find all the zeros for each function.
p(x)=2x^3-3x^2+3x-2
*show work*
Answers
A graph of p(x) shows it has one real zero, at x=1. Dividing that out (and dividing out the scale factor of 2) reveals the remaining factor to be
.. (x -1/4)^2 +15/16
When we set this to zero, we have
.. (x -1/4)^2 +15/16 = 0
.. (x -1/4)^2 = -15/16
.. x -1/4 = i√(15/16)
and the remaining roots are
.. x = 1/4 ±i√(15/16)
.. x = (1 ±i√15)/4
The zeros are x = 1, x = (1 ±i√15)/4.
_____
You could use synthetic or long division to find
.. p(x)/(x -1) = 2x^2 -x +2
and then use any of several methods to determine the zeros of this are
.. x = (1 ±i√15)/4
Related Questions
Which of the following equations can be used to solve for the radius (r)
Answers
Answer:
The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Step-by-step explanation:
The area of a circle is given by :
[tex]A=\pi r^{2}[/tex] ; where r is the radius.
Now, lets find the radius.
[tex]\frac{A}{\pi } =r^{2}[/tex]
[tex]\sqrt{\frac{A}{\pi}} =r[/tex]
or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Therefore, the last option is the correct answer.
I understand that the remainder is 0, I kinda guessed and it told me.
But we're using long division or synthetic division.
Can you explain to me what the quotient is?
Thanks!
Answers
You will have something like:
[tex] \frac{x^{5} + 0x^{4}+ 0x^3+0x^2+0x-32}{x - 2} [/tex]
Then you start the long division process
When you get done you will have [tex]x^4 + 2x^3 + 4x^2 + 8x + 16[/tex]
with a remainder of 0
Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
Answers
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.
Let's analyze the given formulas for Bill's savings:
The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
The explicit formula is: f(n) = 35n
A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.
Recursive Formula Table for 1 ≤ n ≤ 5n = 1: f(1) = 35n = 2: f(2) = 35 + f(1) = 35 + 35 = 70n = 3: f(3) = 35 + f(2) = 35 + 70 = 105n = 4: f(4) = 35 + f(3) = 35 + 105 = 140n = 5: f(5) = 35 + f(4) = 35 + 140 = 175Using the Explicit Formula to Find f(40)The explicit formula f(n) = 35n allows us to directly calculate:
f(40) = 35 * 40 = 1400
This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.
Analyzing the Sequence 5, 6, 8, 11, 15, 20, 26, 33, 41, ...This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).
Help plz and explain. ..........
Answers
in the picture. If you need any clarification, just ask in the comments.
@ajaylounsber Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month?,
Answers
Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .
Answers
4 1/ 3
−1 1/3
the answer in the attached figure
Answer:
The locations of given number are shown on the below number line.
Step-by-step explanation:
The given numbers are
[tex]4\dfrac{1}{3} and -1\dfrac{1}{3}[/tex]
We need to plot these points on the given number line.
In the given number write the integers -4,-3,-2,-1,0,1,2,3,4 on points indicated and two sub point between two consecutive points divides the line in three equal parts.
[tex]4\dfrac{1}{3}=4+\dfrac{1}{3}[/tex]
It means [tex]4\dfrac{1}{3}[/tex] lies next to 4 on right side.
[tex]-1\dfrac{1}{3}=-(1+\dfrac{1}{3})=-1-\dfrac{1}{3}[/tex]
It means [tex]-1\dfrac{1}{3}[/tex] lies next to -1 on left side.
Therefore, the locations of given number are shown on the below number line.
Multiply.
638 × 49
_____
Answers
Is that what you're looking for?
15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?
a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk,
Answers
A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.
Answers
The lateral surface area of the equilateral triangular prism shaped shipping tube is 252 square inches.
Explanation:The question pertains to the calculation of the lateral surface area of a triangular prism shaped shipping tube, more specifically an
equilateral triangular prism
. The lateral area of a triangular prism can be calculated using the formula: Perimeter of the base x length of the prism. Here, the base of the prism is an equilateral triangle, so the perimeter of the base will be 3 x the length of one edge, which in this case is 3 x 6 inches = 18 inches. The length of the prism is given to be 14 inches. Hence, by substituting these values into the formula, the lateral surface area = 18 inches x 14 inches =
252 square inches.
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How to find the derivative of a fraction without using the quotient rule?
Answers
(u/v)'=(u*v^(-1))'=u'*v^(-1)+u*(-1)*v^(-2)*v'=u'/v-u*v'/v²=(u'v-uv')/v²
Final answer:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule.
Explanation:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule. Here's an example:
Let's differentiate the function f(x) = (3x + 2) / (2x + 1).
First, identify the numerator and the denominator. In this case, the numerator is 3x + 2 and the denominator is 2x + 1.Apply the product rule by differentiating the numerator and the denominator separately. The derivative of the numerator is 3, and the derivative of the denominator is 2.Next, apply the chain rule by multiplying the derivative of the numerator by the denominator, and subtracting the derivative of the denominator multiplied by the numerator. In this case, the derivative of f(x) is (3 * (2x + 1) - (2 * (3x + 2))) / ((2x + 1)^2).Simplifying further, the derivative of f(x) is (6x + 3 - 6x - 4) / ((2x + 1)^2) = -1 / ((2x + 1)^2).
Briyana has a $500 bond with a 6% coupon. Briyana purchased this bond for $460. What is the yield of this new bond?
A. 6%
B. 4.6%
C. 6.3%
D. 6.5%
Answers
To find the yield, we first need to multiply the value of the bond by the coupon percent. This is the amount paid to the bond holder.
500 x 0.06 = 30
So Briyana earned $30 on a bond that cost her $460.
30 / 460 x 100 = 6.5%
Answer:
The correct answer is: 6.5%
Step-by-step explanation:
what is the slope? 0 or undefined
Answers
It is undefined when the line is vertical.
Each morning papa notes the birds feeding on his bird feeder. so far tis month he has seen 59 blue jays, 68 black crows, 12 red robins and 1 cardinal. if 300 birds list papa's birdfeeder, how many blue jays can we expect to see?
Answers
First, we need to determine the percent of blue jays that he typically sees.
59 + 68 + 12 + 1 = 140 He saw a total of 140 birds.
59 of them were blue jays. So 59 / 140 = 42% of the birds were blue jays.
Multiply 300 by 42% and we have an expected number of 126 blue jays.
At the end of a factory assembly line, completed widgets are deposited into a box until it is filled. if after 10 minutes the box contains 25 widgets and it takes 2 hours total to fill up a box, how many widgets must each box hold?
Answers
2 hours - 60 minutes / hour * 2 = 120 minutes
after 10 minutes - box contains 25 widgets
this means that it takes 10 minutes to fill - 25 widgets
in 1 minute - 25/10 widgets/minute
therefore within 120 minutes - 25/10 widgets/minute * 120 minutes
the number of widgets a box can hold - 300 widgets
Final answer:
Each box must hold a total of 300 widgets.
Explanation:
To determine how many widgets must each box hold, we need to calculate the rate of production and then use it to find the total number of widgets produced in 2 hours (the total time it takes to fill the box).
First, we'll find out how many widgets are produced per minute. Since 25 widgets are deposited in 10 minutes, we divide the number of widgets by the time (in minutes) to get the rate:
Rate of production = 25 widgets / 10 minutes = 2.5 widgets per minute.
Now, we need to find out how many minutes are in 2 hours:
2 hours = 2 hours * 60 minutes/hour = 120 minutes.
Finally, we multiply the rate of production by the total production time (in minutes) to find out the total number of widgets per box:
Total widgets per box = 2.5 widgets/minute * 120 minutes = 300 widgets.
Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.
Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6
Sample Data
5
4
6
2
1
What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5
Answers
Solution:
we are given with two kind of data set , one is Population data and the other is sample data.
we have been asked to Compare the mean of the population with the mean of the given sample.
Given Population Data
is
[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]
Its mean can be calculated as below
[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]
Now the Sample data is
5,4,6,2,1
[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]
Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]
Answer:
The answer is B. 0.3
Step-by-step explanation:
If you need any help, ask me! :)
Given the arithmetic sequence an = −3 + 9(n − 1), what is the domain for n? all integers where n ≥ 1 all integers all integers where n ≥ 0 all integers where n > 1
Answers
Explanation:
Since this is a sequence, n represents the term number, which is the position in the sequence. We start counting terms of a sequence beginning with term #1, and continue using integers; this means the domain will be all integers greater than or equal to 1.
From an airplane at an altitude of 1200m the angle of depression to a rock on the ground measures 28. Find the distance from the plane to the rock
Answers
thus
sin θ=opposite/hypotenuse
θ=28°
opposite=1200m
hypotenuse=h
thus
sin 28=1200/h
h=1200/sin 28
h=2556.065 m
The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).
Explanation:The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).
Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.
We can use the following formula which is derived from the principles of trigonometry:
Distance to the rock (hypotenuse) = Opposite side / tan(θ)
Plugging the given values into this formula gives:
Distance to the rock = 1200m / tan(28°) This calculation will give the answer.
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True of False: If the measure of theta is A radians and B degrees, then A = 180B/pi. Please explain!
Answers
A = B*π/180 . . . . the form in the statement uses the inverse of the proper conversion factor.
What is the equation of the line?
A) x + 3y = 9
B) 3x - y = 9
C) x - y = 9
D) 3x + y = 9
Answers
The answer is D.
Since the y intercept of the equation is 9 and the slope is negative 3, after multiplying the entire equation by -1, we will get D.
Hope this helps!
If i give my sister 17 dollars, then we will have the same amount of money. if instead she gives me 23 dollars, then i'll have three times as much money as she will have. how much money does she currently have (in dollars)
Answers
You= $97
The total number of dollars my sisters have is $60.
Given that, if I give my sister 17 dollars, then we will have the same amount of money.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of dollars I have be x and number of dollars my sisters have be y.
Now, if I give my sister 17 dollars, then we will have the same amount of money
y-17 = x
x - y = -17 ---------(1)
If she gives me 23 dollars, then I'll have three times as much money as she will have.
3(x-23) = y
3x-69 = y
3x-y = 69 ---------(2)
Subtract equation (1) from (2)
3x-y-(x-y) = 69 - (-17)
⇒ 2x = 86
⇒ x = $43
Put x = 43 in equation (1), we get
43 - y = -17
43+17 = y
y = $60
Therefore, the total number of dollars my sisters have is $60.
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There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?
Answers
24 - 7 = 17.
There were 17 pencils in the box to start with.
being the equation stated
X+7=24
X being the number of pencils before added
To find the answer just do the opposite
24-7=X
and X=17
Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please
Answers
To do this, divide both sides of the equation between -3.
We have then:
(-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
x ^ 4-9x ^ 2-400 = 0
Then, we rewrite the polynomial:
(x-5) * (x + 5) * (x ^ 2 + 16) = 0
From here, we obtain the four roots:
Root 1:
x-5 = 0
x = 5
Root 2:
x + 5 = 0
x = -5
Root 3 and root 4:
x ^ 2 + 16 = 0
x3 = -4i
x4 = 4i
Answer:
all the zeroes of the equation are:
x1 = 5
x2 = -5
x3 = -4i
x4 = 4i
x1 = 5
x2 = -5
x3 = -4i
x4 = 4i
Step 1:
We have the equation
(-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
x ^ 4-9x ^ 2-400 = 0
Step 2: Write it in polynomial equation
(x-5) * (x + 5) * (x ^ 2 + 16) = 0
(x-5) * (x + 5) * (x+4)(x-4) = 0
From the factored form, we can get the roots which are
5, -5, 4, -4
Read the word problem. George has 2 times the amount of points that is 4 less than his sister’s. His sister has 16 points. How many points does George have? What operations are needed to solve this word problem, and in what order should they be used?
addition and subtraction, in that order
addition and multiplication, in that order
subtraction and division, in that order
subtraction and multiplication, in that order
Answers
x: Sister points.
y: George's points.
We write the following mathematical equation:
y = 2 * (x-4)
His sister has 16 points:
y = 2 * (16-4)
y = 2 * (12)
y = 24
Answer:
How many points does George have?
George has 24 points.
What operations are needed to solve this word, and in what order should they be used?
subtraction and multiplication, in that order
D- subtraction and multiplication, in that order.
Step-by-step explanation:
EDG 2022
If you take Coleman's test grade and divide by 2 and add 27, you get 67. Write and solve an equation to find Coleman's test grade.
Answers
To find Coleman's test grade, set up the equation x/2 + 27 = 67, solve for x by first subtracting 27 and then multiplying by 2 to get x = 80.
Explanation:The student is asking to find Coleman's test grade given that if you take Coleman's test grade, divide by 2, and add 27, the result is 67. To solve for Coleman's test grade, we can set up an equation where Coleman's test grade is represented by x. The equation based on the provided information would be x/2 + 27 = 67. We can solve for x by first subtracting 27 from both sides of the equation to get x/2 = 40, and then multiplying both sides by 2 to find x. Therefore, x = 80, which means Coleman's test grade is 80.
To find Coleman's test grade, we can set up an equation: (x/2) + 27 = 67. By solving this equation, we find that Coleman's test grade is 80.
Explanation:To find Coleman's test grade, we can set up an equation using the information given. Let's represent Coleman's test grade as 'x'. We have the equation: (x/2) + 27 = 67.
To solve this equation, we need to isolate 'x'. We can start by subtracting 27 from both sides of the equation: (x/2) = 40.
Next, we need to get rid of the fraction by multiplying both sides of the equation by 2: x = 80.
So Coleman's test grade is 80.
Esther and Jim plan to add a pond to their property. The area of the pond is 11 square meters. What is the radius?
Answers
Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00. The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account? Show your work.
Answers
Each of the steps is shown in the attached work.
He will have $111 left is his account.
The perimeter of the rectangle is 64 cm. Find the value of x.
A. 7
B. [tex] \frac{64}{33} [/tex]
C. 32
D. 50
Answers
11 + 3x =64/2
11 + 3x = 32
3x = 32 - 11
3x = 21
x = 21/3
x = 7
A.
The value of x is 7 and the right option is A. 7.
What is perimeter?Perimeter is the total distance around an object.
To find the value of x, we use the formula of the perimeter of a rectangle.
Formula:
P = 2(L+W)............... Equation 1Where:
P = Perimeter of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 3xW = 11 cmP = 64 cmSubstitute these values into equation 1 and solve for x
64 = 2(11+3x)64 = 22+6x6x = 64-226x = 42x = 42/6x = 7Hence, the value of x is 7 and the right option is A. 7.
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A dress that retails for 160 dollars was on sale 96 dollars by what percent was the dress discounted?
Answers
Which of the following is the image of C after a rotation of 180° about the origin?
(-5, 2)
(-5, -2)
(-2, 5)
Answers
Answer:
Option A.(-5, 2).
Step-by-step explanation:
Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.
As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.
Therefore the new coordinates of C will be C'(-5, 2).
Option A is the correct option.
How do you prove cotx/(cscx-sinx)=secx