The polynomial is x³ + 2x
If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.
That is, a, b and c are roots of the polynomial, then the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.
Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc
Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.
So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).
Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x
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2. Expand each of the following functions in ascending powers of x up to the term in
x³. In each case state the values of x for which the expansion is valid.
Values of x in ascending orders is shown below.
What are exponents?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1. Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion. To illustrate 3 x 3 x 3 x 3 in a straightforward manner, for instance, we could write it as 34, where 4 is the exponent and 3 is the base. It is claimed that the entire statement 34 has power.
Given Data
Expanding the exponents,
[tex]\sqrt{4+x}[/tex]
[tex]4^{1/2}[/tex] + [tex]x^{1/2}[/tex]
2) [tex]\frac{1}{2+x}[/tex]
2⁻¹ + x⁻¹
3) (3-2x)⁻²
(9)⁻¹ - 4x⁻²
4) (8 - 3x)¹⁾³
2 - [tex]3x^{1/3}[/tex]
In Ascending order,
(3-2x)⁻², [tex]\frac{1}{2+x}[/tex] , ([tex]8-3x^{1/3}[/tex]) , [tex]\sqrt{4+x}[/tex]
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if a vector a has components ax < 0, and ay > 0, then the angle that this vector makes with the positive x-axis must be in the range group of answer choices 180° to 270° 0° to 90° 270° to 360° it cannot be determined without additional information. 90° to 180°
The angle vector 'a' makes with the positive x-axis is 90° to 180°.
What is a vector?A vector is a quantity that has magnitude as well as direction one such example of this is velocity where we describe speed and direction also.
Given a vector a with two components one in the x direction and another one in the y direction.
The x component of the vector ax < 0 which is on the 2nd quadrant and the y component of the vector is ay > 0 which we join to the tail of the component ax.
∴ The angle it makes with the positive x-axis is 90° to 180° as it is on the second quadrant.
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On Tuesday, the mailman delivers three check for $5 and two bills for $2 each. If you had a starting balance of $25, what is the ending balance?
PLEASEEE HELP ME ON THIS QUESTION! I HAVE TO SUBMITTHIS IN A BIT PLEASE HELP! :))
Answer: 196.5 lbs
Step-by-step explanation:
[tex]237-9(4.5)=196.5[/tex]
a solid cube has side length 3 inches. a 2-inch by 2-inch square hole is cut into the center of each face. the edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. what is the volume, in cubic inches, of the remaining solid?
The volume of remaining solid is 7 in³.
What is volume of cube?The whole three-dimensional area occupied by a cube is its volume.
A cube is a solid 3-D object with six square faces and equal-length sides.
The cube is one of the five platonic solid shapes and is also referred to as a regular hexahedron.
The cubic units are used to represent the cube's volume.
Imagine performing each cut individually.
A box 2*2*3 is eliminated in the initial cut. Two boxes with dimensions of 2*2*0.5 are removed during the second cut, and the third cut eliminates the same number of boxes on the final two faces.
Therefore, the sum of all cuts is 12 + 4 + 4 = 20.
∴Volume of rest of cube = 3³-20
= 7 in³
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Need help ASAP! will give brainliest!
Answer:
first one.
Step-by-step explanation:
the slope of the line is the rise over run, in triangle STU this is 3 over 2
in triangle FED this is 6 over 4, which simplifies to 3 over 2
proving that the slope of the line is constant.
9th term of 25,150,900
Answer: The 9th term is 41990400
Step-by-step explanation:
As we can see here 25, 150, 900 to find the common ratio i'll divide 150 by 25 which gives me 6
to 25 times 6 is 150
150 times 6 is 900
T=Term
1t=25 2t=150 3t=900 4t=5400 5t=32400 6t=194400 7t=1166400 8t=6998400 9t= 41990400
900*6= 5400
5400*6=32400
32400*6= 194400
194400*6= 1166400
1166400*6= 6998400
6998400*6=41990400
I need help doing this, I dont really know how. show work
Check the picture below.
The segments shown below could form a triangle?
Answer:
yes
Step-by-step explanation:
it would form a acute triangle.
Hello! What graph could be used to find the solutions to the system of equations? Thanks for your help!
The Solution:
Given:
[tex]\begin{gathered} y=\frac{2x-2}{x-3} \\ \\ x-y=1 \end{gathered}[/tex]Required:
To determine the graph that represents the given system.
Below is the graph of the given system:
Therefore, the correct answer is [ option 2 ]
Simplify m^9 m^−3.
A. -m^12
B. 1 / m^27
C. 1 / m^6
D. m^6
I will the law of exponents:
[tex]x^{n} *x^{m} \\=x^{n+m}[/tex]
⇒[tex]=m^{9+(-3)} \\=m^{9-3}\\ =m^{6}[/tex]
Option D is the answer
what is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations? (round your answer to four decimal places.)
The probability that maximum speed differs from the mean value by at most 2.5 standard deviations is 0.8473
Let the required probability that the maximum speed of mopeds differs from the mean speed by 2.5 standard deviations be given by P(U±2.5).
Mean speed U =46.7km/hr
P(46.7±2.5) = (44.2<= X <=49.2)
= P( 44.2<= Z <= 49.2)
= P(44.2 - 46.7/1.75 <= Z <= 49.2- 46.7/1.75)
= P( - 1.4286 <= Z <= 1.4285)
= P(1.4285) - P(-1.4285)
= P(1.43 ) - P(-1.43)
= 0.92364 - 0.07636
= 0.8473
Thus the probability that maximum speed differs from mean value by at most 2.5 standard deviations is 0.8473
the question is incomplete and the full question is "Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. Suppose the maximum speed of a moped is normally distributed with a mean value of 46.7 km/h and a standard deviation of 1.75 km/h. Consider randomly selecting a single such moped
What is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question"
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arabella graphed the following systems equations. she says that (0.5,2.5) is the solution.
what is one way you can use substitution to see if Arabella is correct
substitute __ for ___
Answer:
4x y
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
5, 2, 5/3
Find the 10th Term
Answer:
-22
Step-by-step explanation:
10=a+9d
the first term is 5 and the common difference is -2
a=5
common difference=-3
5+9(-3)
5+(-27)
5-22
answer is -22
for every integer m, 7m 4 is not divisible by 7. construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order.
Answer: CAELYNN YOU WWELCOME
Step-by-step explanation:
7 +7+7+7+7+7
Determine if 0.59136363636363636... is rational or irrational and give a reason for your answer.
Need answer ASAP
Based on the given number which is 0.59136363636363636, we can infer that this is a rational number because it is repeating.
How to know a rational number?A rational number is a number that when the denominator divides the numerator, the result is a decimal that is either terminating, or repeating. This means that the decimal will either stop at some point, or will keep repeating the same numbers.
The number, 0. 59136363636363636, is a rational number because it is a repeating decimal.
The part that is repeating is "63636" so this is a rational number.
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The given recurring decimal 0.59136363636 is a rational number.
Given that,
To determine whether the given recurring decimal value is rational or irrational.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
Here,
The given recurring decimal = 0.591363636
From the above definition,
A rational number is a number that does have a repeating value after a certain value beyond the decimal point, unlike an irrational number that has repetition just after the decimal point.
So, the given number 0.59136363636 = 0.591 + 0.000363636
It is a rational number because it has repetition after 591 of 36 frequently.
Thus, the given recurring decimal 0.59136363636 is a rational number.
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25 > w - 7 solve the inequality for w and simplify your answer as much as possible
Step-by-step explanation:
so when we have 25> w -7 we must move the
-7 to the 25 for the w to stand on it own so
25+7 > w
32 > w
If f(x)= x³+4x² - 15-18 and a + 1 is a factor of f(x), then find all of the
zeros of f(x) algebraically?
Answer:
I believe you typed that wrong.
The third term should be -15X
And the 3 answers are 3 -6 -1
Step-by-step explanation:
Answer: x=-1 x=-6 x=3
Step-by-step explanation:
[tex]f(x)=x^3+4x^2-15x-18[/tex]
Let's isolate the multiplier (x+1) from the expression x³+4x²-15x-18 :
[tex]x^3+4x^2-15x-18=\\\\x^3+x^2+3x^2-15x-18=\\\\x^2(x+1)+3(x^2-5x-6)=\\\\x^2(x+1)+3(x^2+x-6x-6)=\\\\x^2(x+1)+3(x(x+1)-6(x+1))=\\\\x^2(x+1)+3(x+1)(x-6)=\\\\(x+1)(x^2+3(x-6))=\\\\(x+1)(x^2+3x-18)[/tex]
Decompose the polynomial х²+3х-18 into factors:
[tex]x^2+3x-18=\\\\x^2+6x-3x-18=\\\\x(x+6)-3(x+6)=\\\\(x+6)(x-3)[/tex]
[tex]Thus,\\\\x^3+4x^2-15x-18=(x+1)(x+6)(x-3)\\\\[/tex]
[tex](x+1)(x+6)(x-3)=0\\\\x+1=0\\x+1-1=0-1\\x=-1\\\\x+6=0\\x+6-6=0-6\\x=-6\\\\x-3=0\\x-3+3=0+3\\x=3[/tex]
) Write 2350 million in standard form.
As a children's librarian, Jodi Hassam earns $15.35 per hour plus time and a hall for weekend work Last week she worked her regular 40 hours plus 16 hours on the weekend. What was her total pay for the week?
Answer:
Jodi's total pay for the week is $ 982.40
Step-by-step explanation:
Question 8 of 10Which is not a characteristic of the linear parent function?A. The range is positive real numbers (y> 0).B. It goes through the origin.OC. It has a slope of 1.OD. The domain is all real numbers.SUBM
Let's determine the statement which is not a characteristic of the linear parent function.
The linear parent function has the form:
[tex]y=x[/tex]We have the graph below:
The function has the following properties:
• The line goes through the origin.
,• It has a range of all real numbers
,• It has a domain of all real numbers
,• It has a slope of 1.#
Therefore, the statement which is not a characteristic of the linear parent function is:
• The range is positive real numbers (y > 0).
ANSWER:
• A. The range is positive real numbers (y> 0)
136/12 times 12 = ?
Anyone here have pinterest.....
Answer:
136 divided by 12 you get 11.3 times 12 you get 136
Answer:
(136÷12) × 12 = 136
Step-by-step explanation:
You start with the numbers in the parentheses ( which look like "( )" ), which is 136÷12 which is 11.3
1.) 136÷12=11.33
Then you multiply it by 12 which will get you 136.
2.) 11.33× 12=136
Your final answer will be 136
Have a nice day!
ignore the 7. Appreciate if its done quickly. No need to graph. Just solve inequality
Answer:
[tex]x \leq -1[/tex]
Step-by-step explanation:
divide both sides by -4
-2 >= x - 1
(FLIP THE INEQUALITY!!!)
now add 1 to both sides
-1 >= x
flip the equation
x <= -1
that is your answer
2 10) (x y2)4. 2x (2xy-2) y4 A) DP B) +3 8714 1 C) D) 4xºy 2x7 y? 2
We have to solve this expression:
[tex]undefined[/tex]What kind of transformation converts the graph of f(x)=3x+9 into the graph of g(x)=3x–10?
Answer:
See below
Step-by-step explanation:
To get from +9 to -10 you will need to shift DOWN 19 units
Plsss help I don’t know if “B” is right so plsss help me
Answer:
it is C
Step-by-step explanation:
it cannot be A or B because ether angles 2 or 3 would have to be an obtuse angle, which neither of them is. So, this leaves C and D. It is not D because angles 2 and 3 are not corresponding (angles 2 and 4 are). This leaves option C as the only answer.
Pls mark brainliest with the crown
suppose f(x) = 3x + 10 and g(x) = 17x + 4
find (f+g) (x)
Suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14
The function is an expression the show the relationship between one variable and another variable. If one variable is dependent variable another variable will be independent variable. We can also says that the function shows the relationship between set of inputs and set of out puts
The function f(x) = 3x+10
g(x) = 17x+4
We have to find the value of (f+g)(x)
We know,
(f+g)(x) = f(x) + g(x)
Substitute the values in the equation
(f+g)(x) = 3x+10 + 17x+4
Add the like terms
(f+g)(x) = 20x+14
Hence, suppose the function f(x) = 3x+10 and g(x) = 17x+4, then the value of (f+g)(x) is 20x+14
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If you borrow $200 for 12 years atan annual interest rate of 2%, howmuch will you pay altogether?
$248
Explanations:
Let the money borrowed be the Principal, P = $200
Interest rate, R = 2%
Number of years, T = 12 years
The total amount to pay back will be:
Amount = Principal + Interest
Let us calculate the Interest, using the formula:
[tex]\begin{gathered} \text{Interest = }\frac{PRT}{100} \\ \text{Interest = }\frac{200\times2\times12}{100} \\ \text{Interest = 2}\times2\times12 \\ \text{Interest = 48} \end{gathered}[/tex]Interest = $48
Amount = Principal + Interest
Amount = $200 + $48
Amount = $248
You will pay back $248 altogether
Given points J(3,4), A(7.5), and R(5,2), graph AJAR and its reflection image across the given line.Rx-axis
By reflection triangle JAR across x- axis, we get
By comparing the given options, we can see that the answer is option D
d = 4n-2 solve for n
The value of the equation d = 4n - 2 for n is (d + 2) ÷ 4.
Given data, d = 4n - 2
For finding the value of n first add 2 to both the side,
d + 2 = 4n - 2 + 2
d + 2 = 4n
Now, divide 4 into both sides of the equation:
(d + 2) ÷ 4 = 4n ÷ 4
(d + 2) ÷ 4 = n
∴ The value of n after solving the equation d = 4n - 2 is (d + 2) ÷ 4.
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