a student reflects four point across the y ax is and recorded his work

The next two terms of the given given sequence are 9, 1 if the first three terms of arithmetic sequence are 33, 25, 17.

An arithmetic sequence has a constant difference (d) and is defined by

a(n) = a(1) + (n-1)d          ----------- (1)

Here a(1) = 33, a(2) = 25, a(3) = 17

d = a(2) - a(1)

d = 25 - 33 = -8

Substitute the values in (1)

a(n) = 33 + (n-1)(-8)

a(n) = 33 - 8n + 8

a(n) = -8n + 41              ------------- (2)

We have to find a(4) and a(5)

Substitute n = 4 in (2), we get

a(4) = -8(4) + 41 = -32 + 41 = 9

Substitute n = 5 in (2), we get

a(5) = -8(5) + 41 = -40 + 41 = 1

Hence the next two terms are 9, 1.

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Answer: yes

Step-by-step explanation: 64 is a factor of 4 because you can multiply it by 16 to get 64. Remember if you divide and get a whole number it is a factor .

Taking into account the definition of a system of linear equations, the number of adult tickets sold was 50.

A system of linear equations is a set of linear equations in which two or more variables are related.

In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in the  equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

3c + 5a= 340

c + a= 80

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "c" from the second equation:

c= 80- a

Replacing this expression in the first equation:

3×(80- a) + 5a= 340

Solving:

3×80- 3a + 5a= 340

3×80- 3a + 5a= 340

240- 3a + 5a= 340

- 3a + 5a= 340- 240

2a= 100

a=100÷ 2

a= 50

Finally, 50 adult tickets were sold.

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Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34

+7x

4x - 6 = 34

+6

4x = 40

/4

x = 10

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34  Add 7x to both sides

4x - 6 = 34  Add 6 to both sides

4x = 40  Divide both sides by 4

x = 10

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

Now utilize the scale conversion ratio to determine the actual distance:

Therefore, the distance between Hawthorne and Doylestown is:

Answer:

0, 150, 100, 50 |    T=200-50x

Step-by-step explanation:

     So you start with 200 miles to go and you are going 50 miles per hour. In the first hour, 50 miles would have been completed meaning that you subtract 50 miles from the remaining distance. Same with the other hours.

     To put that in an equation, You would start with 200 and for every hour(x)you would subtract 50.

Domain and Range of a Function

The domain of a function f is the set of values of the input (or independent) variable, often called x. The range is the set of values of the output (or dependent) variable, often called y, or f(x).

The function shown in the image has a shape that opens up to infinity (marked with the two arrows). This means that x can have any real value from minus infinity to plus infinity, that is, all real numbers.

Now for the range, we can see not every value of y belongs to the function. The graph decreases down to the vertex of the parabola that is located at (3,-12). This means that from y=-12 and up, the function exists, but not below this value.

Summarizing:

Domain: All real numbers

Range: y ≥ -12

Answer:

5.5 inches

Step-by-step explanation: if you divide it, u will get 5.5 inches

The simplified form of the expression ( 9 × 10⁴ ) × ( 6 × 10⁻⁷ ) in scientific notation form is 5.4 × 10⁻²

The scientific notation form is simply a method of presenting larger or  smaller numbers in a more simple way.

Given the data in the question;

( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )

First, multiply 9 and 6

( 9 × 10⁴ ) × ( 6 × 10⁻⁷ )

9 × 6 ( 10⁴ × 10⁻⁷ )

54( 10⁴ × 10⁻⁷ )

Next, multiply 10⁴ × 10⁻⁷  by adding the exponents.

Using power rule mᵃ × mᵇ = mᵃ ⁺ ᵇ

54( 10⁴ × 10⁻⁷ )

54( 10⁴ ⁺ ⁻⁷ )

54( 10⁴ ⁻⁷ )

Subtract 7 from 4

54 × 10⁻³

Move the decimal point in 54 to the left by place and increase the power of 10⁻³ by 1

5.4 × 10⁻³ ⁺ ¹

5.4 × 10⁻²

Therefore, the simplified form is 5.4 × 10⁻².

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Solution

- The equation of a hyperbola is given s:

- Thus, we can find that:

Final Answer

The equation of the parabola is:

A) The ball in the ground is represented by h(t)=0, that is, the height is equal to 0, the reference level.

Then, we can find for which values of t we have h(t).

We equal h(t) to 0 and calculate t as:

The ball is in the ground at time t=0 (an instant before it is kicked) and then again at time t=4, that is the value we are looking for: the ball landed again in the ground 4 seconds after kicked.

B) The maximum height can be find in two ways:

- By finding the t-value of the vertex, that in this case will be correspond to the maximum height as this is a concave down parabola with only one extreme point.

- Deriving the function and equaling to 0 and finding t.

If we apply the first method, we have:

As the vertex is at time t=2 seconds, the maximum height happens at t=2.

Answer: A) t = 4 seconds B) t = 2 seconds

NOTE for Part B:

If we derive the expression, we get:

Answer:

y = 5

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

AB = CD , that is

7y = 3y + 20  ( subtract 3y from both sides )

4y = 20 ( divide both sides by 4 )

y = 5

Answer: When you graph part a, it has a negative slope.

Step-by-step explanation:

The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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Answer:

Step-by-step explanation:-32x³z³+48x∧4z

The constant of proportionality between the amount of tomatoes he orders (in pounds), and their cost (in dollars) is: 4 dollars per pound

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

pounds , dollars

Calculating the proportion of the amount of tomatoes he orders and their cost we get:

Proportion dollars per pound = Dollars / pound

Proportion dollars per pound = $88/ 22 pounds = 4 $/pound

Proportion dollars per pound = $92/ 23 pounds = 4 $/pound

Proportion dollars per pound = $96/ 24 pounds = 4 $/pound

Proportion dollars per pound = $100/ 25pounds = 4 $/pound

As we could get the constant of proportionality is 4 $/pound

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The Central Limit Theorem states that over a large number of samples, the sampling average of the sample means would be closer to the population mean.

The Central Limit Theorem states that for a random variable X, with mean given by [tex]\mu[/tex] and standard deviation given by [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

This means that over a large number of trials, i.e., of samples from the population, the mean of the sample means will be close to the population mean, with a small standard error, as the standard error is inversely proportional to the square root of the sample size.

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The constant of proportionality for the graph will be P=75. The correct option is C.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

The proportionality of the constant determines the linear relation between two variables. as one increases the another also increases with the same factor.

To calculate the constant of proportionality for the given graph finds the slope of the graph with the points.

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 600 - 450 ) / ( 8 - 6 )

Slope = ( 150 / 2

Slope= 75

Therefore, the constant of proportionality for the graph will be P=75. The correct option is C.

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If two angles be 10x + 5 and 15x - 30 then the value of x = 7.

Let the two angles be 10x + 5 and 15x - 30.

simplifying the above two equations, we get

10x + 5 = 15x - 30

Subtract 5 from both sides

10x + 5 - 5 = 15x - 30 - 5

Simplifying the above equations,

10x = 15x - 35

Subtract 15x from both sides of the equation

10x - 15x = 15x - 35 - 15x

Simplifying the above equation, we get

-5x = -35

Divide both sides by -5

[tex]$\frac{-5 x}{-5}=\frac{-35}{-5}[/tex]

x = 7

Therefore, the value of x = 7.

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To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].

Leave the variable [tex]x[/tex] alone.

Make lettering according to the rule above.

Verify each statement

A) If Cole tutors 5 hours,he will be paid $40------>



B) If Cole tutors 3 hours he will be paid $24



C) If Cole tutors 7 hours he will be paid $64



D) If Cole tutors 4 hours he will be paid $32

Step 1:

Draw the table for the input x and output y.

Step 2:

From the table, we can see that the function is an exponential function.

Step 2:

Find the inverse of the function.

Step 3:

The two graphs below, show the graph of the inverse for both negative and positive square roots of x.

Final answer

The blue graph is the inverse of the red graph.

Answer:

Step-by-step explanation:

Let L be the length and W the width

Perimeter of a rectangle is P = 2L + 2W

We are told that L = W + 14 (m)        [the length is 14 meters more than the width]

Area of a rectangle is A = L*W

We learn that A = 96 m^2

L*W = 96

Since L = W + 14, we can substitute:

L*W = 96

(W + 14)*W = 96 m^2

W^2 + 14W = 96

W^2 + 14W - 96  = 0

The solution to W in the above equation is 5.04 m

This means L = 5.04 m + 14 m

L = 19.04 meters

Perimeter = 2W + 2L

Perimeter = 2(5.04) + 2(19.04) = 96 m^2

The statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

In the given statements

There are no outliers in this distribution.

The shape of the boxplot is fairly symmetric.

The range of the distribution is around 60 cm.

The center of the distribution is around 180 cm.

The statement "The range of the distribution is around 60 cm" is true.

The range is the spread of your data from the lowest to the highest value in the distribution.

In the given graph

Range=200-140

=60

So it is true.

The center of the distribution is around 180 cm is also true.

Hence the statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

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Average rate of change is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate of change, in simplest form, is -1/6.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

The formula for calculating the gradient of a function exists expressed as:

[tex]$m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points from the table (6, 53) and (24, 50).

Substitute the coordinate into the expression:

[tex]$m=\frac{50-53}{24-6} \\[/tex]

[tex]$&m=\frac{-1}{6} \\[/tex]

Therefore, the average rate of change, in simplest form is -1/6.

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The inequality according to the the cost of pack of paper can be written as x ≤ 14.28 and Mr. Valentino can purchase a maximum of 14 packs of paper.

What is inequality?

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. The two most common notations for representing various forms of inequalities are as follows:

The symbol a < b indicates that a is smaller than b.

The symbol a > b indicates that a is bigger than b.

Let's assume he can buy x pack of paper.

Cost of x pack of paper will be equal to the x times cost of 1 pack of paper

i.e. Total cost =  1.75x

Now, Mr. Valentino has $25

Therefore,

1.75x ≤  25

Inequality is ⇒  x ≤ 14.28

It tells us that Mr. Valentino can purchase only 14 packs of paper.

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Answer:

ewan ko po pero yan yung alam ko4.3%

I hope its help

The greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.

As given in the question,

Silvia is going to plant 20 tomato plants and 30 bean plants.

Total tomato plants = 20

Total bean plants = 30

If Silvia would like to plant, the plants in rows where each row has the same number of tomato plants and each row has the same number of bean plants.

Then, the greatest number of rows Silvia can plant is equal to greatest common factor of 20 and 30.

20 = 2×2×5

30 = 2×3×5

Greatest common factor of 20 and 30 = 2×5 = 10

Therefore, the greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.

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The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?

What is simple interest?

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Solution for the above problem is:

The formula to calculate simple interest is:

[tex]S.I. = P \times I \times T[/tex]

Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time

Given in the question:

P = $2500

I = 6% = 0.06 (in decimals)

T = 2

Putting the value in the question:

S.I. = 2500(0.06)(2)

S.I. = 300

Therefore, the simple interest is $300.

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