explain how the unit circle definition of sin and cos is related to the equations sin(theta)=O/H and cos(theta)=A/H

The first step we take is to find the area of the square since the area of the square is equal to the area of the rectangle

       [tex]area-of-rectangle = area- of-square\\area-of-rectangle = 8*8 = 64in^2[/tex]

Another fact we know is that the length of the rectangle is four times the width.

      L = 4W

Now let's put the variables, found above, into the format to find the area of the rectangle

  [tex]area-of-rectangle = L * W, (L = 4W)\\area-of-rectangle = 4W * W\\\\64 = 4W^2\\16 = W^2\\\\W^2 = 16\\\\W = 4[/tex]

Since the Width is 4, L = 4 * W = 4 * 4 = 16 in.

So the length is 16 inches

Hope that helps!

Explanation:

We can make use of the symmetry of the problem and properties of similar triangles.

Here's a "paragraph proof."

Draw line OP perpendicular to chord MN, such that P lies on line MB. Let the point of intersection of OP with chord MN be designated point Q. Line OP bisects angle MON, so has measure y/2.

Triangles OPM and MPQ are similar (by AA similarity; both right triangles contain angle OPM), so angle QMP ≅ angle MOP. As we observed above, angle MOP has measure y/2, so angle QMP has measure y/2.

Angle BMN is another name for angle QMP, so it has measure y/2.

__

Additional comments

By the HL congruence postulate, the perpendicular bisector of chord MN divides triangle MON into two congruent right triangles. (OM≅ON, MQ≅NQ). That means ∠MOQ≅∠NOQ, so OQ bisects angle MON, as we say above.

__

Another way to come to the desired conclusion is to recognize that for any point X on long arc MN, angle MXN will have measure y/2. (inscribed angle theorem) This remains true in the limit as X approaches M. As X approaches M, secant XM approaches tangent line MB. So, in the limit, angle BMN is y/2.

Answer:4323.78cm^3

Step-by-step explanation:

Answer:

y=x+1.75

4x-2y = 4

The answer is (3. 75, 5.5)

Step-by-step explanation:

If you plot the two equations on Desmos' Graphing Calculator, you will see that the solution is intersected at (3.75, 5.5).

Answer:

Step-by-step explanation:

The order of the expression for congruent shapes indicate the

corresponding vertices between the two shapes that are congruent.

The option which is true is D. T = Q.

Reasons:

The given statement is; ΔRST ≅ ΔNPQ

By Corresponding Parts of Congruent Triangle are Congruent, CPCTC, we

have; The sides on ΔRST are congruent to the corresponding sides of ΔNPQ

Therefore;

RS ≅ NP

RT ≅ NQ

ST ≅ PQ

By CPCTC, we have that the angles on ΔRST are congruent to the corresponding angles of ΔNPQ

Therefore;

∠R ≅ ∠N

∠S ≅ ∠P

∠T ≅ ∠Q

Which gives, by definition of congruency;

∠R = ∠N

∠S = ∠P

∠T = ∠Q

Therefore, the true statement is D. T = Q.

give brainliest

Answer:

subtract 9 from both sides

Step-by-step explanation:

m + 9 = 45 ( subtract 9 from both sides )

m = 36

Answer:

Subtract

Step-by-step explanation:

You should subtract since the equation says to add.

You basically do the opposite of what it says.

For example, if it was m - 9 = 45 you would add 9 on both sides, but in this case, you would subtract since its m + 9 = 45

m + 9 = 45

subtract nine by 9 and 45:

m = 36

36 + 9 = 45

Answer:

229 is the remainder.

Explanation:

In order to find the remainder, insert the value of x in the equation.

Given equation:

Given x value:

Find remainder:

[tex]\sf p(4) = 4^4 - 27[/tex]

[tex]\sf p(4) = 256 - 27[/tex]

[tex]\sf p(4) = 229[/tex]

Answer:

229

Step-by-step explanation:

Here we are given a polynomial p(x) and we need to find the remainder when it is divided by (x-4) . As we know that if a polynomial, say [tex]g(x)[/tex] is divided by [tex]x-a[/tex] then the remainder is [tex]g(a)[/tex] .

Firstly equate [tex] x -4[/tex] with 0 , we have;

[tex]\longrightarrow x -4=0\\[/tex]

[tex]\longrightarrow x =0+4\\ [/tex]

[tex]\longrightarrow x = 4 [/tex]

Now substitute [tex] x =4[/tex] in [tex]p(x)[/tex] ,

[tex]\longrightarrow p(x)= x^4-27\\[/tex]

[tex]\longrightarrow p(4)= (4)^4-27\\[/tex]

[tex]\longrightarrow p(4) = 256 - 27 \\[/tex]

[tex]\longrightarrow \underline{\underline{\boldsymbol{ p(4) = 229}}}[/tex]

Hence the remainder is 229 .

answer is tan 7 a 4 a tan4a

The possible outcomes of the fair coin and the dice is the sample space

The items are given as:

Coin = 1

Dice = 1

The sample space of both items are:

Coin = {H,T}
Dice = {1,2,3,4,5,6}

So, the list of possible outcomes is: {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

From the above list, there is only one outcome that has a head and a 3 out of 12 possible outcomes

So, the probability of getting a head and a 3 is:

p = 1/12

Hence, the probability of getting a head and a 3 is 1/12

Read more about probability at:

https://brainly.com/question/25870256

Answer:

10

Step-by-step explanation:

(5+x=15)☞︎︎︎(Equation)

5-5+x=15-5

X=10

Answer:

above is the solution to the question

Answer:For the answer to this It has me stuck between A and B

Explanation and Answer:

The graph of y=[tex]x^2[/tex] is a parabola (it looks like a u) that intersects the graph at the origin. These are all shifted variations of that graph, so from that you can figure out their formula by visualizing it.

You can also try substituting numbers into the equations and drawing a graph from that.

Graph A is the y=x^2, shifted to the left, so it becomes [tex]y=x^2+x[/tex]. It's +x because now negative numbers can be gotten from the equation, as compared to before when x^2 gives only positive numbers.

Graph B is [tex]y=x^2+3x[/tex] . Similar to graph A, but now it moves down by more units, because of the 3x.

Graph C is [tex]y=-x^2+2[/tex]. Imaging y=x^2 flipped, it changes from looking like a u to n. That's y=[tex]-x^2[/tex]

Graph D is [tex]y= x^2-x[/tex]. The opposite of Graph A.

Answer:

[tex] - 3 \times 5 \times - 9 \times - 2 \\ - 15 \times + 18 = 3[/tex]

Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

Problem 2

Why not? Well it's because the angles do not match up perfectly.

The triangle on the left is a 30-60-90 triangle; while the triangle on the right is a 40-50-90 triangle. The numbers mentioned are the angle values.

Only the "90"s match up, but everything else does not. We need to have three pairs of congruent angles to be able to use the angle angle (AA) similarity theorem.

Answer:

-3

Step-by-step explanation:

when you look at it go to where x is -2 then go down to where the blue line goes on the point

x2+y2=9 is not a function

In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation.

For

x

2

+

y

2

=

9

XXXX

if (for example)

x=0XXXX there are two values for y (namely +3 and −3) which satisfy the equation

Answer:

Step-by-step explanation:

As with other forms of direct and inverse variation, the "constant of variation" (k) is the constant multiplier in the equation. "Varies directly" means the independent variable is in the numerator. "Varies inversely" means the independent variable is in the denominator. The variation equation can be solved for missing values of constants or variables.

The equation for "varies directly with v and w, and inversely with z" means the equation is of the form ...

  y = k·v·w/z

Then the values of v or w are ...

  v = y·z/(k·w)

  w = y·z/(k·v)

__

  k = y·z/(v·w) = 5·24/(12·14) = 5/7; the equation is y = 5·v·w/(7·z)

  w = y·z/(k·v) = 18·8/(10·4) = 18/5; the equation is y = 10·v·w/z

  k = 3/2 (read from the equation); y = (3/2)v·w/z = 3·16·24/(2·6) = 96

  k = 8 (read from the equation); v = y·z/(k·w) = 20·2/(8·6) = 5/6

  y = k·v·w/z = 6·12·7/15 = 168/5; the equation is y = 6·v·w/z

Answer: 254.34 yd

Step-by-step explanation:

If the diameter is 18 yd then the radius:

radius = diameter/2

r = 18/2

r = 9 yd

So the area is:

[tex]A = \pi r^2\\= \pi (9)^2\\= (3.14)(81)\\ =254.34 \hspace2yd[/tex]

Therefore, the area of the circle is 254.34 yd

The sample space of Shari's tree diagram is the total possible outcomes of rolling the game piece and spinning the pointer.

It doesn't matter if Shari starts with the spinner or the game piece

The experiment involves:

If Shari starts with the game piece, the sample size (n) would be:

n = 12 * 4

n = 48

If Shari starts with the spinner, the sample size (n) would be:

n = 4 * 12

n = 48

Notice that the sample size remains unchanged irrespective of what he starts with

Hence, it doesn't matter if Shari starts with the spinner or the game piece

Read more about tree diagram at:

https://brainly.com/question/2581880

Answer:

Step-by-step explanation:

Use similarity ΔPQS ~ ΔRQS

Use the ratio of corresponding sides:

Find PS

Use similarity ΔPQS ~ ΔPRQ

Ratio of corresponding sides:

Use similarity ΔPQS ~ ΔPRQ

Ratio of corresponding sides:

Find RS:

Answer options

[tex]\tt \dfrac{3}{8}\times 28.7=10.7625=10.76~kg[/tex]

Answer:

600

Step-by-step explanation: [tex]100\times2\times\frac{180}{60}[/tex]

Cross out the common factor

[tex]100\times2\times3[/tex]

Calculate the product or quotient

[tex]200\times3[/tex]
[tex]600\ YOUR\ ANSWER\ which\ can\ also\ be\ written\ as\ 6\times{10}^2\[/tex]

I hope this helps you

:)

If the initial population of the bacteria is 100, then the population of the bacteria after 180 hours will be 800.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

A colony of 100 bacteria doubles in size every 60 hours.

The exponential relation will be given below.

[tex]\rm P = 100 \times 2^{t/60}[/tex]

Where t is the number of hours

Then the population of the bacteria after 180 hours will be

[tex]\rm P = 100 \times 2^{t/60} \\\\P = 100 \times 2 ^{180/60}\\\\\rm P = 100 \times 2^{3}\\\\\rm P = 100 \times 8\\\\\rm P = 800[/tex]

More about the exponent link is given below.

https://brainly.com/question/5497425

Answer:

I'd say On average, about 50% of students prefer elther extra cheese or pepperoni and On average, 1/4 of students prefer pineapple.

Also i tried my hardest to read the picture you took, so im assuming that the pineapple statement is 1/4 correct me if i'm wrong

Answer:

She sold $1800 worth.

Step-by-step explanation:

290-200=90

90 x 20 because 100÷5=20

90 x 20 = 1800

$1800

Answer:

$820.00

Step-by-step explanation:

x = price yesterday (initital price)

If it is 67% off, then the price is 33% of the initial.

x(.33) = 270.60

divide .37 on both sides

x = 820.00

The price of the suit yesterday is $820.00.

Answer:

A

Step-by-step explanation:

3x and x + 30 are vertically opposite angles and are congruent , then

3x = x + 30 ( subtract x from both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Then

∠ A = 3x = 3(15) = 45°

See <A and x+30 are opposite angles .

We know that opposite angles are equal

so

Now

Option A is correct

Answer:

explicit  definition: [tex]a_n=5n-4[/tex]

recursive definition: [tex]a_n=a_{n-1}+5[/tex]

Step-by-step explanation:

Given arithmetic sequence: 1, 6, 11, 16, 21 ...

Therefore,

Using the general form of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

[tex]\implies a_n=1+(n-1)5[/tex]

[tex]\implies a_n=1+5n-5[/tex]

[tex]\implies a_n=5n-4[/tex]

or [tex]a_n=a_{n-1}+5[/tex]