Mathematics College

please help this is pre calculus

Answers

Answer 1

Step-by-step explanation:

1. First things first, the binomial tells us the zeroes.

[tex] - (x - 2) {}^{2} = 0[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

This root has a multiplicity of 2, so this root will "bounces off the x axis"

[tex](x + 4) = 0[/tex]

[tex]x = - 4[/tex]

Our x intercepts are

2 and -4

This root has a multiplicty of 1, so it will cross thorough the x axis.

Our leading degree is odd and we have a negative leading coefficient so

as x approaches ♾️, f(x) approaches negative ♾️

and as x approaches negative ♾️, f(x) approaches ♾️.

Our y intercept can be found by letting x=0,

[tex] - (0 - 2) {}^{2} (0 + 4) = - ( - 2) {}^{2} (0 + 4) = - (4)(4) = - 16[/tex]

So our y intercept is -16.

For Rational Functions, if the numerator and denominator share the same factor they are considered a removable discontinuity or hole.

Set it equal to 0.

[tex]x + 5 = 0[/tex]

[tex]x = - 5[/tex]

So we have a hole at x=-5.

Next, simplify the fraction.

[tex] \frac{x - 4}{x - 6} [/tex]

Now, plug in -5

[tex] \frac{ - 5 - 4}{ - 5 - 6} = \frac{ - 9}{ - 11} = \frac{9}{11} [/tex]

So we have a hole at (-5,9/11).

To find y intercept, let x=0,

[tex] \frac{0 - 4}{0 - 6} = \frac{2}{3} [/tex]

To find Vertical Asymptote, set denominator equal to 0

[tex]x - 6 = 0[/tex]

[tex]x = 6[/tex]

Draw a vertical dotted line at x=6

To find HA, this is the only case since the numerator and denominator has the same degree.

So using the leading coefficients, divide the numerator leading coefficient/ denominator leading coefficient.

The leading coefficient for both is 1 so

[tex]ha = \frac{1}{1} [/tex]

So our HA is y=1.

Draw a horizon tal dotted line at y=1

We have no slope asymptote.

The graph is above.

Part 3:

(3x-1)(2x+1)>0

[tex]3x - 1 = 0[/tex]

[tex]3x = 1[/tex]

[tex]x = \frac{1}{3} [/tex]

[tex]2x + 1 = 0[/tex]

[tex]2x = - 1[/tex]

[tex]x = - \frac{1}{2} [/tex]

We have three possible regions, when x is positive

When x is less than -1/2When x lies between -1/2 and 1/3When x is greater than 1/3

Pick a random number less than -1/2 and plug it in the inequality to see if it true.

Let use -1

[tex](3( - 1) - 1)(2( - 1) + 1) = ( - 4)( - 1) = 4[/tex]

Since 4>0, Whenever x is less than -1/2, the function is positive (greater than zero)

Let's try the next region.

Let use 0

[tex](3(0) - 1)(2(0) + 1) = ( - 1)(1) = - 1[/tex]

So this solution won't work

Let try the next region, let use 1.

[tex](3(1) - 1)(2(1) + 1) = (2)(3) = 6[/tex]

Since 6>0, Whenever x is greater than 1/3, the function is positive(greater than zero).

Our answer is

(-oo,-1/2) U (1/3,oo).

Part 4:

We know x cannot be -2 because

[tex]x + 2 = 0[/tex]

[tex]x = - 2[/tex]

So -2 can not be in our answer.

[tex] \frac{x - 1}{x + 2} \leqslant 2[/tex]

[tex]x - 1 \leqslant 2(x + 2)[/tex]

[tex]x - 1 \leqslant 2x + 4[/tex]

[tex] - 5 \leqslant x[/tex]

[tex]x \geqslant - 5[/tex]

However x can not be -2. so we say

[-5,-2) U (-2,oo)

Related Questions

A bag contains 10 red balls, 8 green balls, and 6 blue balls. 2 balls are drawn at random at the bag. What is the probability that both balls are red?

Answers

Answer:

Assuming every single ball has an equal chance of being drawn, then if B is the probability of drawing a blue ball and R is the probability of drawing a red ball:

B + R = 1,

since either a red or blue ball will be drawn. Since each ball has an equal chance of being drawn:

16 p = 1, or

p = 1/16

where p is the chance to draw a single ball. Since there are 10 red balls, there are ten independent and different ways to draw a red ball, which means that

R = 10 p = 10/16 = 5/8.

You can either apply the first equation to find that

B = 1 - R = 3/8

or state directly that

B = 6 p = 6/16 = 3/8

since there are six independent and different ways to draw a blue ball from the bag.

Answer:

41.67%

Step-by-step explanation:

10+8+6= 24

10/24

First, you need to calculate your grade in percentages. The total answers count 24 - it's 100%, so we to get a 1% value, divide 24 by 100 to get 0.24. Next, calculate the percentage of 10: divide 10 by 1% value (0.24), and you get 41.67% - it's your percentage grade

Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.

Answers

1 hour 30 minutes take her to do her homework if she has 30 pages to read and 45 math problems to complete.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Karen can read 10 pages and complete 15 math problems in 30 minutes.

So, if she reads 30 pages which is 3 times of 10.

Also, solve 45 maths problem which is 3 times of 15.

So, the time taken to complete 30 pages to read and 45 math problem

= 30 x 3

= 90 minutes

= 1 hour 30 minutes

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8. The price of a four-star dinner was $175 two decades ago. A report says that a dinner is 250% of what it was
20 years ago, how much would a four-star dinner cost today?
a.
Round the numeric answer to the nearest dollar.
I=
b. Use the answer in a meaningful sentence.

Answers

Answer:

Dinner should cost 250 today.

Step-by-step explanation:

Give the following equation: f(x) =square root x-3+4 how will the graph move in comparison to the parent function.

Answers

Graph will shift from(0,0) to (3,4) after the shifting happens due to change in expressions of the parent function.

What is transformation of graph?

Graph transformation is the process by which an parent graph, or graphed equation, is changed to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification in algebraic equations.

The deduced parent function is [tex]\sqrt{x}[/tex]

So, Domain= (0 , ∞)

Range= (0 , ∞)

Let us take (0,0) as the point and see the shifting of the point with respect to (0,0).

So when function is transformed to √x+3

Function shift from (0,0) to (3,0)

and when function is transformed to [tex]\sqrt{x+3} +4[/tex]

then point shifts to (3,4).

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Give an example of bounded sequence that are not conregent?

Answers

Answer The sequence {an = (−a)n}

Step-by-step explanation: The sequence {an = (−a)n} is bounded below by −1 and bounded above by 1, and so is bounded. This sequence does not converge, though; since |an − an+1| = 2 for all n, this sequence fails the Cauchy criterion, and hence diverges.

A container has the shape of an open right circular cone, as shown in the figure above. The container has a radius of 4 feet at the top, and its height is 12 feet. If water flows into the container at a constant rate of 6 cubic feet per minute, how fast is the water level rising when the height of the water is 5 feet?

Answers

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

How to find the rate of change?

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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Write an equation in slope-intercept form for the line with slope 5 and y-intercept -5 . Then graph the line.

Answers

Answer:

Step-by-step explanation: The equation for slope-intercept is y=mx+b

m= slope of the equation, b= y-intercept(what y is when x is zero)

there for the equation is y=5x-5

in a particular shop employees are given a 12.5% discount on any items they purchase.calculate the actual price an employee would pay for each of the following
1200

Answers

The actual price of an item is $1371.49.

Given that, the discount percentage is 12.5% and the selling price is $1200.

What is discount?

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Let the actual price be x.

Now, x-12.5% of x =1200

⇒ x- 12.5/100 ×x=1200

⇒ x- 0.125x=1200

⇒ 0.875x=1200

⇒ x=1200/0.875

⇒ x=$1371.49

Therefore, the actual price of an item is $1371.49.

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round 11,406 to the nearest:tens ,ten thousand , hundred

Answers

Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

Sketch the graph of the exponential function. Label the y-intercept and at least two other points on the graph using both
positive and negative values of x.
f(x) = 5e^x

Answers

Answer:

Take a look at the attachment...

Hope this helps! :)

What word sentence represents this inequality?

A number is at least as large as 8.9

A number is no more than 8.9

A number is greater that 8.9

Answers

The word sentence which is used to represent the given inequality

p ≥ 8.9 is a number is at least as large as 8.9.

As given in the question,

Given inequality is equal to :

p ≥ 8.9

In the given inequality sign of greater than and equals to is used.

Explanation for the given word sentences:

A number is at least as large as 8.9.

Meaning of at least is minimum this much.

At least as large means ( ≥) greater than or equal to

Option is correct.

A number is no more than 8.9.

It represents the symbol (≤ )less than or equal to.

Incorrect option.

A number is greater than 8.9.

It represents the symbol of > greater than only.

Incorrect option.

Therefore, the word sentence which is used to represent the given inequality p ≥ 8.9 is a number is at least as large as 8.9.

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There are three boxes on the table: The first box contains 2 quarters, the second box contains 2 nickels, and the last box contains 1 quarter and 1 nickel. You choose a box at random, then you pick a coin at random from the chosen box. If the coin you picked is a quarter, what's the chance that the other coin in the box is also a quarter?

Answers

The probability of choosing a box and picking two quarter coins in a row is 1/108

What is Probability?

Probability is the branch concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1. 0 indicates impossibility of the event and 1 indicates certainty.

Probability= sample space / total possible outcome

therefore probability of choosing two quarters in a row = 1/6×1/6= 1/36

The probability of choosing the first box =1/3

Therefore the probability of choosing the first box and picking two quarters In a row is 1/36×1/3= 1/108.

Since box two contain no quarter and box three has only one quarter , the probability of choosing two quarters in a row is 0.

Therefore the probability of choosing a box at random and picking two quarters in a row is 1/108.

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Graphing and Solving Inequalities

m-1<-3. -4y <-20. 5+b>1. -18

Answers

Solutions for the given equalities:

m < - 2

y > 5

b > -4

What is inequality in mathematics?

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

The given inequalities are

1) m - 1 < -3

Adding 3 on both sides, we get

m - 1 + 3 < -3 + 3

m + 2 < 0

Subtracting 2 from both the side, we get

m + 2 - 2 < 0 - 2

m < - 2

The graph of this inequality is shown below

2) -4y < -20

Dividing by -4, we get

y > 5

The graph of this inequality is shown below

3) 5 + b > 1

Subtracting 1 from both the side, we get

b + 4 > 0

b > -4

The graph of this inequality is shown below

4) y = -18

This is a point on a number line, and it can be shown as

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A theater is presenting a program on drinking and driving for students and their
parents or other responsible adults. The proceeds will be donated to a local alcohol
information center. Admission is $2.00 for adults and $1.00 for students. However,
this situation has two constraints: The theater can hold no more than 240 people
and for every two adults, there must be at least one student. How many adults and
students should attend to raise the maximum amount of money?
To raise the maximum amount of money,
attend.
adults and
students should

Answers

Using equations, to raise the maximum amount of money, 160 adults and 80 students should attend the theater program on drinking and driving.

What is an equation?

An equation is a mathematical statement of the equality of two or more mathematical expressions, using the equation symbol (=).

In this situation, we form a system of equations, to show the maximum number of adults and students allowed for the program.

We also form an objective constraint of inequality to show the limit of the allowed number of people for the program.

Admission fee for adults = $2.00

Admission fee for students = $1.00

Equations:

The total number allowed in the theater = 240 persons

The ratio of adults to students = 2:1

The sum of ratios is 3

The number of adults = 2x, where, the number of students = x.

2x + x = 240 ... Equation 1

3x ≤ 240 ... Equation 2

If 3x = 240

x = 80

Check:

3x ≤ 240

3(80) ≤ 240

240 = 240

Allowed Admission:

Adults = 160 (2 x 80)

Students = 80 (1 x 80), which meet the second requirement or constraint.

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4×1+1×1/100+9×1/1000
What decimal represents each number

Answers

The decimal that represents the number 4×1+1×1/100+9×1/1000 is given as follows:

4.0119.

How to convert a fraction to a decimal number?

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.

In this problem, we are given two fractions, and their decimal equivalents are given as follows:

1/100 = 0.01.1/1000 = 0.001.

Hence the numeric value of the expression is given as follows:

4×1+1×1/100+9×1/1000 = 4 + 0.01 + 0.0019 = 4.0119.

Which is the decimal number represented by the fraction.

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Which is the graph of g(x) = [x + 3]?

Answers

Answer:

Step-by-step explanation:

................ x2

HELP PLEASE NEED IT FAST

Answers

He needs to climb 40 feet up

He has to climb UP 40 feet

Step-by-step explanation:

please help 3
what is(fog)(3)if f(x)=3x-1 and g(x)=4x2+9

Answers

The value of (fоg)(3) = 134.

What is composition of functions?

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Consider, the given functions

f(x) = 3x - 1, g(x) = 4x^2 + 9

First to find f(g(x)).

Let,

f(g(x)) = 3(4x^2 + 9) - 1

= 12x^2 + 27 - 1

f(g(x)) = 12x^2 + 26

Now, to find f(g(3)).

Plug x = 3 in the above equation,

f(g(3)) = 12(3)^2 + 26

= 12(9) + 26

f(g(3)) = 134

Hence, (fоg)(3) = 134.

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what is the round figure of 2089.17

Answers

2089.17 rounded off to nearest tenths(1 decimal place) is 2089.2

2089.17 rounded off to the nearest one is 2089

When you "round to the nearest _____" regardless of what is in the blank the steps are nearly always the same:

Identify which place value you are rounding off a number. The smaller the place value, the more accurate the final result shall be.

Find the next smallest place value, the digit to the right of the place value you're rounding off to. For example, if you want to round to the nearest ten you would have to find the number at the one's place.

If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round off. Any digits after that number become zeros, or drop-offs if they're located after the decimal point. This is called rounding down a number or a sequence of numbers.

If the smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding off to by one place (+1). Any remaining digits before the decimal point become zeroes, and any digits that are after the decimal point are dropped. This is called rounding up of numbers.

For example, for rounding off a number 838.274, depending on which place value you'll round to, the final rounded-off answer will vary. Rounding off 838.274:

Rounding off the nearest hundred is 800

Rounding off the nearest ten is 840

Rounding off the nearest one is 838

Rounding off the nearest tenth is 838.3

Rounding off the nearest hundredth is 838.27

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Multiple choice: According to the central limit theorem, the standard deviation of the sample means is:
a) less than the population standard deviation
b) the same as the population standard deviation
c) more than the population standard deviation

Answers

According to the central limit theorem, the standard deviation of the sample means is a) less than the population standard deviation.

What is a central limit theorem?

According to the central limit theorem, as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or other distribution.

The sample means' standard deviation (also known as the standard error of the mean) will be less than the population standard deviation and equal to the population standard deviation divided by the square root of the sample size.

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Tia has 28 yards of fabric. If each project needs 3 and one half yards of fabric, how
many projects can she complete?

Answers

Step-by-step explanation:

28-28=1 11111111111111111111111111

It would be much appreciated if someone could aid me in solving question B for this problem. I have been unable to calculate the correct answer. Thank you so much in advance : )

A floating rate mortgage loan is made for $125,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower
and lender have negotiated a monthly payment of $1,000.
Required:

a. What will be the loan balance at the end of year 1?

b. If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year 2 and
year 5 if the payment remains at $1,000?
Complete this question by entering your answers in the tabs below.
Required A Required B
If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year
2 and year 5 if the payment remains at $1,000?
Note: Do not round intermediate calculations. Round your final answers to 2 decimal places.

Loan balance in year 2:
Interest accrued-Year 2:
Interest accrued - Years 2-Year 5:

Answers

The negative amortization at the end of year 1 is $2536.50

For the year 1 there will be still 12% rate of interest going on. There is a negative balance of $200 after payment of 1st month installment.

Thus negative amortization = FV(0.01x12 - 200)

Here 0.01 is the interest per month, 12 is the number of months in a year and -200 is the negative balance in first month

negative amortization = FV(0.01x12 - 200)

The negative amortization at the end of year 1 = $2536.50

The negative amortization at the end of year 5

The loan balance at the end of year 4 = FV(0.13x12x36x800 - 102536)

The loan balance at the end of year 4 = $16132.46

The negative amortization at the end of year 1 is $2536.50

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Evaluate y + (-32.577) for the following values of y.
value of y value of expression
-12.975 -45.552
-41.08
-74.003
-10.304

Answers

For answers see attachment below! :]

Question 3(Multiple Choice Worth 2 points)
(Proportional Relationships MC)

A wheat farmer plows 5 acres of land and collects 135 bushels of wheat. The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.

Is there a proportional relationship between the number of bushels of wheat collected and the number of acres plowed over the two days? Explain.

Yes, it is proportional because the farmer collected 7 bushels for every 1 acre plowed.
Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres plowed are not equivalent.

Answers

Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A wheat farmer plows 5 acres of land and collects 135 bushels of wheat

The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.

Let us create a equation

Bushels/Acres

For first day:

Number of bushels of wheat=135

Number of acres of land=5

135/5=27

Next day:

Number of bushels of wheat=216

Number of acres of land=8

216/8=27

The proportional relation between 1st day and next day is same. It is proportional because the farmer collected 27 bushels for every 1 acre plowed.

Hence, Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

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Find the approximate slope of the line that contains the points (5.1, -2.8) and (6.4,-1.2). State whether the line is increasing, decreasing, horizontal, or vertical.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The slope is (fill in the blank)

B The slope is undefined

Is the line increasing, decreasing, horizontal, or vertical?

Horizontal
Increasing
Decreasing
Vertical

Answers

Answer:

slope = 16/13, increasing

Step-by-step explanation:

solve for the slope

-1.2-(-2.8)/(6.4-5.1)

= 16/13

it's positive meaning it's increasing

When firefighters are trying to put out a fire, the rate at
which they can spray water on the fire depends on the
water pressure. You can find the flow rate f in gallons
per minute using the equation, f = √120p, where p
is the nozzle pressure in pounds per square inch.
What pressure would be required to have a flow rate of
62 gal/min? show work

Answers

The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

What is meant by nozzle pressure?

The velocity of the stream is exactly proportional to nozzle pressure. In the given scenario, instead of a stream moving at 80 mph through the fire's super-heated gases, it moves at 60 mph.

The velocity increases as the pressure decreases in a convergent nozzle, but we know that pressure is inversely related to area.

The following formula can be used to compute the flow rate for a given nozzle. Q represents the flow rate. K = Nozzle K factor. P = Nozzle pressure differential. n = Is a constant that is determined by the type of spray pattern.

Given equation is,

f = √120p

Here p denotes the nozzle pressure in pounds per square inch

Also given that p=62 gal/min

f = √120p

Then,

f= √120(62)

f=√7440

f= 86.25

The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

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The quantity x plus 3, multiplied by negative 7

Answers

Step-by-step explanation:

(x + 3) × -7 = -7x - 7×3 = -7x - 21

6. The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes. If the total value of the coins in the piggy bank is at least $4.35, find the smallest possible number of coins in the bank.

Answers

If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

As per the question statement, The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, and the total value of the coins in this piggy bank is at least $4.35,

Then, we are required to determine the smallest possible number of individual coins in the bank.

To answer this question, first we will need to know the monetary values of nickels and dimes, that is,

(1 dime = 10 cents = $0.1), and (1 Nickel = 5 cents = $0.05).

Now let us assume that, there are "x" nickels and "y" dimes in that bank, Then as per the condition that, the number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, we can write an equation with the above assumed two variables, which is, [x = (2y - 1)]...(i)

And as per the other condition that, the total value of the coins in this piggy bank is at least $4.35, we can write another equation, which is,

[(0.1y + 0.05x) = 4.35]

Or, [100(0.1y + 0.05x) = (100 * 4.35)]

Or, [(10y + 5x) = 435]...(ii)

Now substituting eqn (i) in eqn (ii), we get,

[{10y + 5(2y - 1)} = 435]

Or, [(10y + 10y - 5) = 435]

Or, [(10y + 10y) = (435 + 5)]

Or, (20y = 440)

Or, [y = (440/20)]

Or, (y = 22)

Therefore, [x = {(2 * 22) - 1}]

Or, [x = (44 - 1)]

Or, [x = 43]

That is, If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.

f(x)=?

Answers

The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

How to determine the equation of the parabola?

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

Answers

It will take 12 hours for 15 men to do same job.

How to determine this?

When amount of hour ∝ 1/number of men

When H represent Hour

And M represent the number of men

k to represent the constant

H = k/M as it is inversely proportional

It takes 10 men 18 hours to repair a road

18 = k/10

k = 18 × 10

k = 180

How long will it take 15 men?

When k = 180

H = k/M

H = 180/15

H = 12 hours