Please help me solve question 6 on my algebra homework

Solution:

Given:

A regular pentagon rotated counterclockwise about its center.

To get the angle by which it rotated, we draw lines from each of the vertexes to the center to divide the pentagon into 5 equal triangles as shown;

The angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;

To get angle EOC, we use the property of the sum of angles at a point.

The sum of angles at a point is 360 degrees.

Since it is a regular polygon, each of these angles is equal.

Hence,

Thus, the measure of angle EOC is;

Therefore, the angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;

6The mean number of children each team member will bring

Here, we want to get the mean number of students that each team member willl bring

From the histogram, we can deduce the following;

a) 4 team members will bring no (0) children

b) 3 team members will bring 1 children each

c) 5 team members will bring 2 children each

d) 2 team members will bring 3 children each

e) 1 team member will bring 5 children

So the totla number of children at the party will be;

4(0) + 3(1) + 5(2) + 2(3) + 1(5)

= 0 + 3 + 10 + 6 + 5 = 24 children

The number of team members is 4 + 3 + 5+2 + 1 = 15

So, the mean number each will bring is; the number of children attending the party divided by the number of team members

ANSWER:

911.6 ft

EXPLANATION:

Given:

To find:

The distance between the two ships

Let's go ahead and draw a sketch as seen below;

Let's go ahead and solve for the value of AC by taking the tangent of angle 12.5 degrees as seen below;

Let's now solve for the value of AD by taking the tangent of angle 8 degrees as seen below;

Therefore the distance between the two ships will be;

So the two ships are 911.6 ft

Explanation:

The expression: -5+(-7)

Answer:

Step-by-step explanation:

1. Since we know that an addition sign and a negative sign will make a negative sign, we simply have to do -5-7.

2. The answer is -12.

The are of the octsagon is given by:

where a is the lenght of its side.

Since the second octagon has sile lengths equal to 18.03, its area is:

Therefore the area is 1563.6 squared centimeters

The initial equation is:

so we can move all term with x to the left and the constants to the right so:

Now we divide by 8 bout side of the equation so:

LK = 2.91m

JK = 7.99m

hypotenuse = 8.5m

angle = 20°

LK = side opposite the angle 20°

Since we know the hypotenuse and we need to find the opposite, we would apply sine ratio

sine ratio = opposite/hypotenuse

sin 20° = LK/8.5

LK = 8.5(sin 20°)

LK = 8.5(0.3420)

LK = 2.907

To the nearest hundredth, LK = 2.91m

JK = base = adjacent

We would apply cosine ratio

cos 20° = adjacent/hypotenuse

cos 20° = JK/8.5

JK = 8.5(cos20°)

JK = 8.5(0.9397)

JK = 7.98745

To the nearest hundredth, JK = 7.99m

Total: $65.45

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

Tax rate: 8%

The tax is: $5.236

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

Tip: 20%

Tip: $13.09

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

Total price(Tp)= Total + The tax +Tip

The total price is: $83.776

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

There were four people so the total price is divided into those 4:

Each person should pay: $20.944

ANSWER is hands lens.

This is the best tool to see the animal up close.

2 apples 511 gr

5 apples 1200 gr

8 apples 2016 gr

weight / apples

511 / 2 = x / 6

x = weight of 6 apples

Cross multiply:

6 * 511 = 2 x

3066 = 2x

Divide both sides by 2

3066 / 2 = 2x/ 2

1533 = x

x= 1533

Same with the other rows:

1200/5 = x/6

6*1200 = 5x

7200 = 5x

7200/5= x

x= 1440

2016/8 = x/ 6

6*2016 = 8x

12,096 = 8x

12096/8= x

x = 1512

Average of three results: ( 1533 + 1440 + 1512 )/ 3 = 1495

6 apples would weigh about 1495 grams

EXPLANATION

The coordinate son the plane when x=-3 are y=9 ---> A= (-3,9)

The points on the parabola when y= 16 are x=4 ---> (x_1,y_1) = (4,16) and (x_2,y_2) = (-4,16)

The following information below can be obtained from the image;

Blue Marbles: 6

Red Marbles: 5

Yellow Marbles: 3

Total marbles = 14

The probability of an event, E, is given as:

Hence, the number that belongs in the green box is 3

Answer:15,970

Step-by-step explanation:

ANSWER

0.1069

EXPLANATION

We have two possible outcomes for each experiment: the seed grows or the seed does not grow. So, this follows a binomial distribution, where, in this case, the probability of success is the probability that a seed does not grow - note that we want to find what is the probability that a number of seeds do not grow.

We know that the probability that a seed grows is 85%, so there is a 15% chance the seed does not grow. This experiment is repeated 9 times (9 seeds) and we want to find what is the probability that the number of successes is 3 - remember that "success" is that the seed doesn't grow.

To find this, we have to use the binomial probability formula,

For this problem:

• n = 9

• x = 3

• p = 0.15

• q = 0.85

So we have,

Hence, the probability that exactly 3 seeds don't grow is 0.1069, rounded to four decimal places.

Given that the birth alternates between a boy and a girl, there are 2 options which are as follows.

Let

G = Girls

B = boys

Therefore,

The probability that the youngest will be a boy in this scenario will be

The cost function is,

The cost of 15 ounce container is,

Thus, option (A) is the correct solution.

Given: A high school teacher grades a math test. She wants to see the numerical grade of each student.

Required: To identify which item the teacher should use so she can quickly see

how many students got each score.

Explanation: A line plot is a plot that shows the frequency of data along a number line as shown in the figure below-

The graph of y = - 1/3x + 3 is shown in the photo below

The graph of 1/2x - 5 is shown in the photo below

The graph of y = - 5/x + 10 is shown in the attached photo below

(a)

Given data:

The given expression is x^2 -.......x +16.

The first expression can be written as,

Thus, the unknown value is 8.

the initial function is:

now we replace the values in x that gives the table so:

for -2:

for 0:

for 2:

for 4:

Using the triangle sum theorem, we can conclude:

Now, we can use the law of sines in order to find AB:

To start, we need write the polynomials:

Now we gonna find the difference between first polynomial and second, like this:

tip: Special care with operate signs.

That is the final solution, you can solve that polynomial if you need.

The inverse of cubing a number is applying cubic root

Now, let's go through the examples:

When you want to find the square root of a number x you have to ask yourself:

Which number, when multiplied by itself, will give me x ?

For example,

Because

This way,

Now for the cubic root:

When you want to find the cubic root of a number y you have to ask yourself:

Which number, when multiplied by itself two times, will give me y ?

For instance,

Because

Therefore,

Answer:

Explanation:

Using the graph of both equations, we want to get the correct option

We start by making a plot of the two on same axes

We have the plot of the functions as follows:

Now, let us take a look at the options:

a) This is wrong. The functions have two intersection points

b) This is incorrect. They have equal y-intercepts at y = 2

c) This is correct. The quadratic function have a greater maximum

Part A)

2.7 --- 60%

Therefore in order to know what is the 100% we will do the next operation

2.7 is 60% of 4.5

Part B)

4.2 --- 10%

In order to know the 100% we will do the next operation

4.2 is 10% of 42

Part C)

58 --- 100%

214.6 --- ?

214.6 is 370% of 58

The slope is define as the rate of y coordinate with respect to the x coordinate.

In the line D which is parallel to x axis has the constant y coordinate i.e

y = -3

So, for the numerator of the slop for line D is ( -3) - ( -3) = 0

Thus the slope will be express as :

Thus the slope of line is 0

Now, for the line A :

The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.

i.e. x = -5

So, substitute the value in the expression for the slope :

Slope of line A is not define

In the line B and C, the coordinates of x and y aixs are changes countinously

thus thier slopes will be well define.

Answer : Slope of line A is not define.

Given:

Here a graph of cos function is given in the question.

Required:

We need to find the blank boxes.

Explanation:

First of all start with amplitude of graph

so here the height of graph is 1 so amplitude is 1

now to find the last box we need middle line of graph which is 0

now to find the coefficient x in terms of pi

for this the period of graph is 2

here the period of cosx is 2*pi and here also period is 2 so in the box of coefficient we put pi

now out final equation is

Final answer:

To answer this question, we need to find, first of all, the corresponding probability for the events. Then, we have:

1. The probability of an even number is:

We have that in a single 6-sided die, we have that the only even numbers are 2, 4, and 6. If we roll the die one time, then the probability of this event is:

2. The probability of resulting 1 or 3 is - if the die is rolled one time:

3. The probability of resulting in a 5 is - if the die is rolled one time:

Then, if we add all the corresponding probabilities we have:

To find the expected value of the game, we have to find the product of the probability by the corresponding amount of money of the event as follows:

Or

If we round the answer in terms of dollars rounded to the nearest cent (hundredth), we have that the expected value is:

In other words, if we play the game, we will expect to lose 83 cents of a dollar (per game) or 0.83 dollars.

In summary, we have that the expected value of the game is -$0.83.

Before we calculate the perpendicular line, let's rewrite our line equation in slope-intercept form. The slope-intercept form is

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

Rewritting our equation, we have

This means the slope of our line is equal to - 3.

Two perpendicular lines are related by their slope. Let's say two lines are perpendicular, this means the slope of one of the lines is equal to minus the inverse the slope of the other. If we call the slope of one of those lines as m_1, the slope of the perpendicular line m_2 is given by

Using this relation, we can find the slope of a perpendicular line. Since the slope of our line is equal to - 3, then, the slope of the perpendicular line is

In slope-intercept form, our perpendicular line has the following form

To find our y-intercept, we can use our given point that belongs to this line.

The point is (-3, 1), evaluating this point in our equation, we have

Then, our line is