One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer
Answers
One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are
x = 2, x = 3, and x = 4.(0, -6), (2, 0), (3, 0), and (4, 0). RespectivelyWhat are the x-intercepts?Generally, To find the x-intercepts, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:
f(x) = x^3 - 6x^2 + 11x - 6 = 0
To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:
f(x) = (x - 3)(x^2 - 3x + 2)
If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.
To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:
x^2 - 3x + 2 = 0
We can use the quadratic formula to solve this equation:
x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2
This gives us two more x-intercepts at x = 2 and x = 4.
So the x-intercepts of the graph of f(x) are x = 2, x = 3, and x = 4.
To find the y-intercept, we set x equal to 0 and solve for y. In this case, the equation we need to solve is:
f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6
This gives us a y-intercept at (0, -6).
So the y-intercept of the graph of f(x) is (0, -6).
All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).
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Related Questions
The graph below shows the solution to which system of inequalities?
Answers
Which equations have the same solution as the equation 4y - 3 = -2y + 1?
Choose all that apply.
A. 2y-3=1
B. 4y = -2y + 4
C. -3=-6y +1
D8y-3=-4y + 1
E. 8y-6=-4y+2
Answers
Answer:
B and C
Step-by-step explanation:
B = 4y - 3 + 3 = -2y + 1 + 3
= 4y = -2y + 4
C = 4y - 3 -4y = -2y + 1 -4y
= 3 = -6y +1
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
Daniel cuts a 20.75 ft length of wood into two pieces. One piece is 8 1/4 ft. What is the length of the other piece?
Answers
Answer:12.5 ft
Step-by-step explanation:
20.75-8.25
12.5
Answer:
12.5
Step-by-step explanation:
All in standard Notation please :/ 2.09 x 10^5
9.4387 x 10^4
1.3 x 10^-3
Answers
9514 1404 393
Answer:
209,00094,3870.0013Step-by-step explanation:
Write the power of ten in standard form and do the multiplication.
2.09 × 10^5 = 2.09 × 100,000 = 209,000
9.4387 × 10^4 = 9.4387 × 10,000 = 94,387
1.3 × 10^-3 = 1.3 × 0.001 = 0.0013
Situation: Holly wants to save money for an emergency. Holly invests $800 in an account that pays an interest rate of 4%. A = P(1 + r)¹ P = amount of money invested r = interest rate percentage in decimal form How many years will it take for the account to reach $1,600? Round your answer to the nearest hundredth. Enter the correct answer. DONE
Answers
Answer:
t = 74.897 years
(about 74 years 11 months)
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.04/365)] )
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.00010958904109589)] )
t = 74.897 years
Summary:
The time required to get a total amount of $16,000.00 with compoundeded interest on a principal of $800.00 at an interest rate of 4% per year and compounded 365 times per year is 74.897 years.
(about 74 years 11 months)
Since it wasn't stated howmany times the interest is compunded I took the value of once a year.
Based on the model, approximately how many customers will be on the restaurant when there are 10 cars parked in the restaurant’s parking lot?
A - 7
B - 23
C - 12
D - 28
Answers
Answer:
23
Step-by-step explanation:
From the graph, derive the best fit equation :
Using the points ;
(0,2.5) (100 ,35)
x1 = 0 ; y1 = 2.5 ; x2 = 100 ; y2 = 35
Slope formula, m = (y2-y1)/(x2-x1)
m = (35-2.5)/(100-0)
m= (32.5)/100
m = 0.325
The y intercept, value on the graph where best fit line crosses the y axis = 2.5
The equation :
y = mx + c
c = intercept ; m = slope
y = 0.325x + 2.5
y = Number of cars
x = number of customers
The number of customers if there are 10 cars parked :
10 = 0.325x + 2.5
10 - 2.5 = 0.325x
7.5 = 0.325x
x = 7.5 / 0.325
x = 23.076
x = 23
Planes A and B are shown.
m
n
B
MA
If a new line, p, is drawn parallel to line /, which
statement is true?
O
Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line /
O Line p must be drawn in the same plane as line n.
Answers
The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, so option C is correct.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
The given planes are A and B,
A new line, p, is drawn parallel to line l,
Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.
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The image of the remaining question is attached below.
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form.
Answers
Answer:
y=5x-5
Step-by-step explanation:
The slope of the graph is 5 and the Y intercept is (0,-5). Plug into slope intercept form : y=mx+b to get the equation.
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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Which function represents a reflection of f(x) = 3/8 (4)^x across the y-axis?
Answers
A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:
(x, y) → (-x, y).
\(f(x) = \frac{3}{8} (4)^x\) → \(g(x) = \frac{3}{8} (4)^{-x}\)
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Which deduction is optional
Answers
The deduction that is optional is C. Retirement plan deductions.
How is this deduction optional ?When contributing to a retirement plan like a 401(k) or an Individual Retirement Account (IRA), you receive deductions from your taxable income. Essentially, whatever amount of money contributed towards the retirement fund can be subtracted from your total annual income.
Consequently, the entire amount cannot then be seized for taxation purposes. Let's say, for instance that you earn $50,000 annually and contribute $5,000 into your account; this would imply your taxable revenue reduces to $45,000.
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Options for this question are:
A. State taxes B. Federal taxes C. Retirement planD. FICAwhat is 1,623 x 2,908? please help
Answers
Answer:
1,623 x 2,908 = 4,719,684
Answer:
4719684
Step-by-step explanation:
Tell me if you want one.
2
Jerry flips a coin and rolls a six-sided die. What is the probability of getting heads on the coin and an odd number on the die?
A. 1/4
B. 1/2
C. 1/3
D. 1/12
Answers
What is the slope of the line that passes through the
points (2, 6) and (2, 9)?
0
3
undefined
Answers
BD bisects ABC if ABC=6x+58 find ABD
Answers
The measure of the angle ABD is (3x + 29)
What is Bisecting angles?Bisecting angles is the process of dividing an angle into two congruent angles. In geometry, an angle bisector is a line or ray that divides an angle into two equal parts.
When an angle is bisected, each of the two angles formed is called a half-angle or bisector angle, and the point where the angle is bisected is called the vertex of the angle.
Here we have
BD bisects ABC and ∠ABC = 6x+58
When a straight bisect an angle then the measure of the resultant 2 angles will be equal in measure
Here BD bisected ABC
The resultant angles will be ∠ABD and ∠DBC
Hence,
=> ∠ABC = ∠ABD + ∠DBC
=> ∠ABC = ∠ABD + ∠ABD [ Since two angles are equal
=> ∠ABC = 2∠ABD
From the given data,
=> 6x + 58 = 2∠ABD
=> 2 ∠ABD = 2(3x + 29)
=> ∠ABD = (3x + 29)
Therefore,
The measure of the angle ABD is (3x + 29)
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Algebraic Ages
1)
Amy is a years old.
Zack is 7 years older than Amy.
Using a, write an expression for Zack's age.
2)
Bill is b years old.
Vicky is 4 times Bill's age.
Write an expression for Vicky's age.
3)
oo
Cathy is c years old.
Trey is 12 years younger than Cathy.
Write an expression for Trey's age.
Answers
Answer:
1. a7
2.b4
Step-by-step explanation:
Answer:
1. a + 72. 4b3. c _ 12l hope it helps ❤❤A prism is filled with 59 cubes with 1 2 unit side lengths. What is the volume of the prism in cubic units?
Answers
Answer:
V = 2832 m3 only if that 1 2 is a 12 if that is not a 12 it is wrong
Step-by-step explanation:
32 = 25t ^ 2 - 4 round to the nearest tenth
Answers
Answer:
t = 1.2, -1.2
32 + 4 = 25t^2
36 = 25t^2
Root of 36 = root of 25t
6 = 5t
6/5 = t
Therefore t = +-1/2 or +-6/5
Marco needs to buy some dog food. At the nearest store, 6 bags of dog food cost $16.50. How much
would Marco spend on 5 bags of dog food?
Marco would spend $ 52,50) on 5 bags of dog food,
Answers
Answer:
If he spends $52.50 on 5 bags, add $16.50 to $52.50 and get $69.
Irinkers or both? Acme electronics manufactures MP3 players at three locations. The plant 50% of the MP3 players and 1% are defective. The plant at Memphis manu that plant are defective. The plant at Fort Meyers manufactures 20% and 3% If an MP3 player is selected at random, what is the probability that it is defe Refer to Problem 6.101. An MP3 player is found to be defective. What is th manufactured in Fort Meyers?
Answers
The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.
To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.
Given:
Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.
Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.
No information is provided about the defect rate of the third plant.
To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.
Let's calculate the overall probability:
Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)
Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)
To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:
Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)
Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)
Overall probability of selecting a defective MP3 player is given by:
Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)
Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%
Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.
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Evaluate 4!5!/3!7! Simplify as much as possible
Answers
2. Which statement correctly describes the
perpendicular bisector construction below?
Answers
The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer
What is perpendicular bisector?The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.
Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.
In the picture, the main line is GH while JK is the line constructed to bisect the main line
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While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd. The actual number of cattle in the herd was 600.
What was the percent of error, rounded to the nearest percent?
15%
20%
25%
30%
Answers
The solution is, the percent of error, rounded to the nearest percent is 25%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
now, we have to find the percent of error, rounded to the nearest percent.
so, we get,
Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
so, error = 750 - 600
= 150
so, we get,
the percent of error = 150 * 100 / 600
= 25%
Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.
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refer to the attachment and solve
hlo :(
Answers
The other number is -25/2.
What are fractions?A fraction is a non-integer. It consists of numerators and denominators. An example of a fraction is 1/3.1 is the numerator and 3 is the denominator.
What is the other name?In order to determine the other number, divide 10/3 by -4/15
10/3 ÷ -4/15
10/3 x -15/4 = -25/2
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I am planning an ice cream party for 18 students who are allowed to eat 2 scoops of ice cream each. What constraint could affect our equation
Answers
Number of students = 18
Number of scoops allowed per student = 2
If we are to write the total number of scoops that all the students will recive in linear form:
let the total number represent y
A linear form has the form:
y = mx + c
In this question:
y = 2x
Since there is no constant, the c = 0
m= 2 scoops per person
x = number of persons
The constraint that can affect the equation is the number of scoops.
Since we are told each person will only have 2 scoops.
The constraint:
\(0\leq\text{ scoops}\leq\text{ 2}\)This is because we can't have negative number of scoops of ice-cream.
What is the equation of the line that passes through the points (4, -8) and (-8, 1)
Answers
Answer:
y=-3/4x-5
Step-by-step explanation:
1.find the slope 1-(-8)/-8-4=-3/4
2.y-(-8)=-3/4(x-4)
y+8=-3/4x+12/4
y+8=-3/4x+3
y=-3/4x+3-8
y=-3/4x-5
4/5 • 5/4 = 1 Determine the property illustrated.
Answers
The algebraic property illustrated is the commutative property of multiplication
What are the properties of algebra?
The properties of algebra are those properties mostly used in simplifying algebraic expressions.
Algebraic properties are:
Commutative property of additionCommutative property of multiplicationAssociative property of additionAssociative property of multiplicationDistributive Properties of Addition Over MultiplicationFrom the expression given we have
4/5 • 5/4 = 1
= 4/ 5 × 5/ 4
= 1
Thus, the algebraic property illustrated is the commutative property of multiplication
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Question 8 (1 point)
A real estate agent received a 5.5% commission on the sale of a home. If her
commission was $14,960, how much did the home sell for?
Answers
The amount of the sale of the home is $2090181.82
How to determine how much the home sells for?From the question, we have the following parameters that can be used in our computation:
Commission = 5.5% on the sale of a home
Also, we have
Commission = 114960
using the above as a guide, we have the following:
5.5% on the sale of a home = 114960
So, we have
5.5% * sale of a home = 114960
Divide both sides by 5.5%
sale of a home = 114960/(5.5%)
Evaluate
sale of a home = 2090181.82
Hence, the sale of the home is $2090181.82
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Mai says that the equation 2x+2=x+1 has no solution because the left hand side is double the right hand side. Do you agree with Mai? Explain your reasoning.
Answers
Answer:
i do
Step-by-step explanation:
the equation would be no solution if the sides are equal numbers with the same slope and do not intersect. if you plug in a random number such as 7 for x you would get 16 = 8. always making the numbers parrallel