Mathematics High School

Given f(x)=x^3-6x^2+9x and g(x)=4.
Find the coordinates of the points common to the graphs of f and g.
-find all zeros of f
-if the domain of f is limited to the closed interval [0,2], what is the range of f?

Answers

Answer 1

To find the coordinates of the points common to the graphs of f and g, set f(x) equal to g(x) and solve for x. The zeros of f(x) are approximately x = -1, 2, and 2.98. The range of f when the domain is limited to [0,2] is approximately [-1,9].

To find the coordinates of the points common to the graphs of f and g, we will set f(x) equal to g(x) and solve for x.

f(x) = g(x)

[tex]x^3-6x^2+9x = 4\\x^3-6x^2+9x-4 = 0[/tex]

Using a graphing calculator or software, we can find that the zeros of f(x) are approximately x = -1, 2, and 2.98.

The range of f when the domain is limited to the closed interval [0,2] is the set of y-values that f(x) takes on within that interval.

By using the First Derivative Test, we can determine that the range of f in the interval [0,2] is approximately [-1,9].

Related Questions

eremy is working at 2 jobs to save money for his college education. He makes $8 per hours working for his uncle at Pizza Pie busing tables and $10 per hour tutoring peers after school in math. His goal is to make $160 per week. Part c- After researching the costs of colleges, Jeremy decides he needs to make more than $160 each week. Write an inequality in two variables to represent the amount of money Jeremy needs to make. Then graph.

Answers

If "p" is the number of hours Jeremy works at Pizza Pie, then 8p is the number of dollars he makes from Pizza Pie. In the same way, if "m" is the number of hours he spends tutoring math, then 10m is the amount of money he makes from tutoring math. Together, he makes 8p + 10m dollars each week. But Jeremy needs that amount of money to be MORE than $160. So that becomes the inequality... 8p + 10m > 160 You can graph it by using "m" as one axis and "p" as the other.

Final answer:

Jeremy needs to create an inequality to represent his new earning goal higher than $160 a week, leading to the inequality 8x + 10y > 160. This can be graphed by first converting to intercept form, plotting the intercept and slope, drawing a dashed boundary line, and shading the region above this line.

Explanation:

Jeremy is working two jobs to save for his college education and needs to create an inequality to represent the amount he needs to make each week, now more than $160. Let's denote the number of hours Jeremy works busing tables as x and the number of hours he spends tutoring as y. He makes $8 per hour busing tables and $10 per hour tutoring.

To express Jeremy's goal of making more than $160 a week, we can write the following inequality:

8x + 10y > 160

To graph this inequality:

First, rewrite the inequality as y > (-4/5)x + 16 to get the intercept form.

Plot the y-intercept at (0, 16) on the graph.

Use the slope of -4/5 to determine another point. From (0, 16), move 5 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point.

Draw a dashed line through the two points to represent the boundary of the inequality (dashed because the inequality is strict and does not include the line itself).

Shade above the line to indicate that all solutions to the inequality lie in this area, where Jeremy would be earning more than $160.

6 times the sum of 3 consecutive odd intergers is -18

Answers

The answer: The 3 (three) consecutive odd integers are: -3, -1, 1.
_____________________________________________
Explanation:
_______________
To represent 3 (three consecutive odd integers):
____________________________________
Let "x" be the first odd integer.
____________________________________
Let "(x+2)" be next consecutive odd integer.
____________________________________
Let "(x+4") be the third odd integer.
____________________________________
The sum of these three consecutive odd integers:
__________________________________________
x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ;
_________________________________________
Six ("6") times the sum of these 3 (three) consecutive odd integers =
_________________
6*(3x+6) = 6(3x + 6) = -18 (as given in the problem).
_____________________________________________
Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1"; 
__________________________________________
{6(3x + 6) } / 6 = -18 / 6 ;  to get:
________________________________________
3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation:
__________________________________
3x + 6 - 6 = -3 - 6 ; to get:
__________________________________
3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ;
___________________________________
3x / 3 = -9 / 3 ;  x = - 3 ;
_____________________
Remember, from above:
__________________________
Let "x" be the first odd integer.  We know that "x = -3".
         Is this an odd integer? Yes!
____________________________________
Let "(x+2)" be next consecutive odd integer.  So (x+2) = (-3+2) = -1.
        Is this an odd integer? Yes!  Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes!
____________________________________
Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1.
       Is this an odd integer? Yes!  Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes!
___________________________
So, our 3 (three) consecutive odd integers are: -3, -1, 1.
___________________________
To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?

The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.

6 * -3 = ? -18? Yes!
___________________________





What describes each face on a dodecahedron?


A. equilateral triangle B. equilateral pentagon C. circle D. square ...?

Answers

The correct answer for this question would be option B. EQUILATERAL PENTAGON is the description of each face on a dodecahedron. A dodecahedron is also known as a pentagonal dodecahedron and it is composed of twelve regular pentagonal faces. It is also one of the five Platonic solids. Hope this answer helps. 

Find each unit cost
$12 for 4 square yards
$3.45 for 3.7 oz
$9 for 5 L

Answers

$3 for 1 square yard
$0.93 for 1 oz
$1.8 for 1 L

Express this amount in dozens. (Use decimal form.) 7.5 cupcakes
...?

Answers

0.625 dozen

1/12 x 7.5
= 0.625



Choose what the expressions below best represent within the context of the word problem.

The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?

x best represents .

x + 12 best represents .

Answers

I hope this helps you
The question is what both experssions best represent in the context of the problem.

The expresssion x best represents the width of the rectangle.

The expression x + 12 best reprents the lenght of the rectangle.

This is because if you call x the width, then the length is 12 more than that, i.e. 12 + x.

If you wanted to solve the problem now you could write

2*(width + length) = perimeter

2(x + 12 + x) = 24 and solve for x.

But the answer to the question is:

x best represents the width of the rectangle.

x + 12 best reprents the lenght of the rectangle.


what is the highest common factor of 630 and 1560

Answers

The highest common factor of 630 and 1560 is 30.

630, 1560 | 10
63, 156 | 3
21, 52

Now you multiply 10 by 3 and you get 30. Thirty is the highest number that you can use to divide these two numbers.

A student reads 3/5 of a book in 30 minutes. if the student is reading at the same speed in 40 minute how much of the book will the student read

Answers

He will read 4/5 of the book in 40 minutes

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
If we set the vertex at (0,0) then the curve goes through (30,30) 

y = 1/30 x^2 
x^2 = 30y 

Since the parabola x^2 = 4py has its focus at y=p, 4p=30 and the mic should be 15/2 inches up from the vertex.

solve the equation for y 2x+6y=13

Answers

I hope this helps you



6y=13-2x


y=13-2x/6


y=13/6-1/3x
So here is how we are going to solve for y for the given equation above:
2x+6y=13
Next, transfer 2x to the right side and it will look like this:
6y=13-2x
Now, divide both sides by 6, and it will look like this:
y=13-2x
    --------
       6
So, this is the final answer for y.
Hope this answers your question. Have a great day!

A boat, whose speed in still water is 1.96 m/s, must cross a W = 217 m wide river and arrive at a point D = 111 m upstream from where it starts, as shown in figure below.


To do so, the pilot must head the boat at a 42.9° upstream angle. What is the speed of the river's current?

Answers

if u resolve the inital velocity then u will get the vertical component to be 1.96*cos 42.9 = 0.732 * 1.96=1.434 m / s time taken to cross = 217 / 1.434=151.32seconds distance travelled in x direction = 111m initial velocity in x direction = - 1.96 * sin 42.9 = = -0.680 *1.96= - 1.33 disance = speed * time d = (v of current + velocity of man) * time 111= (v - 1.33)* 151.32 v - 1.33 = 0.733 v= 1.33 + 0.73 = 2.063

If total Revenue is $3000, Cost of Goods is $1500, and total Selling Expense is $500; what is the Profit for the business?

Answers

I would like to see the multiple questions, but i'll try to help.Total Revenue $3000. Cost of goods is $1500. And total selling is $500. What is the profit. $3000 + $ 1500 =$4,500 - $500 = $4,000 Profit. I hope this is correct.
Profit= Total Revenue- Cost of goods- operating expense so the total Profit is $1,000

Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.

How many points was each multiple choice question worth?

Answers

My solution here is as follows:

The scores were the same, so 

18m+19 = 15m+31 

Now solve for m, the # points for each multiple-choice question.

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

Answer:

Each question had 4 points.

Step-by-step explanation:

Let the questions be x points each. As both Gretchen and Ezia received equal scores, we can write the equation as:

18x+19=15x+31   (Let the questions be x points each)

Solving for x;

[tex]18x-15x=31-19[/tex]

=> [tex]3x=12[/tex]

Dividing both sides by 3;

x = 4

Hence, each question had 4 points.

HELLPP MEE PLEAASSEEE!!????
Is ABC DEF?
If so, name the postulate that applies.

A. congruent - SAS
B. congruent - ASA
C. congruent - SSS
D. might not be congruent

Answers

They are congruent by SAS

Devil has 39 toy blocks what is the value of the digit nine in this number

Answers

its the unit 

hope this helps you

Rewrite the following without an exponent ₋7⁻¹.

Answers

The solution to the answer is as follows:

-7^-1 = -1/7

The expression without an exponent would be simplified to be -1/7.


I hope my answers has come to your help. Thank you for posting your questions here in Brainly. We hope to answer more of your inquiries son. God bless and have a nice day ahead!

.
Which of the following is the correctly abbreviated SI unit describing the amount of a substance?




M



kg



mol



g

Answers

the amount of substance unit is mol, the answer is c

what is the GCF of 9, 27,and 63

Answers

The answer is 3.
3×3=9
3×9=27
3×21=63
The factors of 9 are 1,  3,  and 9 .

The factors of 27 are 1,  3,  9,  and 27 .

The factors of 63 are 1,  3,  7,  9,  21,  and 63 .

The common factors of 9, 27, and 63 are 1,  3,  and 9.

Their greatest common factor is  9  .

Which of the following are true statements?

Check all that apply.

A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
B. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it horizontally by a factor of 1/2.
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
D. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it vertically by a factor of 1/2.
...?

Answers

Answer:

A

C

Step-by-step explanation:

Here we must compare a function and its transformation, we will see that the correct options are A and C.

First, we must define the transformations that we will be using here.

Reflection about the x-axis:

For a function f(x) a reflection about the x-axis is written as:

g(x) = -f(x)

Vertical contraction.

For a function f(x) a vertical contraction of scale factor k is written as:

g(x) = k*f(x)

So here we start with:

ƒ(x)=√x

Then we reflect it about the x-axis to get:

ƒ(x)=-√x

Then we shrink it by a scale factor k = 1/2

ƒ(x) = (-1/2)*√x

From this, we can see that the correct options are:

A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.

And C is also true, because we have a reflection about the x-axis, the range changed from positive values to negative values, so:

C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.

Is also a correct option.

If you want to learn more, you can read:

https://brainly.com/question/14536884

$9.00 for 3 pairs of socks

Answers

Sounds like your paying 3 dollars for each pair of socks. 

Benny has saved 42 quarters from washing cars how many cents does Benny have

Answers

We Know, 1 quarter = 25 cents
Then, 42 quarter = 25 * 42  = 1050 cents

So, he saved 1050 cents

Hope this helps!
Um, well if you do 42 x.25 =10.50$. So 1050¢ Hope this helps!

whats the anserr becuse i got this wrong on a home work sheet

Answers

Well to demonstrate the answer, let's look at a basic example:

Sq root of 2^2 = ?
Well 2 ^2 = 2•2 = 4 and the square root of 4 is 2. So whenever you think of what the opposite of squaring or raising something to the value of 2, the reverse would be taking the square root of the number or expression.

So sq root of 14x • sq. root of 14x = (sq. root of 14x) ^2 which is simply 14x.

The solution is 14x.

If a 100(degree) arc of a circle has a length of 8 inches, to the nearest inch, what is the radius of the circle?

Answers

 100(degree) arc of a circle has a length og 8 inches what is og

Which number sentence should be used to solve this problem? Ethan collected 30.4 pounds of recycling in June. He collected 35.5 pounds in July.

How many more pounds of recycling did Ethan collect in July than June?

A.
30.4 + 35.5 = ?

B.
35.5 - 30.4 = ?

C.
30.4 - 35.5 = ?

D.
35.5 + 30.4 = ?

Answers

The answer is B. 35.5 - 30.4=5.1

He collected with 5.1 more pounds in July than in June

triangle PQR is similar to Triangle TUV. the perimeter of triangle PQR is 60 inches. what is the perimeter of triangle TUV?

Answers

I'm assuming you don't know the definition of similarity, which is fine, but I want to clarify just in case you don't: Similarity is when two figures are the same in angles ONLY, and their sizes are proportional. Given this, PQR has a side 20" and TUV's respective side is 6". Now, there's a ratio: 20:6 Now, would you agree that it would then be logical that the perimeter would follow the same ratio? Where 60:P(TUV)? Hope this helps some!

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = s/180 + 2.

Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?

_______ sides

Answers

s = 180° ( n - 2 )
The equation for n is:
 n = s / 180°  + 2
 s = 1,260°
 n = ( 1,260° : 180° ) + 2 = 7 + 2 = 9
Answer:
A polygon has 9 sides.

the answer is 9 hope it helps

Rewrite the fraction as a decimal 57/5

Answers

57/5 as a decimal would be 11.4
Hope this helped!!
it is 11.4

hope this helps you

Deshaun went for a drive in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. For how many hours did he drive?

Answers

62/1  99.2/x 
99.2/62 = x
The answer is 1.6 hours.

Deshaun drove at a speed of 62 miles per hour for 99.2 miles. To calculate the time spent driving, use the formula Time = Distance / Speed. The time taken for his drive is approximately 1.6 hours.

The question pertains to calculating the driving time given the speed and distance traveled by Deshaun in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. To find out how many hours he drove, we use the formula for time which is:

Time (t) = Distance (d) / Speed (v)

Here, the distance d is 99.2 miles and the speed v is 62 miles per hour.

So we calculate the time t as follows:

t = 99.2 miles / 62 miles per hour

The time taken by Deshaun for his drive is approximately 1.6 hours.

Suppose the first term of a geometric sequence is multiplied by a nonzero constant, c. What happens to the following terms in the sequence? What happens to the sum of this geometric sequence? (This question has one right answer.) Give an example of a geometric sequence to illustrate your reasoning. (Many answers are possible.)

Answers

the next  terms in the sequence will be multiplied by c, but the common ratio is still the same

example :

S = [1(3)^4 - 1]/ [3-1]  = 80/2 - 40

Hope this helps

A test for the presence of a certain disease has probability 0.2 of giving a false-positive result (indicating that an individual has the disease when this is not the case) and probability 0.1 of giving a false-negative result. Suppose that 10 individuals are tested, 5 of whom have the disease and 5 whom do not. Let X be the number of positive readings that result.

a. Explain why X does not have a binomial distribution.

b. Find the probability that exactly 3 of the 10 test results is positive?

Answers

For the part b of the question please find the attached image.
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An author uses a road to symbolize a character's journey. It is an unpaved road that is covered with rocks, holes, and mud. What type of journey does the road most likely symbolize? (5 points) A journey that leads to great riches A journey that offers many choices A journey that presents many challenges A journey that proves very easy 1)A discriminant of 0 indicates what type of roots?A)Two ComplexB)One Rational DoubleC)Two RationalD)Two Irrational2)The quadratic 2x2 + 6x + 3 has what type of roots?A)Two IrrationalB)Two ComplexC)One Rational DoubleD)Two Rational3)The quadratic x2 + 20x + 100 has what type of roots?AnswerA)Two IrrationalB)Two RationalC)One Rational DoubleD)Two Complex4)What is the possible discriminant of the graph?(graph in the link)A)0B)11C)73D)255)What is the possible discriminant of the graph?(Graph in the link)A)0B)17C)25D)15 ...? URGENT MATH HELP!Which shows the conversion of 0.21 millimeters to inches? There is 0.03937 inch in 1 millimeter. 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