Which of the following explains why cos 60º = sin 30° using the unit circle?

Answer:

The first option (5^2 + 8^2 = c^2).

Step-by-step explanation:

According to the Pythagorean Theorem, a^2 + b^2 = c^2.

If a is 5 cm, and b is 8 cm, you would have the following equation...

5^2 + 8^2 = c^2.

That matches with the first option.

Hope this helps!

Answer:

17 nickels

Step-by-step explanation:

To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:

quarters= 0.25

dimes= 0.10

nickels= 0.05

pennies= 0.01

(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where

x= the quantity of nickels

Now, you can solve for x:

4.75+3.9+0.05x+0.58=10.08

0.05x=10.08-4.75-3.9-0.58

0.05x=0.85

x=0.85/0.05

x=17

According to this, the answer is that there are 17 nickels in the cup holder.

Answer: The answer is B

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

cos (3pi/4) = -cos(pi - 3pi/4) = -cos(pi/4) = -sqrt(2)/2

=> Option B is correct

Step-by-step explanation:

1/3 and 5/2 can be shown as:

points with 1/6 interval on the number line:

0, 1/6, 2/6, 3/6, 4/6, ..., 15/6

Answer:

Option A

Step-by-step explanation:

The median is the value that lies in the middle of the data when the data set is ordered.

It is also the value that separates the higher half of the dataset from the lower half of the dataset.

Answer:

B

Step-by-step explanation:

Answer

y= 12.5x + 210,000

Step-by-step explanation:

This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b

The value of function that represents the situation is,

⇒ P = 210,000 (1.125)ⁿ

Where, n is number of years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The situation is,

⇒ A population of 210,000 increases by 12.5% each year​.

Now, Let number of years = n

Hence, The value of function that represents the situation is,

⇒ P = 210,000 (1 + 12.5%)ⁿ

⇒ P = 210,000 (1 + 0.125)ⁿ

⇒ P = 210,000 (1.125)ⁿ

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

Answer:

[tex]x = 2, 12[/tex]

Your correct answer is D, since I don't see a -12.

Step 1: Subtracting 2 from both sides

Since we have to find the value of x, we have to factor the equation. To do so, we first have to subtract the two from both sides of the equation so all the values are on one side of the equation.

[tex]x^2-10x-22(-2)=2(-2)\\x^2-10x-24=0[/tex]

Step 2: Factoring the equation

Part 1

After subtracting 2 from both sides of the equation, we have to factor the polynomial to be able to get it into two sets of parentheses, so in order to do that, we will ignore the equal sign and the 0 for now. We are now left with:

[tex]x^2-10x-24\\[/tex]

First, we find the multiples of the first term, [tex]x^2\\[/tex], and the last term, -24. Since there is an invisible 1 before the first term, we are basically finding the multiples of [tex]1x^2[/tex], which is [tex]1x[/tex] and [tex]1x[/tex], or x and x. Now we have to find the correct set of numbers for -24. Do do that, we have to make sure that when we multiply the first set of numbers (x, x) with the second set (?, ?) and add them together, then we would get the number in the middle (-10x). So: Two of the most obvious multiples for 24 are 6 and 4, 12 and 2, and 3 and 8. But, this is a negative 24, so we have to work ahead to find out which pair we use first. If we multiply 8 and 3 with x and x, we get 8x and 3x. When we add them together, we do not get 10x, but instead, we get 11x, so it is the wrong pair. If we do the same thing to 6 and 4, we would get 10x, but since 24 is negative, it is not correct because we would need one of the numbers to be negative. In this case, they equal to 10x, but one of the numbers would have to be negative because (if 6 was the negative):

[tex]-6 * 4=-24\\[/tex]

But:

[tex]4-6\neq 10\\[/tex]

So this is not the correct set either. Our last set is 12 and 2, and when we multiply by x (12x and 2x) and we set one of the numbers to be a negative (-12) and subtract them, we get -10x, so, therefore, this is the correct number pair.

[tex]-12*2=-24\\2-12=-10[/tex]

Part 2

With all that done, we now have to factor the numbers. We take the first numbers (x and x), and we place them in front of each of the two parentheses.

[tex](x,?)(x,?)[/tex]

Now, we place -12 and 2 in those places.

[tex](x,-12)(x,2)[/tex]

To find x, we have to plug in the equal sign and 0 from the beginning.

[tex](x,-12)(x,2)=0[/tex]

Since they both have to equal to 0, then that means there would be two different answers because, for example: 12 - 12 = 0, but 12 - 2 ≠ 0.

To find both solutions, we treat the numbers in each of the parentheses as its own equation, and we solve it from there.

x - 12 = 0

12 - 12 = 0

x - 2 = 0

2 - 2 = 0

12 and 2 are our solutions! Hope this helps :)

Answer:

12  and 2

Step-by-step explanation:

factor the euqation x^2-10x-22=2 and you get (x,-12)(x,2)=0 and when you solve that you get 12 and 2

Answer:

m∠1 + m∠2 = 180°

Step-by-step explanation:

An interior angle and its exterior angle are supplementary (they add up to 180°).

I would really appreciate it if you would mark me brainliest!

Have a blessed day!

Answer:

c

Step-by-step explanation:

Answer:

Hey there!

Eight years ago, Manuel's age was 36/2, or 18.

Now, his age is 18+8, or 26 years old.

So, he is 26 years old now.

Hope this helps :)

Answer:

C.

Step-by-step explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7

Answer:

Option C is the correct option.

Step-by-step explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

[tex] \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} [/tex]

Plug the values

[tex] \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} [/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} [/tex]

Add the numbers

[tex] \frac{y + 1}{x - 2} = \frac{6}{4 - 2} [/tex]

Subtract the numbers

[tex] \frac{y + 1}{x - 2} = \frac{6}{2} [/tex]

Reduce the numbers with 2

[tex] \frac{y + 1}{x - 2} = 3[/tex]

Apply cross product property

[tex]3x - 6 = y + 1[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex]3x - y = 1 + 6[/tex]

Add the numbers

[tex]3x - y = 7[/tex]

[tex] - 3x + y = - 7[/tex]

Hope this helps...

Best regards!

Answer:

[tex]\sqrt{37}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A(- 2, 9) and (x₂, y₂ ) = B(4, 8)

d = [tex]\sqrt{(4+2)^2+(8-9)^1}[/tex]

   = [tex]\sqrt{6^2+(-1)^2}[/tex]

   = [tex]\sqrt{36+1}[/tex]

    = [tex]\sqrt{37}[/tex] ≈ 6.1 ( to 1 dec. place )

Answer:

this is ur answer so memories

Answer:

6,8

Step-by-step explanation:

Answer:

The correct option is;

Exponential function 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

Step-by-step explanation:

The given functions are;

f(x) = 2x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 6, 10, 14, 18

f(x) = 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

f(x) = 2·x² + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 10, 34, 74, 130

f(x) = 3·x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 8, 14, 20, 26

By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2

Answer: The answer is B on edg

Step-by-step explanation:

Answer:

For the drop down menu:

i) x + y

ii) z²

iii) ½ xy

The complete question related to this found on brainly (ID:16485977) is stated below:

Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.

_____finds the area of the outer square by squaring its side length.

_____finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

Find attached the diagram of the question.

Step-by-step explanation:

Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.

Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent ²

From the diagram of the question.

Hypotenuse = z

Opposite = y

Adjacent = x

z² = x² + y²

Area of outer square = area of inner square + 4(area of triangles)

area of inner square = length² = (x+y)²

Expanding area of the outer square:

(x+y)² = (x+y)(x+y) = x²+xy+xy+y²

(x+y)² = x²+y²+2xy

= z² + 2xy

Area of inner square = length² = z²

Area of triangle = ½ base × height

= ½ × x × y = ½ xy

Area of outer square = area of inner square + 4(area of triangles)

(x + y)² = z² + 4(½xy )

Therefore, it is a true equation.

( x + y )² finds the area of the outer square by squaring its side length.

z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

So for the drop down menu:

i) x + y

ii) z²

iii) ½ xy

Answer:

[tex]z=-0.842<\frac{a-30}{7.8}[/tex]

And if we solve for a we got

[tex]a=30 -0.842*7.8=23.432[/tex]

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Step-by-step explanation:

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(30,7.8)[/tex]  

Where [tex]\mu=30[/tex] and [tex]\sigma=7.8[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.80[/tex]   (a)

[tex]P(X<a)=0.20[/tex]   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.20[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.20[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-0.842<\frac{a-30}{7.8}[/tex]

And if we solve for a we got

[tex]a=30 -0.842*7.8=23.432[/tex]

So the value of height that separates the bottom 20% of data from the top 80% is 23.432.  

Answer:

(3.26795, 6.73205)

(6.73205, 3.26795)

Step-by-step explanation:

Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

Answer:

1/1001 < 4/10 < 49/100 < 357/10

Step-by-step explanation:

4/10 => 0.4

49/100 => 0.49

357/10 => 35.7

1/1001 => 0.0009

Ascending order is from smallest to the greatest.

Answer:

1/1001, 4/10, 49/100, 357/10

Step-by-step explanation:

Convert the fractions to decimals.

4/10 = 0.4

49/100 = 0.49

357/10 = 35.7

1/1001 = 0.0009

Arrange in ascending order.

0.0009, 0.4, 0.49, 35.7

Change back to fractions.

Answer:

y = 5  1/4

Step-by-step explanation:

For direct or inverse variation relation

relation between two variable and y can be expresses in form of

y = kx  where k is constant of proportionality .

Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality

__________________________________

Thus, let the inverse relation be

y = kx

given

when y = 6 then x = 8

we will plug this value in y = kx

6 = k*8

=>k = 6/8 = 3/4

Thus,

relation is

y = 3/4 x

we have to find y when x = 7 ,

lets put x = 7 in y = 3/4 x

y = 3/4 *7 = 21/4 = 5 1/4

Thus, when x = 7 then y = 5 1/4

Answer:

c= 7/3

Step-by-step explanation:

To solve for c:

Simplify the equation by moving all numbers to one side and variables to the other

    -9c-4=-25

    -9c= -25+4

    -9c=-21

Now isolate c by dividing both sides by its coefficient (-9)

      c= -21/-9

Since the (-) cancel out, this simplifies to:

      c= 21/9

Now reduce the fraction by dividing the right hand side by a common value of 3:

      c= 7/3

Answer:

36

Step-by-step explanation:

Let's call the # of boys and girls 5x and 3x respectively. We can write:

5x = 3x + 24

2x = 24

x = 12 so the # of girls = 12 * 3 = 36

Answer:

solution,

Let the number of girls be X

Number of boys be 'x+24'

Now,

[tex] \frac{x + 24}{x} = \frac{5}{3} \\ or \: 3(x + 24) = 5x \\ or \: 3x + 72 = 5x \\ or \: 3x - 5x = - 72 \\ or \: - 2x = - 72 \\ or \: x = \frac{ - 72}{ - 2} \\ x = 36[/tex]

hope this helps..

Good luck on your assignment..

Answer:

The numbers at 13 and 13

Step-by-step explanation:

The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.

The two numbers are (13, 13).

Given that,

The sum of the two numbers is 26.

And the sum of their square is minimum.

We have to determine,

The two numbers are.

According to the question,

Let, the first number be x,  

and the second number be y.

The sum of the two numbers is 26.

[tex]x + y = 26[/tex]

And The sum of their squares is a minimum.

[tex]x^2 + y^2 = h[/tex]

Solving both the equation,

[tex]x + y = 26\\\\x = 26-y[/tex]

Substitute the value of x in equation 2,

[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]

Then, The vertex of the parabola is,

[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]

The minimum value of the parabola is 13, which is also the sum of squares.

Therefore, The two number is x = 13 and y =13.

To know more about Parabola click the link given below.

https://brainly.com/question/4074088

Answer: After 210 seconds they with next flash at the same time.

Step-by-step explanation:

Given: Ardem has two lights.

One flashes every 15 seconds the other flashes every 42 seconds.

If they started flashing at the same time, then the number of seconds after that they with next flash at the same time = LCM (15, 42)   [LCM - Least common multiple]

Prime factorization of 15 = 3 x 5

Prime factorization of 42 = 2 x 3 x 7

Then, LCM (15, 42) = 2 x 3 x 5 x 7 = 210

i.e. After 210 seconds they with next flash at the same time.

Answer:

17

Step-by-step explanation:

This is a very neat problem -- for teachers.

Let the number of sides = y

The sum of the interior angles is 180*(y - 2)

We are told that this sum equals 9x^2

So far the equation is

(y - 2)*180 = 9x^2                   Divide both sides by 9

(y - 2)*20 = x^2                       Remove the brackets on the left.

20*y - 40 = x^2

We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3

20*(x - 3) - 40 = x^2

20x - 60 - 40 = x^2       Combine like terms on the left

20x - 100 = x^2             Bring the left side to the right side.

0 = x^2 - 20x + 100      You have a quadratic.

a = 1

b = - 20

c = 100

When you solve the quadratic equation, you get

x = 20

Therefore the number of sides is 17.

Answer:

49

Step-by-step explanation:

7 times 4 equals 49.

Answer:

[tex] \dfrac{1}{a^6} [/tex]

Step-by-step explanation:

[tex] a^{-6}x^0 = [/tex]

[tex] = \dfrac{1}{a^6} \times 1 [/tex]

[tex] = \dfrac{1}{a^6} [/tex]

Answer:

Step-by-step explanation:

In a quadrilateral all the angles equal to 360 degrees

ADC= 136+90+62=288.

360-288=72

A straight line is equal to 180 degrees

CDE= 180-72=108

x=108

Answer:

the value of x is 62 degrees.

Step-by-step explanation:

we know that corresponding angles are equal, so the value of x is 62 degrees as x is an corresponding angle of 62°

Answer:

4a+5b

Step-by-step explanation:

Given:

Apple=£a

Banana=£b

Quantity of Apple=4

Quantity of banana=5

Find the cost of 4 apples and 5 bananas

Total cost=PaQa+PbQb

Where,

Pa=price of Apple

Qa=quantity of Apple

Pb=price of banana

Qb=quantity of banana

Total cost=PaQa+PbQb

=4*a+5*b

=4a+5b

Answer:

The center is (-7,-8) and the radius is sqrt (2/3)

Step-by-step explanation:

( x + 7 )^ 2 + ( y + 8 ) ^2 = 4 /6

The equation of a circle can be written as

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

Rewriting

( x - -7 )^ 2 + ( y - -8 )^ 2 = (sqrt(2/3)^2

The center is (-7,-8) and the radius is sqrt (2/3)

Answer:

center:    (-7,-8)         radius: 2/3

Step-by-step explanation:

i got this from wegnerkolmp2741o. thank you wegnerkolmp2741o!!!!!

also got this correct on khan academy