#13, can you please try to give a detailed run-through on how to identify the variables, and do the problem step by step, I have trouble learning math.

The scenario formed a right triangle with an adjacent side of 24.2 ft. and included an angle of 37°.

First, let's recall the three main trigonometric functions.

In the scenario, the height of the flagpole appears to be the Opposite Side of the right triangle formed.

Since the function that we will be equating involves the Opposite Side and Adjacent Side of a right triangle, we will be applying the Tangent Function to find the height of the flagpole.

We get,

Therefore, the height of the flagpole is 18.2 ft.

Express f (x) = x^2 -2x in the form f(x) = (x - h ) ^2 - k

x^2 - 2x = +2

h = -b/2a and k = h^2

a = 1 , b= -2

h= -(-2)/ 2(1) = 2/2 = 1

k = h^2 = 1^2 = 1

So, x^2 - 2x = (x-1) ^2 - 1

To rewrite the complete equation

f(x) = (x - 1)^2 - 1 - 2

f(x) = (x - 1)^2 - 3,

The minimum value is is -3

Option D is the answer

grow at 200% each year

so, population becomes twice in each year, then after 20 years:

answer: population is 5,242,880 after 20 years

The sets of even and odd counting numbers are both infinite in size (number of elements). However, we can map each even counting number to each odd counting number as follows:

So we have the mapping rule:

Then, we can say that there are as many even counting numbers as there are counting numbers, or equivalently, that both sets have the same cardinality.

Answer: True

Statement Problem: Find the value of x in the diagram below, given the perimeter of a rectangle as 20centimeters.

Solution:

The perimeter of a rectangle is;

Where the length and width of the given rectangle is;

Thus, the value of x is;

Then, we subtract 4 from both sides of the equation, we have;

The value of x is 3

We know that:

MN = 7.3

DC = 8.7

M and N are midpoints of AD and BC respectively.

Since DC - MN = 8.7 - 7.3 = 1.4 and M and N are midpoints, we must have:

AB = 7.3 - 1.4 = 5.9

The median is the centermost data in a set of values.

Since these graphs are for the year 2013, meaning, these graphs contained 365 days of recorded temperature.

For 365 days, the centermost data would be the 183rd day.

Let's take a look at each graph what is the temperature on the 183rd day when data is arranged from lowest to the highest temperature.

As we can see above, the first two bins of the histogram only cover 180 days. Since we are looking for the 183rd day, we moved to the third bin. Hence, the median temperature for City A is between 65 to 75 ℉.

For City B,

The 183rd day in City B is found on the interval 55-75. Hence, the median temperature for City B is between 55-75℉.

Lastly, for City C:

As we can see in the graph above, the 183rd day is approximately closed to the third bin. Hence, for the 183rd day, we can say that the temperature is between 65 to 75℉. The median temperature for City C is between 65 to 75℉.

To perform a product of fractions, we multiply the numerator with denominator and denominator with denominator:

And solve:

And simplify:

The answer is option B. 4/45

Given the following rational exponent:

(x²y³z)^1/5

Putting it into a radical expression will be:

We are asked to convert 11.77 hours into hours and minutes. The first step is to divide the whole number from its decimal part, that is:

Now we convert the decimal hours into minutes. To do that we use the conversion factor 1h = 60 minutes. We get:

Therefore, 11.77 hours is approximately 11 hours and 46 minutes.

You have the following points:

J(2,-1), K(4,-5), L(3,1)

To reflect the previous points around the line x = -1, consider the horizontal distance of each point to the given line x=-1. The reflected point is obtained by using the same distance to the line but in the other side.

You proceed as follow:

J(2,-1)

the distance of the previous point to the line x=-1 is 2-(-1) = 3. You subtract this value to x = -1. Thus, the x-coordinate of the new point is:

-1-3 = -4

and the new point is:

J(2,-1) => J'(-4,-1)

For K(4,-5) you have:

distance to the line x=-1 is 4-(-1) = 5. Subtract this value to the line.

-1-5 = -6

and the new point is:

K(4,-5) => K'(-6,-5)

For L(3,1):

distance to the line x=-1 is 3-(-1) = 4.

-1-4 = -5

and the new point is:

L(3,1) => L'(-5,1)

A plot of the original and reflected points is given below:

where the figure with black lines is the original figure and the figure with blue lines is the reflected one.

If DE = 6x - 7 and AE = 4x + 9, find DB.

DE and AE are line segments. We need to equal DE = AE

Now, DB = DE + EB

x = 8

DB is 82

We know that the point-slope forumal is given by:

where the terms: m, y₁ and x₁ are numbers.

Given that the line passes through a given points we have that:

m is the slope of the line

y₁ is the y value of that given point

x₁ is the x value of that given point

In this case we have that

1. It has a slope of 2, then m = 2

2. The line intercepts the point (-2, 1). Since (-2, 1) = (x₁, y₁) then

x₁ = -2 and y₁ = 1

We have that

m = 2

x₁ = -2

y₁ = 1

Let's replace those values in the first formula:

7 more than t

The algebraic expression is:

Answer: t + 7

Data

Point (4, 4)

Equation

y = -6x + 5

Procedure

As the straight line is parallel we use the same slope of the original straight line.

m = -6

Now we will calculate y-intercept

The equation would be:

Now in the standard form: 6x+y=28

The area of the given parallelogram is:

A = b·h

b: base = 13 1/5 = (65 + 1)/5 = 66/5 = 13.2 yd

h: height = 27 1/2 = 13.5 yd

A = (13.2 yd)(13.5 yd) = 178.2 yd²

Answer:

To find the equation of the line passes through (-5,4) and perpendicular to the line y=3/4 x +4

The slope of the line y=3x/4 +4 is 3/4

Let m be the slope of the required equation of the line,

Since these two lines are perpendicular to each other.

we know that,

Product of the slopes of the perpendicular lines is -1

That is,

Slope of the required line is -4/3

Passes through the point (-5,4)

The equation of the line passes through the point (x1,y1) and m as its slope is

Substitute x1=-5, y1=4 and m=-4/3

we get,

The required slope-intercept form of the equation of the line is y=-4/3 x-8/3.

Slope intercept form

y= mx + b

Where:

m= slope

b= y-intercept

So, first, we have to solve for y:

-6x +2y = 10

2y = 6x + 10

y = (6x + 10) /2

y = 3x + 5

Slope = 3

y-intercept = 5

From the question, we can deduce the following:

• slope, m = -2

• The line goes through the points: (7, -1)

Let's find the equation of the line in slope-intercept form.

Apply the slope-intercept formula of a line:

y = mx + b

Where m is the slope and b is the y-intercept.

Here, the slope, m is = -2

We also have the point:

(x, y) ==> (7, -1)

Substitue -2 form, 7 for x, and -1 for y to find b.

y = mx + b

-1 = -2(7) + b

-1 = -14 + b

Add 14 to both sides:

-1 + 14 = -1 + 14 + b

13 = b

The y-intercept is 13.

Therefore, the equation of the line in slope-intercept form is:

y = -2x + 13

ANSWER:

y = -2x + 13

Answer:

750000

Step-by-step explanation:

You have to identify which dot in the graph corresponds to p(x)=-4

p(x)=-4 → this expression indicates that the value of the "output" is -4, in the graph, it will correspond to the dot that has y-coordinate= -4

The dots in the graph have the following coordinates:

The coordinates are always given in the following order (x,y), the first coordinate corresponds to the value of x (input) and the second coordinate corresponds to the value of y (output)

From the dots, the only one that has the y-coordinate -4 is the one located in the fourth quadrant with coordinates (2,-4)

to find the line parallel to th egiven line:

the line parallel to the given equation is

The graph is,

Answer:

543/9 meters below the surface.

Explanation:

First, we need to transform the mixed numbers into fractions, so 80 5/9 meter and 20 2/9 meters are equivalent to:

Now, to calculate the location where she stops for a break, we need to take 182/9 and subtract it from 725/9. So:

Therefore, Makayla stops for a break at 543/9 meters below the surface.

We need to find f(5) and g(-3)

First, we will solve f(5), for this, we have the following function:

Second, we will solve g(-3), for this, we have the following function:

In conclusion, f(5) = -16 and g(-3) = 39

Given that the point (-2, 1) is translated 3 units down and 2 units to left. The coordinate of the new point would follow the translation rule

Therefore, the coordinates of the new point following the translation rule are:

The correct answer is (-4,-2)

Given:

To Determine: The probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth

Solution

Using normal distribution formula below

Substitute the given into the formula

Hence, the probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth is 0.014

Okay, here we have this:

Considering the provided function, we are going to graph it, so we obtain the following:

First, we are going to start with the graph of the basic function, so the graph so far is:

Now, we are going to add 1 inside the square, which is reflected in a shift of the graph one unit to the left, so we have:

We continue, multiplying the entire function by -2, which results in a compression of the graph, and in a reflection on the x-axis due to the change of sign, now we have:

And finally we add two units to the whole function, therefore it means that the graph will move up two units, leaving the following graph:

Finally we obtain that the correct answer is the first answer choice.

ANSWER

EXPLANATION

We want to find the first term of the sequence.

The general equation for the nth term a geometric sequence is written as:

where a = first term; r = common ratio

Let us use this to write the equations for the third term and the fifth term.

For the third term, n = 3:

For the fifth term, n = 5:

Let us make a the subject of both formula:

and:

Now, equate both equations above and solve for r:

Now that we have the common ratio, we can solve for a using the first equation for a:

That is the first term.

Question:

Solution:

Consider the following equation:

this is equivalent to:

that is:

Multiplying both sides by (x-1), we obtain:

this is equivalent to:

solving for x, we obtain that the correct solutions are:

and

The equation of a circle with radius r and center at (h,k) is given by:

(x + h)² + (y + k)² = r²

If r = 8 and (h,k) = (4,-9), we have:

(x-4)² + (y + 9)² = 8²