Select the correct answer.
Estimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y=9

Answer:

  y = 18

Step-by-step explanation:

Direct variation means y will change by the same factor x does. When x changes by a factor of 15/10 = 1.5, the value of y will change by that same factor

  x = 10, y = 12

  x= 15, y = 1.5×12 = 18

The new value of y is y = 18.

_____

Written as a proportion, you have ...

  y/15 = 12/10

  y = 15×12/10 = 18

__

Written as a direct variation equation, you have ...

  y = kx

  12 = k·10   ⇒   k = 1.2

  y = 1.2·15 = 18 . . . . for x=15

Answer:

ay manuck im in 7th grade it sucks but you can get a OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Answer:

Step-by-step explanation:

#a

[tex]\\ \sf{:}\dashrightarrow -2(-4.5)=9.0[/tex]

#b

[tex]\\ \sf{:}\dashrightarrow (-8.7)(-10)=8.7[/tex]

#c

[tex]\\ \sf{:}\dashrightarrow (-7)(-2)=14[/tex]

#d

[tex]\\ \sf{:}\dashrightarrow (-9)(-10)=90[/tex]

Answer:

8/7A - C = B

Step-by-step explanation:

A= 7/8(B+C)

Multiply both sides by 8/7

8/7A = B + C

Subtract C

8/7A - C = B

[tex]5y+2x = -7~~~~~......(i)\\\\y = -2x +5 ~~~~~~.....(ii)\\\\(i) -(ii):\\\\5y+2x -y = -7-(-2x+5)\\\\\implies 4y +2x = -7 +2x -5\\\\\implies 4y +2x -2x = -12\\\\\implies 4y = -12\\\\\implies y = - \dfrac{12}4 = -3\\\\\\\text{Substitute}~ y=-3~ \text{in equation (ii):}\\\\\\-3 = -2x +5\\\\\implies 2x = 5 +3 \\\\\implies 2x = 8\\\\\implies x = \dfrac 82 =4\\\\\text{Hence,}~ x = 4[/tex]

[tex]\\ \sf\Rrightarrow 0.02349[/tex]

[tex]\\ \sf\Rrightarrow 0.0235\times 10^{-1}[/tex]

[tex]\\ \sf\Rrightarrow 2.35\times 10^{-3}[/tex]

Option C is correct

[tex]0.002349 \\ estimate \: \: \: it \\ = 0.00235 \\ = 0.00235 \times 1000 \\ = 2.35 \\ therefore \\ 0.00235 \\ = 2.35 \times \frac{1}{1000} \\ = 2.35 \times {10}^{ - 3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

yes they form a proportion

Answer:

Step-by-step explanation:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Answer:

[tex]f(x)\div g(x)=x-10[/tex]

Step-by-step explanation:

[tex]\frac{x^2-19x+90}{x-9}[/tex]

[tex]\frac{(x-10)(x-9)}{x-9}[/tex]

[tex]x-10[/tex]

Answer:

[tex]f(x)\div g(x)=-10[/tex]

Step-by-step explanation:

Solve [tex]f(x)[/tex]

[tex]f(x)=x^2-19x+90[/tex]

[tex]x^2-19x+90[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]\left(x^2-9x\right)+\left(-10x+90\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-9x[/tex]

[tex]=x(x-9)[/tex]

[tex]\mathrm{Factor\:out\:-10\;from}\:\:-10x+90[/tex]

[tex]=-10(x-9)[/tex]

[tex]=x\left(x-9\right)-10\left(x-9\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x-9[/tex]

[tex]\bold{\left(x-9\right)\left(x-10\right)}[/tex]

Solve [tex]g(x)[/tex]

[tex]g(x)=x-9[/tex]

[tex]\bold{x-9}[/tex]

[tex](x-9\right)\left(x-10)}\div \:x-9[/tex]

Now, solve:

[tex](x-9\right)\left(x-10)}\div \:x-9[/tex]

[tex]=\frac{(x-9)\left(x-10)}{:x-9}[/tex]

[tex]= -10[/tex]

Therefore, [tex]f(x)\div g(x)=-10[/tex]

[tex]32^{-\tfrac 25}\\\\=(2^5)^{-\tfrac 25}\\\\=2^{-2}\\\\=\dfrac 1{2^2}\\\\=\dfrac 14[/tex]

Answer:

The answer is C. (a + -a = 0 )

Step-by-step explanation:

"The additive inverse of a number a is the number that, when added to a, yields zero"

Answer:

B)

Step-by-step explanation:

10/5 + 4(72 - 6)

10/5 + 288 - 24          Distribute the 4 to 72 and 6

2 + 288 - 24               Divide

2 + 264                       Combine the like terms

262                        

a) Write an expression to describe the journey of the yellow submarine.

-> ((0 - 40) + 30) - 25

[] Sea level = 0

[] The descend 40 meters = -40

[] After examining the sea, they rose 30 meters = + 30

[] They dove 25 meters to look at an octopus = -25

b) At what depth did they stop to look at the octopus?

-> -35 meters

[] The started at 0 (0), descended 40 (-40), rose 30 (-10), and then sove 25 (-35) to see the octopus

[] Another way to think of this is to simplify our previous expression completely

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

-3; (8, -20)

Step-by-step explanation:

to find the rate of change we do (y2 - y1) / (x2 - x1)

basically we choose 2 points on y and subtract them while using the 2 points on x and subtracting them

after subtracting them we divide change of y by change of x

for this one i chose (3, -5) and (6, -14)

-14 - (-5) = -9

6 - 3 = 3

-9 / 3 = -3

the rate of change is three

to find the y intercept we can use this equation

y = -3x + b

and then plug in things

ill plug in the first set of coordinates

-5 = -3(3) + b

-5 = -9 + b

b = 4

so the y intercept is b

using this equation

y = -3x + 4

we can find out what value y is when the x value is 8

-3(8) + 4 = -20

Answer:

x = -3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Distributive Property

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

3x + 2 = x + 4(x + 2)

Step 2: Solve for x

Answer:

x=-3

Step-by-step explanation:

3x+2=x+4(x+2)

3x+2=x+4x+8

3x=5x+6

3x-6=5x

-6=2x

x=-3

I suppose you mean to convert 58₁₀ to base 2, and not 5810₁₀ to base 2.

Write 58 as the sum of the largest powers of 2 that you can:

58 = 32 + 26

58 = 32 + 16 + 10

58 = 32 + 16 + 8 + 2

58 = 2⁵ + 2⁴ + 2³ + 2¹

58 = 1×2⁵ + 1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰

⇒   58₁₀ = 111010₂

To convert from base 2 to base 10, write out and simplify the decimal expansion as in the last line of the previous example.

10111₂ = 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 1×2⁰

10111₂ = 16 + 0 + 4 + 2 + 1

⇒   10111₂ = 23₁₀

#a

[tex]\\ \sf\Rrightarrow (58)_{10}[/tex]

[tex]\\ \sf\Rrightarrow (2+8+16+32)_{10}[/tex]

[tex]\\ \sf\Rrightarrow (2^1+2^3+2^4+2^5)_{10}[/tex]

[tex]\\ \sf\Rrightarrow 0(2^0) 1(2^1)+0(2^2)+1(2^3)+1(2^4)+1(2^5)[/tex]

[tex]\\ \sf\Rrightarrow (111010)_2[/tex]

#b

[tex]\\ \sf\Rrightarrow (10111)_2[/tex]

[tex]\\ \sf\Rrightarrow 1\times 2^0+1\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4[/tex]

[tex]\\ \sf\Rrightarrow 1+2+4+16[/tex]

[tex]\\ \sf\Rrightarrow (23)_{10}[/tex]

Answer:

Part of the time

Step-by-step explanation:

This is a linear line, meaning it is an infinite straight line. Part of the time it will be more than 0, part of the time it will be less than 0.

Answer:

Yes there would be a positive correlation on a graph.

Step-by-step explanation:

Say we use 0 as our X value. We get 4 as our Y value. Another example we can use is 10. We get 34 as our Y intercept.

Answer:

210

Step-by-step explanation:

so first i found out how many shirts each prints in a minute

the first machine produced 15/min

the second produced 20/min

now I added the 2 together and got 35

7,350/35 is 210

Answer:

The answer should be y= -4x + 20.

Answer:

There’s a subtle, but important difference between these 2 methods of handling events. If you’ll use the first method, event handlers, the difference is that if you add two event handlers for the same button click, the second event handler will overwrite the first and only that event will trigger

Step-by-step explanation:

i hope this answer your questions

Answer:

Q6. 49π or about 153.94

Q7. 42

Q8. 17.5

Step-by-step explanation:

6. the formula for the area of a circle is πr², and you have that r, or the radius, is 7. then, you just plug that in, which would be π·7² = π·49 = 49π.

7. the formula for the area of a parallelogram is base times height, and you have base = 6 cm and height = 7 cm. this means the area is 6 · 7 = 42.

8. The formula for the area of a triangle is base times height divided by 2, and you have base = 5 and height = 7. this means the area is 5 · 7 ÷ 2 = 35÷2 = 17.5

Answer: -1.9f - 21

Step-by-step explanation:

Combined the like terms.

Correct me if I am incorrect.

Answer:

1. if x + 5 = 12, then x = 7

:Subtraction property of equality

2. If x + y = 20, and y = 5, then x + 5 = 20.

:Substitution property of equality

3. If 2x3 = 11, then 11 = 2x - 3.

:Symmetric property of equality

Answer:

y = 4 (-3) - 2

y = -12 - 2

y = -14

Step-by-step explanation:

Answer:

First what does x represent. For example x could equal 5 so (5)2 +2 simplified is 10 +2 which is 12 :)

Step-by-step explanation:

Answer:

the start numbew woould be 26

Step-by-step explanation:

6 less than 26 is 20

Answer:

n=26

Step-by-step explanation:

The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.

First part;

Second part;

Third part;

Reasons:

First Part;

Considering a unit circle with the center at the origin of the graph, we have;

The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.

The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;

The coordinates of point P = (cos(θ), sin(θ))

In the four quadrant, we have;

First Quadrant; All trigonometric ratios are positive

Second Quadrant; sine is positive

Third Quadrant; Tan is positive

Fourth Quadrant; Cosine is positive

Second part;

We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;

sin(60°) = sin(120°) = 0.5·√3

However, the x-coordinate of the point P is in the negative direction, therefore, we get;

cos(120°) = -cos(60°) = -0.5

Similarly from the quadrant relationship, we have;

240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;

sin(240°) = -sin(60°) = -0.5·√3

cos(240°) = -cos(60°) = -0.5

300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;

sin(300°) is negative and cos(300°) is positive

Which gives;

sin(300°) = -sin(60°) =  -0.5·√3

cos(300°) =  cos(60°) = 0.5

Third part;

[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]

[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]

The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°

Also, due to the mid location of the angle 45° on the quadrant, we have;

Another angles is the sines and cosine of (90° + 45°) = 135°

Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°

[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]

Therefore,

[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]

Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex]  = 30° can be used to find the sine and cosine of 150°,  210°, and 330°.

[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]

[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]

Learn more about the sine and cosine of angles here:

https://brainly.com/question/4372174

Answer:

Step-by-step explanation:

The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.