XIXIXI
Name:
amount paid (in dollars)
Movie Mania Tickets
ty
72
63
54
45
36
27
10 00
18
9
0
CINEMA
ADMIT ONE
12345
ADMIT ONE
nyum
Movie Ticket Sales
12345
2 4 6
8
# of tickets
72=6=12
X
10
Perfect Picture Tickets
Only $65.50 for 5 tickets!
65÷5=13
# of tickets
Date:
Fantastic Flicks Tickets
3
6
9
12
amount paid (in dollars)
38.25
76.50
114.75
153
Periods:
The Big Screen
Which movie theater is the cheapest?
Pertert Picture
Which movie theater is the most expensive?
Movie mania
What is the constant of proportionality (slope) of each option?
movie minin. = 12
Perfect Pictures (3
·Fantastic Flick5= 12.75
The Big screen= 12.90
Write an equation to represent all four options.
12345
CINEMA
ADMIT ONE
y = 12.90x
NEMA
ADMIT ONE
12345
12.75

We have the following pair of functions:

And we need to find (fog)(2). In order to do this we can start by calculating the composite function (fog)(x)=f(g(x)). Its expression is given by taking the equation of f(x) and replacing x with the expression of g(x). Then we get:

We need to find (fog)(2) so we just need to take x=2 in the equation above:

Then the answer is 88.

Notice that the angle labelled as 3y and the angle with a measure of 72° are supplementary angles. Then:

Substract 72 from both sides of the equation:

The angle labelled as x and the angle labelled as 3y are corresponding angles. Then, they have the same measure:

Since 3y=108, then:

On the equation 3y=108, divide both sides by 3 to find the value of y:

Finally, notice that the angle labelled as 3z+18 and the angle labelled as x are corresponding angles. Then, they have the same measure:

Substitute x=108 and isolate z to find its value:

Therefore, the measure of the angles labelled as 3z+18, x and 3y is 108°. The values of x, y and z are:

You have to write an equation parallel to the line: y=-4x+7 that crosses the point (3,8)

One characteristic that two parallel lines share is that they have the same slope.

The slope for the known line corresponds to the coefficient multiplying the x-term and is m=-4

The line you have to find must have the same slope.

Using the point-slope form you can determine said line. The general structure is:

Where

m is the slope

x₁, y₁ are the coordinates of a point crossed by the line.

Using (3, 8) and m=-4

Now you have to solve it and write it in slope-intercept form. First step is to solve the term in parentheses by applying the distributive propperties of multiplication:

Next pass "-8" to the other side of the equal sign:

The equation for the line parallel to y=-4+7 is y=-4x+20

In this case, we'll have to carry out several steps to find the solution.

Step 01:

7.

Data

point 1 ( -4 , -2) x1 = -4 y1 = -2

point 2 ( 3 , 3 ) x2 = 3 y2 = 3

Step 02:

Slope formula

m = (y2 - y1) / (x2 - x1)

Slope-intercept form of the line

y = mx + b

intercept (0 , 1 )

b = 1

m = 5 / 7

y = 5/7 x + 1

The answer is:

y = 5/7 x + 1

The values that are represented by the dots are close to the horizontal line, so they are a non-random pattern, because they follow the horizontal line without going to far from it

Since these points are all around the horizontal line, they also represent a linear model

So the answer for hte first box is "non-random" and the answer for the second box is "linear"

Given from the number line that the total number of segments between 0 and 1 is 12 segments.

1) Therefore, the length of each segment on the number line is

Hence, the answer is

2) There are 8 segments between 0 and K.

Therefore, point K represents

Hence, the answer is

3) The opposite of K is

Hence, the answer is

The given information is:

- The initial amount is $600

- The interest rate is 2% (compounded annually)

The given formula is:

Where B is the balance (final amount), p is the principal (starting amount), r is the interest rate as a decimal, and t is the time in years.

By replacing the known values we obtain the balance after 3 years:

The answer is $636.72

Based on the given information, we can determine the constant and the variable payment.

• He gets $2100 as based salary (never changes, constant).

• The additional $70 depends on ,N ,(variable).

This information can help us build the equation:

Therefore, if he sells 27 copies, then the total payment is:

Answer:

P( 27 ) = $3990

Answer

1, 2, 3, 4, 5

Explanation

Given the following data

a(0) = 0

a(i + 1) = a(i) + 1

Find a(0) to a(5)

Step 1: find a(i) when i = 0

a(0 + 1) = a(0) + 1

Where a(0) = 0

a(1) = 0 + 1

a(1) = 1

Find a(2) when i = 1

a(i + 1) = a(1) + 1

a(1) = 1

a(1 + 1) = 1 + 1

a(2) = 2

find a(3) when i = 2

a(2 + 1) = a(2) + 1

a(3) = 2 + 1

a(3) = 3

Find a(4) when i = 3

a(3 + 1) = a(3) + 1

a(4) = 3 + 1

a(4) = 4

Find a(5) when i= 4

a(4+1) = a(4) + 1

a(5) = 4 + 1

a(5) = 5

Therefore,

a(1) = 1

a(2) = 2

a(3) = 4

a(4) = 4

a(5) = 5

The answer is 1, 2, 3, 4, 5

Since Ahmed will start with $7.50 per hour

Then the sequence must start with 7.50

Then the answer should be A or B or C

Since his hourly rate will increase by $0.25 per hour

Then the number in the sequence should be increased

Then the answer is B or C because A is decreasing

We have to add 0.25 to the first rate to get the second rate

Then the correct answer is

$7.50, $7.75, $8.00, $8.25, $8.50

The answer is B

The area is given as

We can either divide the area by the side given and get the other side

OR

We can simply factorize the area and hence determine the two factors that were multiplied together. Note that one factor has already been given (that is x-3).

To factorize the polynomial;

This means the other side is also (x - 3)

a) 24.3 is a rational number

b)

c) 7 is a rational number

d)

Answer: Letter B

hello

to solve this question, we have to understand that a soccer field is rectangular in shape and we can find this length from factoring the area

formula of area of a rectangle

we can proceed to solve this by dividing the polynomial or simply checking it from the options

from the options given,

we have option A

3x + 10

let's multiply both the L and W to see if it gives us the answer

option A is incorrect

let's test for option B

L= 6x + 10

option B is correct

let's test for option C

L= 6x + 1

option C is also incorrect and so it'll be for option D

from the calculations above, only option B corresponds with the value of length for the soccer field

Answer: The result of 392,196 divided by 87 is 4,508

The rate of emptying the lake is -1/8.

The rate of filling the lake is 1/15

Let t be the time in weeks to empty the lake,

Now, add the given rate to get the total rate of emptying of -1/t.

Thus,

Therefore, it will take 17 weeks and 1 day to empty the lake.

Total number of kittens = 6

Gray kittens= 1 female+2 males = 3

Black kittens= 2 female+ 1 male =3

Probability of picking one black kitten = black kittens/ total kittens = 3/6 =1/2

PROBLEM

Total

16 cheddar cheese

8 mozzarella cheese

Solution

He uses

For example, we can look at the variations of temperature by the time of the day.

We can write it in a two column table, where we can write the hour in one column and the temperature in the other column.

This will show us a relationship between them that is oscillating.

We can graph this and have something like:

Then, we can adjust a function to that, like a trigonometrical function that can model this relation between temperature and hour of the day. There you wil have an expression for this pattern.

Answer:

C. The initial amount in the account was $2,500.

Explanation:

The function that represents the amount, in dollars, in a savings account after x years is given as:

When x=0 (Initially)

Therefore, the initial amount in the account was $2,500.

The slope formula is givenb by:

To get the slope from the graph, we will pick out two points lying on the line:

Point 1: (x, y) = (-6, 10)

Point 2: (x, y) = (0, -8)

We will then proceed to use these points to calculate the slope, we have:

The slope (m) = -3

The first five terms are:

-20, -10, -5, -2.5, and -1.25

Given that:

For n = 2

For n = 3

For n = 4

For n = 5

Therefore, the first five terms are:

-20, -10, -5, -2.5, and -1.25

Given:

It is required to create a table that represents a proportional relationship between two quantities.

Let the first table: represents the relation between the money saved every month and the number of months

Let the number of months = x, And the total saving = y

Assume we save $2 per month

so, we will have the following table:

Given:

The total length of carriers A and B, T=4198 feet.

The difference in lengths of the carriers is, D=10 feet.

The length of football field, L=100 yards.

Let a be the length of carrier A and b be the length of carrier B. It is given that carrier A is longer than carrier B.

Hence, the expression for the difference in lengths of the carriers can be written as,

The total length of carriers A and B can be written as,

Add equations (1) and (2) to find the value of a.

We know, 1 yard=3 feet.

So, 1 feet=(1/3) yard

The length of carrier A in yards is,

We know, the length of a football field is l=100 yards

Now, the ratio between a and l can be found as

Hence, we can write

Since l is the length of a football field, the length of carrier A is about 7.0 football fields.

x ----> is the smaller number

x+6 ----> is the greater number

the equation is

Using compound interest formula:

Where:

A = Amount

P = Principal = 8200

r = Interest rate = 6% = 0.06

n = Number of times interest is compounded per year = 2

t = time = 5

so:

Therefore, the interest is the amount minus the amount invested:

Answer:

$2820.11

We're going to find the volume of the cylinder using the following equation:

Since the radius measures 5 ft, the height measures 12 ft and the problem tells us that we should take pi as 3, we could replace:

Therefore, the volume is approximately 900ft3.

SOLUTION:

We are to find the measure of an interior angle of a regular decagon.

A decagon is a plane figure with ten straight sides and angles.

To find the sum of interior angles in a decagon;

(n - 2) x 180 (where n = 10)

(10 - 2) x 180

= 8 x 180

= 1440 degrees

The measure of an interior angle of a regular decagon is;

1440 / 10

144 degrees

In b we need to find:

It's important to recal that the secant is equal to:

Another important property that will be useful is:

Where m is any integer. Let's see if we can write 18*pi using this. We can take x=0 so we have:

If we divide both sides by 2*pi:

Since m is an integer then we can assure that:

Then the secant is given by:

So the answer to b is 1.

In c we need to find:

Here we can use the following properties in order to write those angles as angles of the first quadrant:

So we have:

If we convert these two angles from radians to degrees by multiplying 360° and dividing by 2*pi we have:

And remeber that:

So we get:

Then we can use a table of values:

Then:

So the answer to c is (√3)/2.

In d we need to find:

In order to do this using the table we can use the following:

So from the first one we have:

We convert pi/12 into degrees:

So we need to find the sine and cosine of 15°. We use the second equation:

Then we use the third:

And from the fourth equation we get:

We can use this in the previous equation:

So we found the cosine. For the sine we use the expression with the sine and cosine multiplying:

Then the tangent is:

Then the answer to d is:

Answer:

Triangles ABC and CDA share the side AC, therefore they have three congruent sides. Since AB is congruent to CD and BC is congruent to DA then by the SSS criteria we get that triangles ABC and CDA are congruent.

To determine the age of jiri:

Let P represent Pamela age

Let J represent Jiri age

p + j = 29 (their ages added together is 29)

p = j - 15 (Pam is 15 years younger (less) than Jiri)

We have a value for Pam, so plug it in:

j -15 + j = 29

2j - 15 = 29

Add 15 to both sides:

2j = 44

Divide by 2:

j = 22

Now find Pamela's age:

p = 22 - 15

p = 7

check:

7 + 22 = 29

29 = 29

Therefore the age of Jiri is 22 years