Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back five generations? twelve generations?

Draw the triangle ABC.

Determine the length of side AC.

So side AC is equal to 18.9 m.

Determine the measure of angle A.

So mesure of angle A is 66.9 degree.

EXPLANATION

Given that the wheel has a radius of 12 meters and it takes 16 seconds to complete one full revolution, if we call t to the time in seconds and since the top of the wheel is 28 meters above the ground, the bottom is 4 meters above the ground.

Now, we need to consider that the equation that applies is the following:

As theta is the angle between the radius from the center of the wheel to the bottom and the rider's coordinate, we need to represent the angle as a function of the time. We have that it takes 16 second to complete one full revolution, this means that the wheel rotates 360 degrees in 16 seconds. Now, we can use the angular velocity: w= 360/16 = 22.5 degrees/s

Then, we need to represent the angular velocity in radians, as 360 degrees is 2π radians, the obtained angular velocity would be: w = 2π/16 = π/8 rad/s

Hence the appropiate equation as a function of the time would be as follows:

25 square kilometers

Explanation

the volume of a cube is given by:

Step 1

Let

volume = 125 cubic kilometers

Step 2

replace and solve for "side"

Step 3

now, we have the length of a side, to find the area, make

Area of a square is

replace to find the area

Let side = 5 km

EXPLANATION

The function that represents the exponential decay is as follows:

Where a=initial amount and b= decay coefficient

Since the initial amount is 8cm^2, the is the value of the coefficient a is 8.

Now, we need to compute the decay rate:

We can obtain this by substituting two given values, as for instance (0,8) and (1,6) and dividing them:

Simplifying:

The value of b is 3/4:

1) There will be 3/4 of the burn area each week.

2) The equation representing the area of the burn, after t weeks will be the following:

3) After 7 weeks, the area will be represented by the following expression:

Computing the power:

The two European nations took control of the regions in the Middle East that had been controlled by the Ottoman Empire are Britain and France.

The Ottoman Empire had long held the top position among Islamic nations in terms of geography, culture, and theology. Due to the division of the Ottoman Empire after the war, Western powers like Britain and France came to dominate the Middle East, and the modern Arab world and the Republic of Turkey were established.

The Turkish National Movement initiated opposition to these forces, but it did not extend to the other post-Ottoman states until the time of quick decolonization following World War II.

Learn more about Ottoman Empire on:

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Sheliqua, this is the solution:

a. 13 divided by 5

13/5 = 2 3/5

b. 9/5

9 divided by 5

c. 7 divided by 8

7/8

d. 1 2/3

5/3

5 divided by 3

Let x be the total number of books each student recieved, since one third of them is an english book we have that the expression is:

Looking at the graph

we have a horizontal line

the equation is

y=-5

The slope of a horizontal line is equal to zero

so

m=0

The y-intercept is the point (0,-5)

therefore

b=-5

The answer is

Remember that

y=mx+b

substitute

m=0

b=-5

y=(0)(x)-5

y=-5

Explanation

the volume of a hemisphere is given by:

where r is the radius

then

now, replace.

so, the answer is

I hope this helps you

We are asked to find the reference angle for a standard angle of 334°

Recall that the reference angle is the angle that is measured with respect to the x-axis.

First, we need to find out in which quadrant the given standard angle lies.

334° lie in the 4th quadrant (180° to 360°)

So, the reference angle can be found as

Therefore, the reference angle is 26°

First let's put the equation 4y + 9 = 2x in the slope-intercept form:

Where m is the slope and b is the y-intercept. So we have that:

The slope of this equation is 1/2. In order to the second line be parallel to this line, it has to have the same slope. Also, since the second line passes through the point (7, 2), we have:

So the second equation is:

Equations

We are given the equation:

4x - 2y = 11

And it's required to find the missing coordinate in the ordered pair (-3, ?).

The first coordinate is x=-3, thus we need to calculate the y-coordinate by solving the equation for y, using the value of x.

Substituting:

4(-3) - 2y = 11

Operating:

-12 - 2y = 11

Adding 12:

-2y = 23

Dividing by -2:

y = 23/(-2)

y = -23/2

The ordered pair is:

The angle indicated is a right angle, so the triangle is a right triangle.

Thus, we can apply the Pythagora's Theorem:

Where c is the hypotenuse, the angle opposite to the right angle, and a and b are the legs.

x is the hypotenuse in this case, so:

Let's use the variable x to represent the spaces between posters.

So the spaces at the left and right of the group will be 3x.

Drawing the diagram, we have:

Writing an equation to solve for x, we have:

So the space between each pair of posters is 0.75 feet.

The perimeter of a rectangle is given by:

P = 2w + 2h

Where:

w = width = 2x

h = height = x

P = 18

Replacing the data into the equation:

18 = 2(2x) + 2(x)

18 = 4x + 2x

18 = 6x

Solving for x:

x = 18/6

x= 3

Therefore:

w = 2(3) = 6m

h = 3m

---------------------------------------------------------------------------------

P = x + 2x + (x + 3)

23 = 3x + x + 3

23 = 4x + 3

Solving for x:

23 - 3 = 4x

20 = 4x

20/4 = x

5 = x

Therefore its sides are:

x = 5 ft

2x = 2(5) = 10ft

x + 3 = 5 + 3 = 8ft

Given data:

The total number of oranges is: 24

The total number of people is: 14

The expression to calculate the number of oranges a person has is,

Thus, each person gets 1 orange and 5/7 of an orange.

Given:

Find: the manimum value of the function.

Explanation:

ar x=-2,

the function will be

Answer:

49π

Step-by-step explanation:

πr^2   <---- The formula for the area of a circle.

let "a" represent area of the circle.

a = π × 7^2

Simplify by the use of the exponent.

7^2 = 49

Your answer:

49π

For a determined product you can buy 12Kg for $8.39. To determine how much 1Kg of said product costs, you can apply cross multiplication to calculate it:

If 12 Kg cost $8.39

1 Kg costs $x:

The cost is $0.70/Kg

The peak of the mountain is 14, 494 ft above sea level therefore the number can be represented as follows as an integer

The mountain is plus 14,494 ab

According to the given data we have the following equation:

6x+y=12

To rewrite the following equation in slope-intercept form we would have to make the following steps:

6x+y=12

Move 6x to the other side, by doing this it would change its sign

So,

y=-6x + 12

So, equation in slope-intercept form would be y=-6x + 12

x = 1, y = 3

The given system of equations is:

y = 4x - 1.......................(i)

y - 2x = 1..................(ii)

Substitute equation (i) into equation (ii)

4x - 1 - 2x = 1

4x - 2x = 1 + 1

2x = 2

x = 2/2

x = 1

Substitute x = 1 into equation (i)

y = 4x - 1

y = 4(1) - 1

y = 4 - 1

y = 3

The solution to the system of equations is x = 1, y = 3

__________________

Just replace in value of x in the function

f(0.1) = 100* (0.1)^2 / ((0.1)^2 + 0.17) = (1)/(0.18) = 5.56

f(0.1) = 5.56

f(0.8) = 100* (0.8)^2 / ((0.8)^2 + 0.17) = (64)/(0.81)= 79.01

f(0.8) = 79.01

_______________________

derivative of a quotient

Q(x)= f(x)/g(x)

Q'(x)= (f'(x)*g(x) - f(x)*g'(x)) / (g(x) ^2)

_____________________________

If f(x) = 100* (x^2) / (x^2 + 0.17),

f'(x)= 100 * ( 2x* (x^2 + 0.17) - 2x*x^2 ) / (x^2 + 0.17)^2

f'(x)= 100 * ( 2x^3 + 2x* 0.17 - 2x^3 ) / (x^2 + 0.17)^2

f'(x)= 100 * ( 2x* 0.17 ) / (x^2 + 0.17)^2

f'(x)= 34*x/ (x^2 + 0.17)^2

_________________________

Just replace in value of x in the function

f'(0.1)= 34*(0.1)/ (0.1^2 + 0.17)^2

f'(0.1)= 3.4/ (0.18)^2

f'(0.1)= 104.9

f'(0.8)= 34*(0.8)/ (0.8^2 + 0.17)^2

f'(0.8)= 27.2/ (0.81)^2

f'(0.8)= 41.46

The graph of the parabola given by the equation:

has a vertex when y=0 which happens iff

Therefore the graph is:

The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates

We have this number and we have to sort them from least to greatest.

We start by expressing them in decimals in order to compare them easily.

Take into account some of them are irrational, so they will be expressed approximately by a decimal (for example, pi).

Then, we have:

The least will be the negative numbers of this group, so we start with the negative value with the most absolute value: -3.27.

Then, we continue with -2.

Then, we start with the positive values: 3.07, pi, 13/4, sqrt(12) and 22/2.

Then, we can write them in order as:

the volume of a pyramid is

where A is the area of the basis and h is the height of the pyramid.

Then the volume is

Then rounding the number, the answer is B).

To transform

Make it a perfect square

since 8x/2 = 4x, then

We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1

Now we will make the bracket to the power of 2

Add 1 to both sides

The answer is C

we have the expression

step 1

Combine like terms

so

therefore

The Solution.

Assuming the radius is 1.

Therefore,

So, the correct answer is option D

We are given the following equation.

we are asked to find an equation for "t". To do that, we are going to solve for "t", first by subtracting "p" on both sides, like this:

Now we will divide both sides of the equation by "pr"

A thus we found a relationship for "t".