Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
The binomials x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
How to derive the equations of the factors of a polynomial
Herein we know the x-values of a polynomial such that the expression is equal to zero. Mathematically speaking, these x-values are known as roots and the mathematical expressions that contain them are known as factors, which are represented by binomials of the form:
a · r - b = 0
Where a, b are real coefficients.
If we know that x₁ = 4, x₂ = - 1, x₃ = 3 / 2, then the factors of the polynomials are listed below:
x₁ = 4:
x - 4 = 0
x₂ = - 1:
x + 1 = 0
x₃ = 3 / 2
2 · x - 3 = 0
x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
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Related Questions
Given the functions f(x) = x ^ 2 + 3x - 1 and g(x) = - 2x + 3 determine the value of (f + g)(- 2)
Answers
Start by finding (f+g)(x)
[tex](f+g)(x)=(x^2+3x-1)+(-2x+3)[/tex]simplify the equation
[tex]\begin{gathered} (f+g)(x)=x^2+(3x-2x)-1+3 \\ (f+g)(x)=x^2+x+2 \end{gathered}[/tex]then, replace x by -2
[tex]\begin{gathered} (f+g)(-2)=(-2)^2+(-2)+2 \\ (f+g)(-2)=4-2+2 \\ (f+g)(-2)=4 \end{gathered}[/tex]Which equation could be represented by the number line? A. 3 OB.-4 5=1 OC. 1+ -5)= OD. -3+4 -1
Answers
According to the given number line, we have to go back from the second point to the first point 4 spots. In other words, the equation has to include a sum with -4.
Therefore, the answer is A since it's expressing an initial number 3, then the sum with -4.if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years?
Answers
Solution:
From the question, we use the population decay formula expressed as
[tex]\begin{gathered} P(t)=P(1-r)^t \\ where \\ P\Rightarrow initial\text{ population} \\ r\Rightarrow decay\text{ rate} \\ t\Rightarrow time \\ P(t)\Rightarrow population\text{ at time t} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} P=158000 \\ r=8\%=\frac{8}{100}=0.08 \\ t=5 \end{gathered}[/tex]By substituting these values into the population decay formula, we have
[tex]\begin{gathered} P(t)=158000(1-0.08)^5 \\ =104134.88066 \end{gathered}[/tex]Hence, the population in 5 years will be
[tex]104134.88066[/tex]Jordan’s of Boston sold Lee Company of New York computer equipment with a $7,000 list price. Sale terms were 4/10, n/30 FOB Boston. Jordan’s agreed to pay the $400 freight. Lee pays the invoice within the discount period. What does Lee pay Jordan’s?
Answers
I’m sorry to hear about your issues. When a vendor invoice includes terms of 4/10, n/30, the "4" represents 4% of the amount owed, the "10" represents 10 days, the "n" represents the word "net," and the "30" represents 30 days. The terms 4/10, n/30 indicate that the buyer may take an early payment discount of 4% of the amount owed if the amount owed is remitted within 10 days instead of the normal 30 days. In other words, the buyer can choose either of the following:
Pay within 10 days and deduct 4% of the net amount owed (the invoice amount minus any authorized returns and/or allowances), or
Pay in 30 days and take no discount.
Free On Board (FOB) Contract is a trade term requiring the seller to deliver goods on board a vessel designated by the buyer. When used in trade terms, the word "free" means the seller has an obligation to deliver goods to a named place for transfer to a carrier. That is not relevant to the price though.
So Lee would be paying $7000 with a 4% discount; or $280 off. So Lee would pay $6,720 if Jordan pays the freight.
I do certainly hope you find this information helpful. My goal is to make sure you are satisfied with the information provided. In the event you have any further questions or need further information, I am going to be available for the next few hours.
A recycle bucket weighs 3.5 lb at the beginning of the school year in August. At the beginning of December it weighed 21.5 lb. Determine the weight gain per month.
Answers
Answer:
4.5 pounds
Step-by-step explanation:
21.5 - 3.5 = 18
We divide that by 4 (Aug., Sept, Oct. Nov.)
18/4 = 4.5
Answer:
6.144
Step-by-step explanation:
In a class of 36 students, 25
study Chemistry, 22 study
Maths and 25 study Physics, 17
study Physics and Maths,18
study Physics and Chemistry
and 15 study only one of the
three subjects. Find the;
a) number of students who
study all three subject?
b) number of students who
study only Maths and
Chemistry?
c) Probability that a student
selected at random study only
two of the three subjects?
Answers
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = 1/36
Define Probability
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
As it is given total number of students is = 36
The subject are Physics, Maths, and Chemistry
Let, physics = p
maths = m
chemistry = c
The possible combination are,
p, c, m, pm, cp, cm, pcm (means 7 combination total)
Let x be the number of student who study all three subjects.
The students who study physics and maths = 17 - x
The students who study physics and chemistry = 18 - x
The number of student who study physics = 25
Now, with the expression we can find the students who study only physics
25 - ((x) + (18 -x) + (17- x))
⇒25 - (x + 18 - x + 17 - x)
⇒25 - (35 - x)
⇒25 - 35 + x
⇒x - 10
Let y be the number of student only chemistry and mathematics.
Now, with the expression we can find the students who study only chemistry
25-(x + (18- x)) + y
⇒25 - 18 + y
⇒ 7 - y
Now, with the expression we can find the students who study only maths
22 - (x + (17 - x)) + y
⇒ 22 - 17 + y
⇒ 5 - y
The possible combination and expression for each
pcm → x
cm → y
pc → 18 - x
pm → 17 - x
p → x - 10
c → 7 - y
m → 5 - y
____________
Total → 37 - y
But the number of students is 36 , so y = 1
That means,
The number of student who take only chemistry = 7 - y
= 7 - 1 = 6
The number of student who take only maths = 5 - y
= 5 - 1 = 4
The 15 students takes only one of the three subject
the number that take only physics is 5
so, x - 10 = 5
x = 15 (the student who takes all 3 subjects)
The student who takes only physics and chemistry = 18 - x
= 18 - 10 = 3
The student who takes only physics and Maths = 17 - x
= 17 - 15 = 2
To cross check put the values of x and y,
pcm → 15
cm → 1
pc → 3
pm → 2
p → 5
c → 6
m → 4
____________
Total → 36
Therefore, the answers :
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = ( 3 + 1 + 2) / 36 = 1/36
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find the solution of this system of equations-7y=-34-2x2x+4y=10
Answers
we have the system
-7y=-34-2x ------> equation A
2x+4y=10 ------> equation B
In the equation A
Multiply by -1
-2x+7y=34------> new equation A
Adds new equation A and equation B
-2x+7y=34
2x+4y=10
------------------
7y+4y=34+10
11y=44
y=4
Find the value of x
Substitute the value of y in equation A or equation B
2x+4(4)=10
solve for x
2x+16=10
2x=10-16
2x=-6
x=-3
therefore
the solution is the point (-3,4)What is the value of y in the solution set of the system of linear equations shown below?y = -x + 124x - 2y = 36A.10B. 8C. 6D. 2
Answers
y = 2 (option D)
Explanation:y = -x + 12
4x - 2y = 36
rewriting the equations:
y + x = 12 ....equation 1
-2y + 4x = 36 ....equation 2
Using elimination method:
we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.
2y + 2x = 24 ....equation 1
-2y + 4x = 36 ....equation 2
Add both equations:
2y + (-2y) + 2x + 4x = 24 + 36
2y-2y + 6x = 60
6x = 60
x = 60/6 = 10
Insert the value of x in any of the equation. Using equation 2:
4(10) - 2y = 36
40 -2y = 36
-2y = 36 - 40
-2y = -4
y = -4/-2
y = 2 (option D)
Find the limit. (If an answer does not exist, enter DNE.)
Answers
Given:
[tex]\lim _{\Delta x\to0}\frac{6(x+\Delta x)-6x_{}}{\Delta x}[/tex]Solve as:
[tex]\begin{gathered} \lim _{\Delta x\to0}\frac{6x+6\Delta x-6x}{\Delta x}=\lim _{\Delta x\to0}\frac{6\Delta x}{\Delta x} \\ =6 \end{gathered}[/tex]Hence, the required answer is 6.
the following augmented matrix is in row-echelon form and represents a linear system. solve the system by using back-substitution if possible.
Answers
Given the matrix:
Given that it represents a linear system, we have the set of equations:
(1)x + 3y = 6
0x + (1)y = -1
x + 3y = 6..................equation 1
y = -1.........................equation 2.
Let's solve the system using substitution method.
Substitute -1 for y in equation 1:
x + 3(-1) = 6
x + (-3) = 6
x - 3 = 6
Add 3 to both sides:
x - 3 + 3 = 6 + 3
x = 9
From equation 2, we have the value of y:
y = -1
Therefore, the solution to the system is:
x = 9, y = -1
In point form:
(x, y) ==> (9, -1)
ANSWER:
x = 9, y = -1
f (x) = 4x^2+2x+6find the value of the discriminate of f and how many distinct real number zeros f has.
Answers
The Solution:
Given:
Required:
To find the discriminant of f.
By formula, the discriminant (D) is:
[tex]D=b^2-4ac[/tex]Where:
[tex]\begin{gathered} a=4 \\ b=2 \\ c=6 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} D=2^2-4(4)(6)=4-96=-92 \\ No\text{ real root since D}<0 \end{gathered}[/tex]Therefore, the correct answers are:
Discriminant = -92
No distinct real root.
Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth
Answers
We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:
[tex]\begin{gathered} 1.5x-3y=7\to y=0 \\ 1.5x-3\cdot(0)=7 \\ 1.5x=7 \\ x=\frac{7}{1.5} \\ x\approx4.67 \end{gathered}[/tex]The x value of the x-intercept of the equation is approximately 4.67.
This is a linear equation, to build the graph we just need 2 points and join them with the line.
The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:
[tex]\begin{gathered} 1.5x-3y=7\to x=0 \\ 1.5\cdot(0)-3y=7 \\ -3y=7 \\ y=\frac{-7}{3} \\ y\approx-2.33 \end{gathered}[/tex]With this, the other point we can use to graph the equation is (0, -2.33).
Drawing both points on a cartesian plane:
Both points (x and y-intercepts) are drawn in red.
Suppose that you earn $15
Answers
Answer: 800 hours
Step-by-step explanation:
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write?
Answers
From the question, It takes Ary an hour to write one thank you card.
So, the rate at which she writes the thank you card is;
[tex]\text{Rate R}=1\text{ card/hour}[/tex]To determine the number N of thank you card she would write in 8 hours.
[tex]N=R\times T[/tex]Where;
R is the rate = 1 card/hour
T is the time taken = 8 hours
Substituting the values we have;
[tex]\begin{gathered} N=1\text{ card/hour}\times8\text{ hours} \\ N=8\text{ cards} \end{gathered}[/tex]The number of thank you cards she write is 8 cards
I need help on this
Answers
To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]9. Solve the system of equations algebraically. Show your reasoning.2y = x -44x + 3y = 5
Answers
I) 2y = x - 4
II) 4x + 3y = 5
First, we put all the variables on the same side subtracting x from both sides of equation I:
I) 2y - x = -4
II) 3y + 4x = 5
Now, we multiply equation I by 4:
I) 8y - 4x = -16
II) 3y + 4x = 5
Then, we add equation I to equation II:
I) 8y - 4x = -16
II) 11y = -11
Therefore, we got from equation II:
y = -11/11 = -1
Applying this result on equation I, we got:
-8 - 4x = -16
4x = 8
x = 8/4 = 2
Final answer: (x,y) = (2,-1)
Hi, can you help me to solve this exercise please, it’s about Function Evaluation & Applications!
Answers
Given
[tex]f(x)=\lvert x\rvert+4[/tex]Part A
[tex]\begin{gathered} we\text{ want to find f(4)} \\ we\text{ only n}eed\text{ to substitute the value of 4 to x in the given function} \\ f(4)=\lvert4\rvert+4 \\ f(4)=4+4_{} \\ f(4)=8 \end{gathered}[/tex]Part B
[tex]\begin{gathered} we\text{ want to evaluate f(-4)} \\ \text{note that the absolute value returns postive values} \\ \text{thus, }\lvert-4\rvert=4 \\ f(-4)=\lvert-4\rvert+4 \\ f(-4)=4+4 \\ f(-4)=8 \end{gathered}[/tex]Part C
[tex]\begin{gathered} To\text{ find f(t), we only n}eed\text{ to replace t with x} \\ f(t)=\lvert t\rvert+4 \end{gathered}[/tex]If the price of bananas goes from $0.39 per pound to $1.06 per pound, what is the likely effect of quantity demanded?
Answers
When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.
What is demand?The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.
Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.
A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.
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Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Answers
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
May I please get help finding the length to this. I tried many times.m but I couldn’t find answer for it
Answers
Both triangles are similar, so:
[tex]\frac{x}{3}=\frac{6}{4.5}[/tex]Solving for x:
4.5x = 3(6)
4.5x = 18
x = 4
2x^2 +6x=-3 can you compute this?
Answers
The general formula for a quadratic equation is ax² + bx + c = 0.
To solve
[tex]2x^2+6x=-3[/tex]You can follow the steps.
Step 01: Write the equation in the general formula.
To do it, add 3 to each side of the equation.
[tex]\begin{gathered} 2x^2+6x+3=-3+3 \\ 2x^2+6x+3=0 \end{gathered}[/tex]Step 02: Use the Bhaskara formula to find the roots.
The Bhaskara formula is:
[tex]x=\frac{-b\pm\sqrt[]{\Delta}}{2\cdot a},\Delta=b^2-4\cdot a\cdot c[/tex]In this question,
a = 2
b = 6
c = 2
So, substituting the values:
[tex]\begin{gathered} \Delta=b^2-4\cdot a\cdot c \\ \Delta=6^2-4\cdot2\cdot3 \\ \Delta=36-24 \\ \Delta=12 \\ \\ x=\frac{-6\pm\sqrt[]{12}}{2\cdot2} \\ x=\frac{-6\pm\sqrt[]{2\cdot2\cdot3}}{4} \\ x=\frac{-6\pm2\cdot\sqrt[]{3}}{4} \\ x_1=\frac{-6+2\sqrt[]{3}}{4}=\frac{-3+\sqrt[]{3}}{2} \\ x_2=\frac{-6-2\sqrt[]{3}}{4}=\frac{-3-\sqrt[]{3}}{2} \end{gathered}[/tex]Answer:
Exact form:
[tex]x=\frac{-3-\sqrt[]{3}}{2},\frac{-3+\sqrt[]{3}}{2}[/tex]Decimal form:
[tex]x=-2.37,\text{ -0.63}[/tex]Gina want to estimate the total of three bills she has to pay. the bills are for $125,$115,and $138. Gina wants to make sure that she has enough money. she wants the estimate to be greater than the total of the bills. should she round to the nearest ten or hundred
Answers
The bills are:
125
115
138
Since she wants an estimate that is greater than the actual total, she can round these numbers to the nearest ten.
125 will be rounded to the next tens, which is 130
115 will also be rounded to the next tens, which is 120
138 gets bumped to the next tens, that is 140
The total estimate is the sum of the 3 estimates we just made. That is:
130 + 120 + 140 = $390
A side of the triangle below has been extended to form an exterior angle of 133º. Find the value of x. 133° 21° xo
Answers
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
so we have the next equation
21+x+(180-133)=180
21+x+47=180
x=180-21-47
x=112°
helpppppppppppppppppppppppppppppp
Answers
skill issue hahahahahhaahahhahaha
Why can the big candy makers produce candy that is less expensive per piece
Answers
Answer:
Step-by-step explanation:
The reason behind the big candy makers producing candy that is less expensive per price is that the cost that they have to bear for production will be less in comparison to small candy makers.
bc a lot of people buy their products, so they have enough money to make a profit even if they sell it at a lower cost.
What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
Answers
The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]Pattern Exercise Mins Components Fitnes 0 5 1 9 2 25 3 89 4 ? What do you notice about the pattern of components from minute to minute? 2. State the value for the question mark. I E O BI
Answers
We can calculate how much each component increases, this is shown in the following image:
So we can see that the pattern in which the components increase from minute to mites is that starts by adding 4, then they add 4x4=16, then they add 16x4=64, and so on:
So the rule is that the next increase is the previous increase multiplied by 4.
Thus, the next increase in components (the question mark) should be:
The previous one +256, which gives:
[tex]?=89+256=345[/tex]Answer: 345
what is the slope of a line perpendicular to this linewhat is the slope of a line parallel to this line
Answers
Answer:
• Slope perpendicular to the line: 8/5
,• Slope parallel to the line: –5/8
Explanation
Given
[tex]5x+8y=7[/tex]To know the result, it is better if we work with the slope-intercept form:
[tex]y=mx+b[/tex]Then, to get this kind of form we have to isolate y from the given equation:
[tex]8y=7-5x[/tex][tex]y=\frac{7-5x}{8}[/tex][tex]y=-\frac{5}{8}x+\frac{7}{8}[/tex]Thus, in this case, m = –5/8 and b = 7/8.
Perpendicular lines have negative reciprocal lines:
[tex]m_2=-\frac{1}{m_1}[/tex]where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.
Then, replacing the values:
[tex]m_2=-\frac{1}{-\frac{5}{8}}[/tex][tex]m_2=\frac{8}{5}[/tex]Finally, the slopes of parallel lines are the same, meaning:
[tex]m_2=m_1[/tex]where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.
i need help please help
Answers
Answer:
I think d)
Step-by-step explanation:
if A (0, 2) and B (2, 0) dilation is a transformation, which is used to resize the object, so it can only mean that both are bigger and like the same number, hope that makes sense
Find the equaton of the line in point-slope form that passes through (-4,6) and (-2,5)