I need help with this question please Identify the binomial that is a factor of the polynomial
Answers
(x-2)
1) Let's use the Rational Roots Theorem so that we can factor this Polynomial and find the factors that make up this Polynomial.
2) Taking all the factors of the constant and the leading coefficients we have:
[tex]P(x)=3x^3-11x^2-2x+24[/tex]
Let's enlist these factors:
[tex]\begin{gathered} 24\colon\pm1,\pm2,\pm4,\pm3,\pm6,\pm8,\pm12,\pm24 \\ 3\colon\pm1,\pm3 \end{gathered}[/tex]2.2) Let's pick any number on the numerator and divide it by any number of the denominator, to get possible roots:
[tex]\begin{gathered} \frac{\pm1,\pm2,\pm4,\pm3,\pm6,\pm8,\pm12,\pm24}{\pm1,\pm3}=\pm1,\pm2,\pm\frac{4}{3}, \\ \end{gathered}[/tex]Proceeding with that let's do a Synthetic Division, testing 2
[tex]\begin{gathered} \frac{3x^3-11x^2-2x+24}{(x-2)}= \\ (x-2)(3x^2-5x-12) \\ (x-2)(3x+4)(x-3) \end{gathered}[/tex]Note that we have three factors. After factoring out
3) Hence, the answer is (x-2)
Related Questions
Peter, a cyclist, rides 5.673 kilometers, takes a break, and then rides an additional 4321 meters.a. How many hectometers total did he ride?How many decimeters did he ride?
Answers
Explanation:
a) First Distance = 5.673 kilometers
2nd distance = 4321 meters
Total distance = 1st distance + 2nd distance
Total distance = 5.673 kilometers + 4321 meters
Conversion from kilometers to meters:
1 kilometer = 1000meters
5.673 kilometers = 5673 meters
Total distance in meters = 5673 meters + 4321 meters
Total distance in meters = 9994 meters
Conversion of meters to hectometers:
100 meters = 1 hectometers
9994 meters = x
cross multiply:
100(x) = 9994(1)
100x = 1994
x = 1994/100
x = 19.94 hectometers
Hence, he rode 19.94 in hectometers
b) converting to decimeters:
It is easier to convert from meters to decimeters
0.1 meters = 1 decimeter
9994 meters = y
y(0.1) = 1(9994)
0.1y = 9994
y = 9994/
without using a calculator prove whether 1728 is a perfect cube
Answers
Since the prime factors of 1728 can be grouped into triples of equal factors, it is a perfect cube.
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies what is the probability that you don't get a coupon when your in line
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies.
We are meant to find the probability that you don't get a coupon when you are in the line.
Step 2:
We can see that the probability that the person was in the line and got a coupon is:
[tex]\frac{1}{10}[/tex]Then, the probability that the person did not get a coupon when he was in the line is:
[tex](\text{ 1 -}\frac{1}{10})\text{ = }\frac{9}{10}[/tex]Calculate the average (mean) of the data shown, to two decimal placesx8.325.313.423.9129.312.31.4
Answers
Given the set of of data:
x
8.3
25.3
13.4
23.9
12
9.3
12.3
1.4
We are to find the average (mean).
To find the means of a set of data, we first add up the data and divide by the total number of data.
The Formular for mean (m)
Mean (m) = sum of the terms
number of terms
number of terms = 8
Mean (m) = 8.3 + 25.3 + 13.4 + 23.9 + 12 + 9.3 + 12.3 + 1.4
8
Mean (m) = 105.9
8
Mean (m) = 13.2375
Mean (m) = 13.24 ( two decimal places).
y=3sin(1/2 x+pi/6)please find amplitude period and phase shift
Answers
The given function is
[tex]y=3\sin (\frac{1}{2}x+\frac{\pi}{6})[/tex]We have to use the following form
[tex]a\sin (bx-c)+d[/tex]Where the amplitude is a, the period is 2pi/b, and the phase shift is c/b. In the given function a = 3, b = 1/2, and c = pi/6.
[tex]\begin{gathered} a=3 \\ T=\frac{2\pi}{b}=\frac{2\pi}{\frac{1}{2}}=4\pi \\ \theta=\frac{c}{b}=\frac{\frac{\pi}{6}}{\frac{1}{2}}=\frac{2\pi}{6}=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the amplitude is 3, the period is 4pi, and the phase shift is pi/3.1. The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p = -8x + 600. What quantity x maximizes revenue (R= xp)? What is the maximum revenue? What price should the company charge to maximize revenue?2. Jeff invested some money at 7% simple interest and $5000 more than that amount at 15% simple interest. After 1 year, his total interest from the two accounts was $1300. How much did he invest at each rate?
Answers
1.The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. $11875 he invest at each rate.
Given that,
In the question there are 2 question.
1.The market equation p = -8x + 600.
We have to determines how much a specific product costs in dollars and how many units are sold. What value of x optimizes profit (R=xp)?
We know,
R = px
R = p(-8p+160)
R= -8p² +160p
R(16) = -8(16)² +160(16)
R(16) = -2048 + 2560
R(16) = 512
R'= -16p + 160 = 0
Revenue maximizing price p= 160/16 = 20/2 = 10
Maximum revenue R(10) = -8(10)² + 160(10) = -800 + 1600 = 800
x=-8p+160
x =-8(10)+160
x = -80 + 160
x = 80
We get,
792 = -8p² +160p
8p² -160p + 792 = 0
2p² - 40p + 198 = 0
p² -20p + 99 = 0
(p-9)(p-11) = 0
p = 9 or 11 as the prices that give at least 792 in revenue
Therefore, The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. Jeff put some money into investments at 7% simple interest and another $5,000 at 15% simple interest. His combined interest from the two accounts after a year was $1300.
We have to find at which rate did he invest how much.
Let C represent the sum Bryan invested in the CD. Then he made a savings account deposit of $5,000 C. Add the interest amounts to reach $1300.00: 15% of the amount in the certificate of deposit is 0.15C, and 7% of the amount in the savings account is 0.07(5,000-C). As a result, we can construct and settle the equation:
0.15C+0.07(5000-C)=1300
0.15C+350-0.07C=1300
0.08C+350=1300
0.08C=1300-350
0.08C=950
C=950/0.08
C=11875.
Therefore, $11875 he invest at each rate.
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A gold bar is similar in shape to a rectangular prism. A gold bar is approximately 7 1 6 in. x2 in. x 1 in. If the value of gold is $1,417 per ounce, about how much 8 2 is one gold bar worth? Use the formula w ~ 11.15n, where w is the weight in ounces and n= volume in cubic inches, to find the weight in ounces. Explain how you found your answer.
Answers
ANSWER and EXPLANATION
We want to find how much the gold bar is worth.
First, we have to find the volume of the gold bar.
The volume of a rectangular prism is:
[tex]\begin{gathered} V=L\cdot W\cdot H \\ L=\text{length;} \\ W=\text{width;} \\ H=\text{height} \end{gathered}[/tex]Therefore, the volume of the gold bar is:
[tex]\begin{gathered} V=6\cdot2\frac{7}{8}\cdot1\frac{1}{2} \\ V=6\cdot\frac{23}{8}\cdot\frac{3}{2} \\ V=25.88\text{ cubic inches} \end{gathered}[/tex]Now, convert the volume to weight y using:
[tex]\begin{gathered} w\approx11.15n \\ \text{where w = weight in ounces; n = volume in cubic inches} \end{gathered}[/tex]Therefore, its weight is:
[tex]\begin{gathered} w\approx11.15\cdot25.88 \\ w\approx288.56\text{ ounces} \end{gathered}[/tex]Finally, multiple the weght by the value of gold:
[tex]\begin{gathered} \text{Worth}=288.56\cdot1417 \\ \text{Worth}=\text{ \$}408,889.52 \end{gathered}[/tex]Therefore, the volume of the gold bar is about 25.88 in³, so the weight is approximately 288.56 ounces. So one gold bar is worth about $408,889.52
for the function y=1/2-x at what values of x will the rate of change of y with respect to x equal 1/16
Answers
Given:
[tex]y=\frac{1}{2-x}[/tex]To Determine: Using the increament method the rate of change of y with respect to x
[tex]\begin{gathered} y+\Delta y=\frac{1}{2-(x+\Delta x)} \\ \Delta y=\frac{1}{2-(x+\Delta x)}-y \end{gathered}[/tex]Substitute for y
[tex]\begin{gathered} \Delta y=\frac{1}{2-(x+\Delta x)}-\frac{1}{2-x} \\ \Delta y=\frac{2-x-(2-(x+\Delta x)}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{2-x-(2-x-\Delta x)}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{2-x-2+x+\Delta x}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{\Delta x}{(2-(x+\Delta x)(2-x)} \end{gathered}[/tex][tex]\begin{gathered} \text{Divide through by }\Delta x \\ \frac{\Delta y}{\Delta x}=\frac{\Delta x}{(2-(x+\Delta x)(2-x)}\times\frac{1}{\Delta x} \\ \frac{\Delta y}{\Delta x}=\frac{1}{(2-(x+\Delta x)(2-x)} \end{gathered}[/tex][tex]\frac{dy}{dx}=\frac{1}{(2-x)(2-x)}[/tex]Hence, the rate of change of y with respect to x is
[tex]\frac{dy}{dx}=\frac{1}{(2-x)^2}[/tex]Find the area of a circle with a diameter of 15 units round your answer to the nearest whole
Answers
The area of the circle is 177 units^2
Explanation:Given:
diameter of the circle = 15 units
To find:
the area of the circle
The formula for the area of a circle = πr²
let π = 3.14
diameter = 2(radius)
radius = diameter/2
radius = 15/2 = 7.5 units
[tex]\begin{gathered} Area\text{ of the circle = 3.14}\times7.5^2 \\ \\ Area\text{ of the circle = 176.625} \\ \\ To\text{ the nearest whole number, the area of the circle is 177 units}^2 \end{gathered}[/tex]For an arch length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r=4.28 ft, θ= 2.79, s=?
Answers
The area of a sector S follows the equation:
[tex]S=\frac{1}{2}r^2\theta[/tex]Where θ is the angle and r the radius.
In this case, we have:
• r = 4.28ft
,• θ = 2.79
We write:
[tex]\begin{gathered} S=\frac{1}{2}(4.28)^2\cdot2.79 \\ S\approx25.554168 \end{gathered}[/tex]Then, the answer, rounded up to two decimal places is
[tex]S=25.55[/tex]Write 11/80 as decimal Round to four decimal places as needed
Answers
The fraction is given
[tex]\frac{11}{80}[/tex]ExplanationTo determine the decimal form .
[tex]\frac{11}{80}=0.1375[/tex]AnswerHence the answer in decimal form is 0.1375.
Mrs worthy estimate the weight of her puppy to be 20 pounds. The actual weight of the puppy is 25.4 pounds. what is the percent error of Mrs worthy estimation?round to the nearest tenth
Answers
Given data:
The estimate weight of the puppy is E=20 pound.
The actual weight is A=25.4 pounds.
The expression for the percentage error is,
[tex]e=\frac{A-E}{A}\times100[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} e=\frac{25.4-20}{25.4}\times100 \\ =\frac{5.4}{25.4}\times100 \\ =21.26 \end{gathered}[/tex]Thus, the percentage error is 21.26%.
Then he drove home at a speed of 5 blocks every 4 minutes. How do I graph that?
Answers
We have to graph the position versus time.
We start by identifying the segments.
1) The initial position (x=0, y=0) is his house.
2) He drove for 4 minutes at a speed of 1 block/min. This means that we have a line with slope m=1 from x=0 to x=4. The value of y when x=4 is also 4.
Then, the final point of this segment is (4,4).
3) He spent 3 minutes in the store. This means that y=4 between x=4 and x=4+3=7.
The final point of this segment is (7,4).
4) He drove at a speed of 2 blocks/minute (slope m=2) for 6 blocks until he got to the bank. Then, the new position is y=7+6=13. If the slope is m=2, then he will spent 6/2=3 minutes to reach the bank. As he already spent 7 minutes, he arrived to the bank at x=7+3=10.
Then, the final position of this segment will be (10,13).
5) Then, he returns at a speed of 5 blocks every 4 minutes. This correspond to a slope m=-5/4. This slope is negative as he is now returning to his house and, then, y is decreasing.
Graph the line x=3 .
Answers
According to the given equation, x=3, the line that represents it is a vertical line that passes throught the x axis at x=3.
This is a constant line, which means that for all the values of y, x will always be 3.
The graph of this line is the following:
x = Round to the nearest hundredth or keep as a s
Answers
x=6.67
1) Examining that figure, we can state that we have two similar triangles with proportional sides and congruent angles.
2) So let's write a proportion so that we can find the measure of x
[tex]\begin{gathered} \frac{hipotenuse}{hipotenuse\text{ 2}}=\frac{\text{Leg}}{\text{leg 2}} \\ \frac{18}{10}=\frac{12}{x} \\ 18x=120 \\ x=\frac{120}{18} \\ x=\frac{20}{3}\text{ }\cong6.66667 \end{gathered}[/tex]3) Since the answer must be rounded to the nearest hundredth we have
the answer as x=6.67
a) Rotation, then reflectionb) Translation, then rotationc) Rotation, then translationd) Translation, then reflection
Answers
the answer is the option
d) Translation, then reflection
because
First translation
the rule is
(x,y) -------> (x+6, y-3)
6 units at righ and 3 units down
Second Reflection
the reflection is across the vertical line locate 3 units at left figure 2
see the attached figure to better understand the problem
please wait a minute
Brad thinks that 2.2.2.2 is represented by 4^2.What is wrong with this answer?
Answers
There is nothing wrong in the answer because
[tex]2\cdot2\cdot2\cdot2=4\cdot4=4^2[/tex]but it should be represented by
[tex]2\cdot2\cdot2\cdot2=2^4[/tex]A line cuts the y-axis at (0, -6) and passes through the point (9, -3). Find the equation of the line.
Answers
point 1 (0,-6) and point 2 (9,-3)
the equation is
[tex]y-y1=m(x-x1)[/tex]where m =
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3-(-6)}{9-0}=\frac{-3+6}{9}=\frac{3}{9}=\frac{1}{3}[/tex]answer: the equation of the line is
[tex]\begin{gathered} y-(-6)=\frac{1}{3}(x-0) \\ y+6=\frac{1}{3}x \\ y+6-6=\frac{1}{3}x-6 \\ y=\frac{1}{3}x-6 \end{gathered}[/tex]For each scenario, use the tape diagram to help answer the question. Think of different labels to use for the diagram depending on the situation. Mai has picked 1 cup of strawberries for a cake, which is enough for 3/4 of the cake. How many cups does she need for the whole cake?Priya has picked 1 1/2 cups of raspberries. which is enough for 3/4 of a cake. How many cups does she need for the whole cake?
Answers
Answer:
The number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Explanation:
Given that;
[tex]1\text{ cup of strawberries can make }\frac{3}{4}of\text{ a cake}[/tex]To get the number of cups of strawberries needed for a whole cake.
Let us multiply both sides by 4/3;
[tex]\begin{gathered} 1\times\frac{4}{3}\text{ cup of strawberries can make }\frac{3}{4}\times\frac{4}{3}of\text{ a cake} \\ \frac{4}{3}\text{ cup of strawberries can make 1-whole }of\text{ a cake} \end{gathered}[/tex]Therefore, the number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 5° = ____
Answers
we want to calculate the following value
[tex]\sin (5)[/tex]Using a calculator, we have that
[tex]\sin (5)=0.08715574274765817[/tex]so, rounded to the nearest hundredth, we have that
[tex]\sin (5)\approx0.09[/tex]The table gives the temperature in degrees Fahrenheit in five cities at 6 AM on the same day used to table to answer the questions.
Answers
Looking at the table, the temperature in Boston at 6 AM is -8°F.
(a)
If the temperature had risen by 17°F at noon, then the new temperature is:
[tex]-8\degree F+17\degree F=9\degree F[/tex](b)
The 6 AM temperature in Toronto was -16°F, and -25°F in Fairbanks. The difference is:
[tex]-16\degree F-(-25\degree F)=-16\degree F+25\degree F=9\degree F[/tex]In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
Answers
So,
First of all, the player has a 1/4 chance of drawing any of the 4 prizes.
This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.
To find the fair price, we need to find the expected value of this problem:
This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.
This is:
[tex]\begin{gathered} 4\cdot\frac{1}{2}+26\cdot\frac{1}{4}+241\cdot\frac{1}{4} \\ \\ =\frac{275}{4}=68.75 \end{gathered}[/tex]Therefore, the fair price of this game is $68.75.
[tex]1 + ( - 2)[/tex]what is answer this
Answers
This problem involves the addition of integers. When we add up a positive number and a negative number, it results in subtraction. The final answer will have a sign the same as the higher number.
In this problem, the negative number has a higher value than the positive number, hence, the final answer is a negative number. Doing the operation, we get
[tex]1+(-2)=-1[/tex]Answer: -1
-15-3r=6r+3c Solve for r.
Answers
Answer:
[tex]r=\frac{-c-5}{3}[/tex]Explanation:
We want to solve for r in the equation below;
[tex]-15-3r=6r+3c[/tex]We need to move all terms of r to one side and divide both sides by the coefficient of r.
firstly subtract 6r from both sides;
[tex]\begin{gathered} -15-3r-6r=6r-6r+3c \\ -15-9r=3c \end{gathered}[/tex]then add 15 to both sides;
[tex]\begin{gathered} -15+15-9r=3c+15 \\ -9r=3(c+5) \end{gathered}[/tex]divide both sides by -9;
[tex]\begin{gathered} \frac{-9r}{-9}=\frac{3(c+5)}{-9} \\ r=\frac{-(c+5)}{3} \\ r=\frac{-c-5}{3} \end{gathered}[/tex]Therefore;
[tex]r=\frac{-c-5}{3}[/tex]Hello, how do I factorize this expression 1-36x^ { 2 } +y ^ { 2 } . Thanks :3
Answers
Solution:
Given the expression:
[tex]1-36x^2+y^2[/tex]To obtain the result of the factoring of the above expression, we factor out the common factor.\
In the above expression, there is no common factor.
Hence, the expression cannot be factored.
Provide reasons for the proofGiven line m is parallel to line nprove angle 1 is supplementary to angle 3
Answers
The first reason is Given.
The second is corresponding angles theorem.
The third one is definition of congruent angles.
The fourth is definition of linear pair.
The fifth is linear pair theorem.
The sixth is definition of supplementary angles.
The seventh is addition property of equality.
The eighth is definition of supplementary angles.
The function f(x) = =+ 1 has a vertical asymptote atA. I = 0OB. I = 1OC. A=-1OD. f(x) = -1Reset Selection
Answers
The function is given to be:
[tex]f\left(x\right)=\frac{-4}{x}+1[/tex]The vertical asymptote is when the denominator is equal to 0. T
Therefore, we have the vertical asymptote to be at:
[tex]x=0[/tex]OPTION A is the correct option.
Solve the equation for t:8t - r = 12t
Answers
ANSWER
[tex]t=-\frac{r}{4}[/tex]EXPLANATION
We want to solve the given equation for t:
[tex]8t-r=12t[/tex]To do this, separate the variables of the equation and simplify it:
[tex]\begin{gathered} 8t-12t=r \\ -4t=r \\ t=\frac{r}{-4} \\ t=-\frac{r}{4} \end{gathered}[/tex]That is the solution to the equation for t.
Choose all of the options below that are expressions.
5t +1
9+4t
16=t
2-17t
6-t
3t=0
Answers
Answer:
here are the answers
Step-by-step explanation:
5t +1 2-17 3t=0 so yeah those are the answers
I think?
Which number is located between 8710and95?
Answers
-8 7/10 and -9 2/10
-8-7/10 = -87/10
-9 - 2/10= -92/10
Answer is -9 1/10 = -91/10
because -91 is between -87 and -92
Answer is OPTION B))