Priya wants to sketch a graph of the polynomial f defined by f(x)=x^3+5x^2+2x-8. She knows f(1)=0, so she suspects that (x-1) could be a factor of x^3+5x^2+2x-8 and writes (x^3+5x^2+2x-8) = (x-1) (?x^2+?x+?) and draws a diagram.
1. Finish Priya's diagram
2. Write f(x) as the product of (x-1) and another factor.
3. Write f(x) as the product of three linear factors.
4. Make a sketch of y=f(x).
Answers
Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.
Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;
18 = 2 x 9
18 = 2 x 3 x 3
18 = 3 x 6
In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.
2. Now, to write f(x) as the product of (x-1) and another factor.
x³+5x²+2x-8 = (x-1)(x²-6x+8).
3. Now, to write f(x) as the product of three linear factors.
x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)
4. Look at the sketch below.
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Related Questions
a man is 18 years older than his son. 3 years ago he was 4 times as old as his son how old is the man now
Answers
Answer:
The man is 27 years old.
Step-by-step explanation:
You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.
3x+2=0 i need the answer quick
Answers
Answer:
[tex]\huge\boxed{\sf x = -2/3}[/tex]
Step-by-step explanation:
Given equation:3x + 2 = 0
Subtract 2 to both sides
3x = 0 - 2
3x = -2
Divide 3 to both sides
x = -2/3
[tex]\rule[225]{225}{2}[/tex]
can someone please help mee(20 points and i will give brainliest!!!)
Answers
Answer:
(5,2)
Maximum
5
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{\:Coordinates of vertex = (5,2)}[/tex]
[tex]\texttt{The graph has a maximum} [/tex]
[tex]\tt \: Axis\:\: of \:\; symmetry : x = 5\ [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Coordinate of vertex is the point where there's a unique (only one) value of y for x :
[tex]\qquad \tt \rightarrow \: (5,2)[/tex]
Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]
and hence, it has a maximum, at the vertex.
Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.
it is the line passing through vertex and parallel to y - axis.
[tex]\qquad \tt \rightarrow \: x = 5[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
0.84(7/6)^x Find the rate of growth/decay.
Answers
In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.
How to determine the rate of growth of an exponential function
In this question we need to analyze an exponential function of the form:
y = a · (1 + r)ˣ (1)
Where r is the growth rate. Please notice that there is a decay for r < 0. Thus, we find the following finding by comparing the given expression to (1):
y = 0.84 · (1 + 1/6)ˣ
In accordance with the comparison of the given expression to the definition of exponential function, we conclude that the rate of growth is 1/6.
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The table of values represents a linear function g(x) where c is the number of days that have passed and g(x) is the balance in the bank account
Answers
After 7 days, the balance will be Rs. 628.
(A) The slope of the given function is 40.
(B) In point - slope form it is y - 600 = 40x
In Slope - intercept form it is y = 40x + 600
In Standard form it is 40x - y + 600 = 0
(C) g(x) = 4x + 600
(D) After 7 days, the balance will be Rs. 628
Let g(x) = y
(A) We know slope = change in y/change in x
= 720-600/3-0
= 120/3
= 40
Therefore, the slope of the given function is 40.
(B) We know that the equation of a line
in point - slope form is y - y₁ = m(x - x₁)
where ( x₁, y₁ ) is a point on the line
where m is the slope
Therefore, substituting the values, we get,
y - 600 = 40(x - 0)
=> y - 600 = 40x --(i)
What is the Slope - intercept form?
Slope - intercept form is y = mx + b
where m is the slope
and b is the y-intercept
To find y intercept, we substitute x = 0 in equation (i)
=> 40*0 - y + 600 = 0
=> -y + 600 = 0
=> y = 600
Therefore, substituting the values, we get,
y = 40x + 600
in Standard form is ax + by = c
where a, b, and c is constant
Converting the equation found above into the standard form
=> y = 40x + 600
=> 40x - y + 600 = 0
(C) As we had assumed g(x) to be y
=> From equation (i),
y - 600 = 40x
can be written as g(x) - 600 = 4x
=> g(x) = 4x + 600 --(ii)
(D) We need to find the balance in the bank account after 7 days
=> Balance [g(x)] when x = 7
Therefore, substituting the value of x in equation (ii)
=> g(x) = 4*7 + 600
= 28 + 600
= 628
Therefore, after 7 days, the balance will be Rs. 628.
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what is b when the slope is 7/6 and the points are (10, -9)
Answers
Answer:
y = 7/6x - 62/3
Step-by-step explanation:
The equation for slope:
y = mx + b
m is the slope and b is the y-intercept
y = 7/6x + b
-9 = 7/6(10) + b
-9 = 35/3 + b
-62/3 = b
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 2
4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.
Enter
Answers
The expected value of the winnings from the game is $4
How to determine the expected value?The payout probability distribution is given as:
Payout ($) 2 4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
The expected value is then calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
This gives
E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05
Evaluate the expression
E(x) = 4
Hence, the expected value of the winnings from the game is $4
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if pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answers
Answer:
can you rephrase it? how many pounds are there?
Step-by-step explanation:
Answer each question below.
14. In angle LMN, the exterior angle adjacent to angle L has a measure of 5x+12. If the measure of angle M= 3x-2 and the measure of angle N= 50. Find the measure of angle L.
Answers
Answer:
[tex]\huge\boxed{\sf L = 78\°}[/tex]
Step-by-step explanation:
Given that:Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
Statement:Exterior angle is equal to the sum of non-adjacent interior angles.So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
Measure of angle M:= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
Measure of angle L:We know that,
Sum of all the interior angles of triangle is 180 degrees.L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
[tex]\rule[225]{225}{2}[/tex]
Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
Answers
The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.
Given the table
x f(x)
-2 -46
-1 -22
0 -10
1 -4
2 -1
We have to choose which statement describes better about function
Let us assume [tex]f(x)=ab^x+c[/tex]
at x=0, f(0)=-10
So, -10 =a+c
Similarly, by satisfying the above table in the f(x)
[tex]f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}[/tex]
[tex]f'(x) > 0[/tex]
So we can say that f(x) is an increasing function.
[tex]g(x) = - 18 (\frac{1}{3} )^ x + 2[/tex]
[tex]g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)[/tex]
ln(1/3) < 0
So, g^ \prime (x) > 0
So, g(x) is an increasing function.
For any x∈f(x) and x∈g(x) [tex]g'(x) > f'(x)[/tex]
So, g increases at a faster average rate
Thus, Both functions are increasing, but function g increases at a faster average rate.
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its math help me out
Answers
Answer:
60 minutes
Step-by-step explanation:
we can see that the number of minutes increases by 8 each day
(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)
So, because we have the value for the previous day (day 6) we know that we can simply add 8
52 + 8 = 60
So, the predicted number of minutes for day 7 is 60
hope this helps!!
John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps. Two times Johan’s collection is eleven less than five times John’s collection, and three times Jonathan’s collection is three less than seven times John’s collection.
Answers
The number of postage stamps in John’s collection is 27.
We have given that,
John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps.
What is an elimination method?The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Johan and Jonathan have the same number of stamps.
Let x be the Johan and Jonathan postal stamps.
Let y be the John postal stamps.
Two times Johan’s collection is eleven less than five times John’s collection.
2x = 5y - 11............(1)
Three times Jonathan’s collection is three less than seven times John’s collection.
3x = 7y - 3............(2)
Multiply equation 1 with 3
3(2x = 5y - 11)
⇒ 6x = 15y - 33.........(3)
Multiply equation 2 with 2
2(3x = 7y - 3)
⇒ 6x = 14y - 6.............(4)
Subtract equation 4 from equation 3
⇒ 6x - 6x = 15y - 33 - (14y - 6)
⇒ 0 = y - 27
⇒ y = 27
Hence, the number of postage stamps in John’s collection is 27.
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There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
Answers
73-22=51
58-29=29
Now add them,
51+29=80
substract the people who uses everything which was
80-11=69
69 in the answer
What is the gradient of the line y = -7x + 13?
Answers
Answer:
y = 7 x - 13. y=7x−13. Swap sides so that all variable terms are on the left hand side. Swap sides so that all variable terms are on the left hand side.7x-13=y. 7x−13=y. Add 13 to both sides. ... 7x=y+13. 7x=y+13. Divide both sides by 7. ... \frac{7x}{7}=\frac{y+13}{7} 77x=7y+13 Dividing by 7 undoes the multiplication by 7.
Step-by-step explanation: hope this helps
Answer:
-7
Step-by-step explanation:
sara scores -4 marks if she got 3 correct answers how many were incorrect
Answers
The number of answers that were incorrect will be 7.
How to depict the information?From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:
3 - x = -4
where x = incorrect answer
3 - x = -4
-x - 4 - 3
-x = -7
x = 7
In conclusion, the number of answers that were incorrect will be 7.
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Where is the error in the proof? select all that aply
Answers
The correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
What is the Linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.
Therefore the correct answer is option D the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
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What decimal is equivalent to ?
7-25
Answers
Explained
7/25
Divide 7 by 25 = .28
Hint: the slash between the 7 and 25 (numerator and denominator) is a division sign
what is equivalent to the given equation -8(x+13)=2(x-7)+4x
Answers
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation;
⇒-8(x+13)=2(x-7)+4x
⇒-8x-13×8 = 2x-2×7+4x
⇒-8x-104=2x-14+4x
⇒-8x-104=6x-14
(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).
Hence, option C is correct.
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How many grains of Fermiun will remain after 15 days? 50 25 12.5 6.25
Answers
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1
Given right triangle QRS, what is the value of sin(30°)?
Answers
The value of sin(30°) is 1/2.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
The diagram is attached below:
We know,
sin 30= Perpendicular/ Hypotenuse.
As, the hypotenuse is the opposite side of the right angle and the perpendicular is opposite to the given angle.
So,
sin 30 = 5/10
sin 30 = 1/2
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The ratio table shows the numbet of miles karen can drive for 1,2,3 and 4 gallons of gasoline.Based on the table, How far would she be able to drive on 8 gallons of gasoline
Answers
Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:
D(n) = 30n.
She has n = 8 gallons, hence the distance is given by:
D(8) = 30 x 8 = 240 miles.
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A line with slope 2 passes through the point (2, -4). Find the coordinates of another point on the line.
Answers
Answer:
(3, -2)
Step-by-step explanation:
We can view slope as: [tex]\frac{rise}{run}[/tex] (rise / run)
"rise" is the change in y from one point to another
"run" is the difference in x from one point to another
So, if the slope of a line is 2, it rises 2 every time it runs 1 (2 = 2/1)
So, we can find another point on the line by adding 2 to the y-value, and adding 1 to the x-value.
(x, y)
(2, -4)
+ 1 + 2
(3, -2)
So, another point on this graph is (3, -2)
Hey guys need help here
Answers
Answer:
[tex]\boxed {D) -\frac{2y}{x}}[/tex]
Step-by-step explanation:
Solving :
[tex]\implies \mathsf {\frac{(-2xy^{2})^{3}}{4x^{4}y^{5}}}[/tex]
[tex]\implies \mathsf {\frac{-8x^{3}y^{6}}{4x^{4}y^{5}}}[/tex]
[tex]\implies \mathsf {\frac{-2y}{x}}[/tex]
Evaluate the function when x = - 2, 0 and 5.
Answers
[tex]h(x) = - x - 7 \\ \\ when \: x \: is \: - 2 \\ h(x) = - ( - 2) - 7 \\ h(x) = 2 - 7 \\ h(x) = - 5 \\ \\ when \: x \: is \: 0 \\ h(x) = 0 - 7 \\ h(x) = - 7 \\ \\ when \: x \: is \: 5 \\ h(x) = - 5 - 7 \\ h(x) = - 12[/tex]
Consider a political discussion group of 8 democrats, 8 republicans and 6 independent suppose the teo groups meme bet are randomly selected in succession to attend a policial convection find the probability of selecting two demo
Answers
Answer:
The probability of selecting two democrats is 1/380
Step-by-step explanation:
Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.Probability of an event = Number of favourable outcomes / Total number of outcomes.Here we are given the people as,
8 democrats, 8 republicans and 6 independent.
So total number of people are: 8+6+6=20
Probability of choosing first democrat = 1/20
Probability of choosing first democrat = 1/19
Thus P( two democrats in succession ) = 1/20 ×1/19
= 1/380
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The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is required to make 1 litre of fuel?
Answers
The amount of oil required for 1 liter of fuel is 111.11 mL.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.
The total part of the fuel is 8+1=9
the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9
the portion of the oil = parts of oil /total parts of the fuel= 1/9
Now we have to calculate the amount of oil required for 1 liter of fuel.
As discussed before, 1/9 parts of the fuel is oil.
So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL
Similarly, we can calculate the amount of petrol which will be
the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL
Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.
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This is a sketch of the curve with equation y = f(x).
The curve has a minimum point at M(-1, -3).
Write down the coordinates of the minimum point
of the curve with equation
y = f(x) - 2
Answers
Answer:
(-1, -5)
Step-by-step explanation:
Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.
A point on the shifted graph will be ...
(x, f(x) -2)
Then for x = -1, the point is ...
(-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)
The minimum on the shifted curve is M'(-1, -5).
_____
Additional comment
f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.
Which phrase best describes the relationship indicated by the scatter plot?
OA constant correlation
B. negative correlation
C. positive correlation
D. no correlation
Answers
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
Phrase D best describes the relationship indicated by the scatter plot. There is no correlation.
Hence option D is correct.
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Answer:
no correlation
Step-by-step explanation:
The equation of a line is -2x+5y = -20
What’s the x-intercept of the line?
Answers
Y = mx + c
What is the value of x/2 + 4 when x = 6?
Answers
Step-by-step explanation:
solution:
here,
x/2+4
= 6/2+4 ( x = 6 )
= 3+4
= 7
Answer:
7
Step-by-step explanation:
x/2 + 4
=> 6/2 + 4 (x=6)
=> 3 + 4
=> 7
