1. What are the horizontal shift and vertical shift for the function below? Use complete sentences and explain your reasoning.

Answer: The values of x and y are x = 16 and y = 4

Step-by-step explanation:

We can use the information given to set up two equations, as follows:

p = x + 7y = 29 (the cost of making 7 articles)

p = x + 5y = 21 (the cost of making 5 articles)

We can then solve for x and y using either substitution or elimination method.

Substitution method:

Solving the first equation for x:

x = 29 - 7y

Then substitute this value of x into the second equation:

29 - 7y = 21 + 5y

Solving for y:

y = 4

Now we can substitute this value of y back into the first equation:

x = 29 - 7(4) = 5

So the values of x and y are x = 5 and y = 4

elimination method:

Subtracting the second equation from the first:

x = 8 + 2y

Now we can substitute this equation into the first equation:

29 = 8 + 2y + 7y

Solving for y:

y = 4

Now substitute this value of y back into the first equation:

x = 8 + 2(4) = 16

So the values of x and y are x = 16 and y = 4.

Note that both methods give the same solution, but the values of x are different because the two equations are not independent and therefore not the same.

An equation for how much Ann's gym charges for x visits in a one month is y = 20x + 5.

An equation for how much Blake's gym charges for x visits in a one month is y = 20x + 5.

A solution to this system of equations is the ordered pair (0.2, 9).

In order to write an equation that model this situation, we would assign variables to the cost charged by Ann's gym and the cost charged by Blake's gym respectively, and then translate the word problem into algebraic equation as follows:

For the cost charged by Ann's gym, we have the following equation:

y = 20x + 5.

For the cost charged by Blake's gym, we have the following equation:

y = 30x + 3.

In this exercise, we would use an online graphing calculator to plot the given system of equations in order to determine the solution as shown in the image attached below.

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Answer:

Equation = (6*3) - 2

Solution

Let x represent the unknown number

The number is multiplied by 6

= (6 × x )

= 6x

two is subtracted from the product

= 6x - 2

The product is equated to 3

= 6x-2= 3

Hence the equation is 6x-2= 3

To solve this inequality, you can add 1 to both sides of the inequality to get:

−7 + 1 < x − 1 + 1 < 8 + 1

-6 < x < 9

This inequality is a compound inequality, which is made up of two separate inequalities joined by the word "and".

The linear equation:

1 - (4/3)x = (1/2)*(-x + 7)

Has one solution.

So here we have a linear equation:

1 - (4/3)x = (1/2)*(-x + 7)

To solve it, let's isolate the variable x.

1 - (4/3)*x = -(1/2)*x + (1/2)*7

-(4/3)*x + (1/2)*x = 3.5 - 1

-(8/6)*x + (3/6)*x = 2.5

(-5/6)*x = 2.5

x = (-6/5)*2.5

x = 3

So the linear equation has a single solution, thus, the correct option is A.

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Answer:

Step-by-step explanation:

b= -3

Answer:

Step-by-step explanation:

The ratio of cocoa powder to one cup of milk is 1/4 cup of cocoa powder to 3 3/4 cups of milk or 1/4 : 3 3/4 or 1 : 15.

The required solution of the equation is -16.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given :six more than the quotient of a number and 8 is equal to 4

To solve this, we can convert the statement into an algebraic equation, Express it in an equation:

6+(x/8) = 4

subtracted 6 from both sides,

x/8 = -2

multiplied both sides by 8,

x = -16

Therefore, the required solution of the equation is -16.

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The project is considered to be complete when the EV is equal to the AC. So option b is correct.

When a project is considered complete, it means that the total amount of work that was planned to be done (referred to as the Budget at Completion or BAC) has actually been completed and the amount spent on completing the work so far EV is equal to the BAC.

In project management, Earned Value (EV) and Actual Cost (AC) are two key measurements used to quantify the exhibition of a project.

Earned Value (EV) addresses the arranged value of the work that has been finished. It is calculated by multiplying the arranged completion rate by the Budget at Completion (BAC).

Actual Cost (AC) addresses the actual measure of cash spent on the project in a limited way of time. It is the amount of the multitude of costs caused for the finished work and the work underway.

At the point when the Earned Value (EV) is equivalent to the Actual Cost (AC), it implies that all the arranged work has been finished and all the budget has been spent.

This is a decent indication that the project is on target and is probably going to be finished within the arranged budget.

Thus, when the Earned Value (EV) is equivalent to the Actual Cost (AC), the project is thought of as complete.

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Answer:

ask ur teacher

Step-by-step explanation:

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

now , put the value of x= -3 in given eqⁿ ∼

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

The correct description of the set {4,8,12,16,...} is {x|xEN and x is a multiple of 4 greater than 0}.

What is a set?

The way a person always represents a set is as a collection of items or elements with definite boundaries. A set is indicated by a capital letter. The number of items in a finite set is known as the cardinal number of the set.

We are given a set {4,8,12,16,...}

In the given set, we can see that they are all multiples of 4 but not -4.

Also, 4 is not an odd integer.

Therefore, it is a multiple of 4 greater than 0.

Hence, the correct description of the set {4,8,12,16,...} is {x|xEN and x is a multiple of 4 greater than 0}.

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Answer:

The student's GPA is 3.06

This student did not make the dean's list because their GPA is less than 3.20

(I can't see the drop down choices - I am using my own words)

Step-by-step explanation:

The process of computing the overall GPA based on letter grades with quality points and the number of credit hours for each course is as follows:

We have the following data

Course         Letter          Quality     Credit       Points x Credit Hours
                     Grade         Points      Hours    
-----------------------------------------------------------------------------------------------  
1                        A                4               5                      4 x 5 = 20

2                       C                2               3                      2 x 3 =   6  

3                        B               3                5                      3 x 5 = 15

4                        A               4                3                       4 x 3 = 12

5                        D               1                 2                       1 x 2 =  2
------------------------------------------------------------------------------------------------
Totals                                                    18                                 55

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

Overall GPA = 55/18 =  3.06

Since the minimum GPA to make the dean's list is 3.20 and 3.06 is less than 3.20, the student did not make the dean's list

The simplified exponential notation of the given expression is 9a²b

What is an exponential expression?

An expression in the form of a²  is called exponential expression.

The simplified exponential notation of the given expression is 18 * a³ b² / 2ab

The given expression is: 18a³b² / 2ab

We can write the above expression as:

(18/2 ) (a³ / a ) (b² / b )

We know that

aˣ / aⁿ= aˣ⁻ⁿ

a³ / a = a³⁻¹ = a²

b² / b = b²⁻¹= b

So,  ( 18/2) ( a³/a) (b²/ b) = 9 a²b

Hence, The simplified exponential notation of the given expression is 9a²b

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Answer:

Let x be the amount of alloy 1 used, and y be the amount of alloy 2 used.

We know that:

x + y = 53 (total weight of alloy 3 is 53 pounds)

0.35x + 0.69y = 0.40(53) (40% of the alloy 3 is titanium)

We can use the first equation to solve for one of the variables in terms of the other:

y = 53 - x

Substitute this expression into the second equation:

0.35x + 0.69(53-x) = 0.40(53)

0.35x + 36.97 - 0.69x = 21.2

-0.34x = -15.77

x = 46.44 pounds of alloy 1.

y = 53 - x = 6.56 pounds of alloy 2.

There are zero number of solutions the system of equations have.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=5/2x+2 ------(I) and 2y=5x+8 ------(II)

Substitute equation (I) in (II), we get

2(5/2x+2)=5x+8

5x+4=5x+8

5x-5x=8-4

Therefore, there are zero number of solutions the system of equations have.

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"Your question is incomplete, probably the complete question/missing part is:"

How many solutions does the following system of equations have? y=5/2x+2 and 2y=5x+8

Answer:

11, 13, 15, 17, 19

Step-by-step explanation:

The numbers: (x)+(x+2)+(x+4)+(x+6)+(x+8)

Given: (x)+(x+2)+(x+4) = 3+(x+6)+(x+8) => 3x + 6 = 2x + 17 => x = 11

The integers: 11, 13, 15, 17, 19

Answer:

7, 8, 9, 10 and 11

Step-by-step explanation:

Let:

a = smallest integer

Then the five consecutive integers in ascending order will be:

a, (a + 1), (a + 2), (a + 3), (a + 4)

According to the statement in the question:

a + (a + 1) + (a + 2) = (a + 3) + (a + 4) + 3

3a + 3 = 2a + 10

a = 7

A) The probability that you will join them is 0.523;

B)  If you end up joining them, the probability your friends have decided to visit a national park is 0.50.

Note that probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

In the above case, Note that to determine the probability that you will join them, we need to use the formula for conditional probability, which is:

P(A and B) = P(A|B) * P(B)

In this case, A is the event that you join them, and B is the event of your friends deciding to visit either a national park or a city in the USA.

Given the above, we have:

P(join and national park) = P(join|national park) * P(national park) = 0.75 * 0.35

P(join and city) = P(join|city) * P(city) = 0.40 * 0.65

Thus to obtain the probability that you will join them: we must add the two probabilities: P(join and national park) and P(join and city)

⇒ P(join) = P(join and national park) + P(join and city)

= 0.75 * 0.35 + 0.40 * 0.65

= 0.523

Thus, it is correct to state that the probability or likelihood that you join them is: 0.523

B) If you decide to join them, the probability that your friends have decided to go to a national park is determined using the Bayes Theorem.  This theorem is given as:

P(B|A) = P(A|B) * P(B) / P(A)

Where A is the event of you going with them, and B is the event of your friends deciding to go to a national park.

P(national park|join) = P(join|national park) * P(national park) / P(join)

= 0.75 * 0.35 / 0.525

= 0.5019120459
[tex]\approx[/tex] 0.50

Thus, it is correct to state that the probability your friends have decided to visit a national park is 0.57 if you eventually join them.

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Answer:

Step-by-step explanation:

a) ST

b) SR or RU or RT

c) VW

d) It's 4 units since RU = ST/

Answer: 4/7

Step-by-step explanation:

(16/21)/(4/3) = (16/21)*(3/4) = (16*3)/(21*4) = 48/84 = 4/7

Equation of graph of f is : y = (-1/2)x + 4

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

Given,

The graph of f passes through (- 8, 8)

Line that has

x- intercept a = 1

y-intercept b =  - 2.

Intercept equation of the line

x/a + y/b = 1

x/1 + y/-2 = 1

x - y/2 = 1

-y/2 = 1-x

y = 2x - 2

Comparing it with slope intercept equation of the line y = mx + c

slope m = 2

Product of slopes of two perpendicular lines = -1

If m' is the slope of its perpendicular

then m.m' = -1

        2.m' = -1

         m' = -1/2

Equation of the line

y - y₁ = m'(x - x₁)

Graph of f passes through (-8, 8) and is perpendicular to line y = 2x - 2

y -8 = (-1/2)(x - -8)

y - 8 = (-1/2)(x+8)

y - 8 = (-1/2)x - 4

y = (-1/2)x + 4

Hence, y = (-1/2)x + 4 is the equation graph of f.

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Quantitative research is a form of qualitative research that focuses on gathering and evaluating data that can be measured and quantified. This study style use numerical data and statistical approaches to uncover patterns, correlations, and trends in data.

Data is frequently collected through surveys, questionnaires, or standardised tests, and the findings are generally evaluated using statistical software. Response options in quantitative research are frequently constrained and organised, with participants picking from a pre-determined range of answers.

The goal of quantitative research is to produce data that is trustworthy, valid, and generalizable to a broader population. Based on the data acquired, this form of study is frequently used to test hypotheses.

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One term is referred to as a polynomial function (where n = 1), a 2 polynomials (when n = 2), and a 3 polynomials (when n = 3) depending on the value. Example: The polynomial is categorized according to the quantity of terms as: Monomial: One phrase, three times.

There are three different forms of polynomials, depending on how many terms they contain. Monomial, binomial, and trinomial are the three. A polynomial can be divided into zero polynomial, straight polynomial, cubic polynomial, and cubic polynomial depending on its degree.

How can you tell what degree a phrase is?

The degrees of a component in the polynomials equation is given as a+b if a and b are the proponents of the many variables in a term. For instance, the polynomial contains the equation x2y5, whose degree is 2+5 and hence equals 7.

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Classify each polynomial by its degree and number of terms.

Answer: yes the triangles are similar

Step-by-step explanation: a congruent comparison would have the exact same size and shape, similar triangles have the same shape but can be smaller or larger than the original

Answer:

m = 20

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Let's pick 2 points (0,5) ( 1 , 25)

The y increase by 20, and the x increase by 1, so the slope is

m = 20

Answer:

The slope is 20.

Step-by-step explanation:

To find the slope of the line, we pick two points on the line and use the slope formula.

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

The points I used were ( 0,5) and ( 1,25).

m = ( 25-5)/( 1-0)

   = 20/1

   = 20

The slope is 20.

For the given number line plot the inequality obtained is { -∞ < x < -2 and 5 < x < ∞}.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To represent inequalities on a number line show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.  

An open circle shows it does not include the value.

A closed circle shows it does include the value.

Let the unknown value be x.

The first range is starting form -2 and moving towards -∞.

Since the circle is open it will not include the value.

So the inequality is -∞ < x < -2.

The second range is starting form 5 and moving towards ∞.

Since the circle is open it will not include the value.

So the inequality is 5 < x < ∞.

Therefore, the inequality is { -∞ < x < -2 and 5 < x < ∞}.

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In a sample of size 100, the median splits the data into two equal parts of 50 observations each. So, 50 observations are below the median and 50 observations are above the median.

The first quartile (Q1) separates the lowest 25% of the data from the rest, so 50 observations are between the median and Q1.

The interquartile range (IQR) is defined as the difference between the third quartile (Q3) and Q1, and represents the range of the middle 50% of the data. Since the IQR contains both Q1 and the median, it encompasses all observations between Q1 and the median,

or a total of 75 observations.

therefore the answer is 25,50,75

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