What transformations take f(x)=3x+1 to g(x)=-3x-5?

Answer:

Step-by-step explanation:

The amount of money Mr.Sykes will spend on calculators is £629.2.

Given:

Total Number of students in year 11 = 104

Cost of each calculator =  £6.05

Now to calculate the total cost of all the calculators we have to multiply the number of students by the cost of one calculator.

Amount of money Mr.Sykes will spend on calculators = Total Number of students × Cost of each calculator

= 104 × 6.05

= £629.2

Hence, the total amount of money Mr.Sykes will spend on calculators is £629.2.

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The value of the greatest integer is -9.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the sum of an integer and 4 times the next consecutive integer is -46.

Assume that the integer is x. Then, its consecutive integer will be (x + 1).

Then we can write -

x + 4(x + 1) = - 46

x + 4x + 4 = - 46

5x + 4 = - 46

5x = - 50

x = - 10

Then -

x + 1 = - 9, which is also greater than -10

Therefore, the value of the greatest integer is -9.

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The distance from the car to the gate to magic kingdom is 1 1/12 miles.

From the information given, it was stated that get from their car in the parking lot to the gate at the magic kingdom they walk 1/4 mile take a tram for 1/3 their total distance and take a monorail for 1/2.

Therefore, the distance from the car to the gate to magic kingdom based on the information will be the addition of the fractions given. This will be:

= 1/3 + 1/2 + 1/4

= 4/12 + 6/12 + 3/12

= 13/12

= 1 1/12

The distance is 1 1/12 miles.

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Answer:

a. 245 m

b. 40 m

c. The g-value of Mars is smaller than that of Earth.

Step-by-step explanation:

From the question, the distance the object has fallen due to gravity is given by

[tex]\boxed{d = gt^{2} }[/tex]

Earth

Given that g= 9.8 m/s²,

d= 9.8t²

(a) When t= 5,

d

= 9.8(5²)

= 9.8(25)

= 245 m

Moon

Given that g= 1.6 m/s²,

d= 1.6t²

(b) When t= 5,

d

= 1.6(5²)

= 40 m

Mars

(c) Relationship: smaller g, smaller d

Given the same value of t, which is 5 seconds, we are given that the distance (d) is 46.25 m.

This distance is smaller that than when dropped near the surface of the earth, but larger than that when dropped near the surface of the moon.

In summary,

Thus, we can conclude that the g-value on Mars is smaller than that of the Earth.

The value of "k" in the following equation 72 + k = 54 for which the given linear equation is true is k = -18

As per the question statement, we are supposed to find the value of "k" in the following equation 72 + k = 54 for which the given linear equation is true.

The solution is given below:

72 + k = 54, subtracting 72 from both sides

k = 54 - 72

k = -18

Therefore the value of "k" in the following equation 72 + k = 54 for which the given linear equation is true is k = -18

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Answer:

7 hours 30 minutes and 0 Seconds

Step-by-step explanation:

The unit rate of the can in Hefty bird grocery store is 3

The unit rate of the can in  bulky grocery is 4

The unit rate  at Hefty bird grocery store can be calculated as follows

15= 75

1= x

cross multiply both sides

15x= 75

x= 75/15

x= 3

The unit rate at bulky grocery can be calculated as follows

8= 32

1= y

cross multiply both sides

8y= 32

y= 32/8

y= 4

Hence the unit rates are 3 and 4 respectively.

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Based on the correlation coefficient between rent and square footage of 0.84, the relationship between the two variables is Strong and Positive.

The Correlation Coefficient can be negative, positive, or 0. When it is 0, then no relationship exists between the variables. A negative coefficient means that the relationship is negative.

A positive correlation means that the relationship is positive which means the variables increase (decrease) together. A correlation coefficient above 0.8 indicates that the correlation is strong.

In this case, it means that the correlation of 0.84 between rent and square footage is strong and positive.

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m in the linear equation that represents the scenario is expressed as: m = (C - 12)/a.

A linear equation, in slope-intercept form y = mx + b or y = b + mx, can be used to model a scenario where:

In the scenario described above, given that C = 12 + am represents the equation of the monthly pone cost, we have the following:

Monthly phone cost (y) = C

Additional charge per minute (m) = a

Number of minutes (x) = m

Base fee (b) = 12

Thus, to find what m equal in the equation, make m the subject fo the formula:

C = 12 + am

C - 12 = 12 + am - 12

C - 12 = am

(C - 12)/a = m

m = (C - 12)/a

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Answer:

Step-by-step explanation:

whoops, does anyone know how to delete an answer?

Answer:

y=x+4

Step-by-step explanation:

The slope of the line is [tex]\frac{3-4}{-1-0}=1[/tex].

Since the y-intercept is 4, the equation is y=x+4.

Using transformations, it is found that:

25. The function underwent a reflection over the y-axis.

26. The function undergoes a vertical compression by a factor of 1/2.

27. the changes from f(x) = |x| to g(x) = -2|x - 1| + 2 are given as follows:

The graph of g(x) is given at the end of the answer.

The transformations used are given as follows:

The function for g(x) is given by:

g(x) = f(-x).

This rule is for a reflection over the y-axis.

The function for g(x) is given by:

g(x) = 0.5f(x).

The multiplication by a number less than 1 means that it underwent a vertical compression, with the coefficient representing the scale factor.

For this problem, the parent function is:

f(x) = |x|.

The transformed function is:

g(x) = -2|x - 1| + 2.

The changes are given as follows:

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The value of value of 13 squared is 169 and this is between 168 and 170.

It should be noted that a square of a particular number simply means the multiplication of the number by itself.

Based on the information, the value of 13 squared will be:

= 13 × 13

= 169

It should be noted 169 will be between 168 and 170.

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Writing 4.1012 in words will be represented as D. four point one zero one two.

It should be noted that writing in words simply means spelling or calling out of the numbers that are given.

Based on the information, it should be noted that (.) is illustrated as a point when calling out the decimal numbers. Other values include:

4 = four

1 = one

0 = zero

2 = two

Therefore, based on the illustration, the correct option is D.

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Answer:

B

Step-by-step explanation:

he's wrong

We know that the cost of the meal is $40 and the tip is the 10%.

And we must find the total cost.

The total cost will be we cost of the meal plus the tip.

Now, we must find the cost of the tip.

Since the tip is the 10% we must multiply the cost of the meal by 10%. (We can represent 10% as 0.1)

Then, the total cost is

Finally, the total cost of the meal is $44.

The slope of the line shown in this graph is equal to 3/5 or 0.6

A pitch is also referred to as slope and it can be defined as the ratio of the vertical distance (rise) measured to the horizontal distance (run) measured.

Mathematically, the pitch (slope) of a geometric figure or line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the given graph, we would select the following points:

Rise = 6, 0

Run = 10, 0

Substituting the selected points into the formula, we have;

Pitch (slope) = (6 - 0)/(10 - 0)

Pitch (slope) = 6/10

Pitch (slope) = 3/5 or 0.6

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Complete Question:

The graph shows how many cups of water are needed for each cup of flour in a pizza dough recipe. In this activity, you will find the slope of the line shown in the graph.

To calculate slope, you need to know the rise and the run of the graph. Use the graph to find the rise and the run from one point you selected to the other.

Answer: Part A

Answers will vary. The sample answers throughout this Lesson Activity assume the points chosen are (0, 0) and (5, 3).

Part B (Answer)
Between the points (0, 0) and (5, 3), there is a rise of 3 units and a run of 5 units.  
Part C ( Answer)
Between the points (0, 0) and (5, 3), the rise is 3 and the run is 5. The slope is the ratio of rise to run. Therefore, the slope of the line is 3/5.

Step-by-step explanation:

Questions
Part A - To calculate slope, you need two points. Choose two points on the line.

Part B - To calculate slope, you need to know the rise and the run of the graph. Use the graph to find the rise and the run from one point you selected to the other.

Part C

Using the rise and run from part B, what is the slope of the line?

The linear function modelling the daily inventory in t days after August 31 is given by:

I(t) = 110 - 22t.

Using the given function, they must restock the store on September 3.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In the context of this problem, we have that:

Thus the model is given as follows:

I(t) = 110 - 22t.

They must have at least 25 phones in stock at all times, hence:

I(t) >= 25

110 - 22t >= 25

22t <= 85

t <= 85/22

t <= 3.86.

Rounding down, as after 4 days they would have less than 25 phones, they must restock the store on September 3, which is 3 days after August 31.

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Answer:

50

Step-by-step explanation:

in this equation you will have to add and multiply the Ns together then you will divide whatever value you get by 250

(2N-7N+4N) x (9N-14N)=250

(-1N) x (-5N)=250

5N=250

N=50

The difference in elevation between the bottom of the canyon and the birds nest is 679.8 feet.

What is a numerical expression ?

A numerical expression is an statement written in form of numbers with mathematical operations.

According to the given question

A bird flies from the bottom of a canyon that is59 1/5 feet below sea level to a nest that is 620 3/5 feet above sea level.

59 1/5 feet

(59×5 + 1)/5

59.2 feet

Let assume that the sea level is at 0 feet.

= (620×5 + 3)/5

= 620.6 feet.

From the given data we write an expression which is the difference in elevation between the bottom of the canyon and the bird nest is

( 620.6 ) - ( -59.2 ) feet

=  620.6 + 59.2 feet

= 679.8 feet.

Hence, The elevation difference between the birds' nest and the canyon's base is 679.8 feet.

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Answer:

I think its 5.00 N

Step-by-step explanation:

Answer:

[(2, 8),(3, 7),(4, 6)]

Graph the equation like normal.

Use the procedures explained below to answer the next question.

Step-by-step explanation:

To obtain 3 points, choose any values for x and substitute into the equation for corresponding values of y. To make this easier, I'm going to use function notation instead. But, this works the same using slope-intercept form.

[tex]f(x)=-x+10\\f(2)=-2+10=8 \rightarrow (2,8)\\f(3)=-3+10=7 \rightarrow (3,7)\\f(4)=-4+10=6\rightarrow(4,6)[/tex]

All I did was substitute three different values of x, to get the corresponding values for y.

So, the three points that are on the line are (2, 8), (3, 7), and (4, 6). Now, you can graph the equation as you normally would.

As shown in the attached screenshot, the three points that we found are correctly on the graphed line.

Use the same procedures to answer the next question.

The type of number that gets a mathematician in trouble the most when trying to use a function to model a real-world situation are irrational numbers and zero.

        y = k/x, where k is a fixed number, say 10.

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Answer:

3:4

Step-by-step explanation:

for every set that Natasha and Richard do and since 1 hour is 60 minutes the ratio is 45:60 and then you divide both sides by 15 to get 3:4

a) To calculate the overall mean, you must take the total wages divided by the total number of workers. What Stacy is doing is calculating the average of the means, which is incorrect as both the total wages and the quantity of workers are both different (or she's just using the wrong method of calculation)

b) First, we find the total wages of the 56 workers : 42 x 9.5 + 14 x 13.5 = 588 (pounds)

So, the overall mean is : 588 : 56 = 10.5 (pounds/h)

Answer:

£ 10.50

Step-by-step explanation:

a) Stacy is wrong because she found the mean of the £9.50 and £13.50. She has to find the mean of wage of 42 packers and wage of 14 truck drivers.

[tex]\sf b) Overall \ mean \ wage = \dfrac{sum \ of \ wages \ of \ 42 \ packers+ Sum \ of \ wages \ of \ 14 \ truckers}{number \ of \ packers + numbers \ of \ truck \ drivers}[/tex]

Sum of wages of 42 packers = 42 * 9.50

                                                = £ 399

Sum of wages of 14 truck drivers = 14 * 13.50

                                                       = £ 189

[tex]\sf Overall \ mean \ wage = \dfrac{399+189}{42+14}\\\\[/tex]

                            [tex]\sf = \dfrac{588}{56}\\\\[/tex]

                            = £ 10.50

Answer:

15

Step-by-step explanation:

Mel's Age = x

Rahfat's Age = x-3

Aurelio's Age = 2x

2x + x +x -3 = 57

4x -3 = 57

4x = 60

x = 15