex] ⇔ 10x = 6(x + 5) ⇒ x = 7.5 cm

Answer:

4*[tex]\sqrt3[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

I think 55°% is less