Answer:
Complex roots for polynomials equations will always come in conjugate pairs. Since 1-2i is a root, 1+2i will also be a root. (Just switch the sign of the imaginary part to its opposite.)
Step-by-step explanation:
So far we have 1-2i and 1+2i as roots. We need two more to make a 4th degree polynomial.
x=1 with multiplicity of 2 means that we count the root twice when we write down the polynomial: (x - 1)(x - 1) = (x - 1)2
Putting it all together, we can construct our polynomial of degree 4 as
y = f(x) = (x - 1)(x - 1)[x - (1-2i)][x - (1+2i)]
Multiply the factors (FOIL):
[x - (1-2i)][x - (1+2i)] =
x2 - (1+2i)x - (1-2i)x + (1-2i)(1+2i) =
x2 - x - 2ix - x + 2ix + (1 + 2i - 2i + 4) =
x2 - 2x + 5
(x - 1)(x - 1) = x2 - x - x + 1 = x2 - 2x + 1
Now multiply the two underlined expressions:
y = (x2 - 2x + 5)(x2 - 2x + 1)
= x4 - 2x3 + 5x2 - 2x3 + 4x2 - 10x + x2 - 2x + 5 by multiplying term by term
= x4 - 4x3 + 10x2 -12x + 5 by collecting like terms.
16.
.
The number of economy-size cars rented in w weeks is represented by 152 + 3w. The number of full-size cars
rented in w weeks is represented by 99 + 2w. Write a simplified polynomial that represents how many more
economy cars are rented in w weeks than full-size cars.
The simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is 53 - w.
Linear equation:Linear equation is an equation in which the highest power of the variable is equals to one.
Therefore, the number of economy-size cars rented in w weeks is represented as follows:
152 + 3wThe number of full-size cars rented in w weeks is represented as follows:
99 + 2wwhere
w = number of weeks
A simplified polynomial that represents how many more economy cars are rented in w weeks than full-size cars is as follows:
152 + 3w - (99 + 2w)152 + 3w - 99 - 2w53 - wlearn more on polynomial here: https://brainly.com/question/2566362
How many triangles can be formed with segments measuring 4. 7 m, 1. 6 m, and 2. 9 m? none one more than one.
The sum of the length of the two sides of the triangle must be greater than the length of the third side. None of the triangles is formed. Then option A is correct.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
The sides of the triangle are 4.7 m, 1.6 m, and 2.9 m.
The condition will be
[tex]1.6 + 2.9 \ngtr 4.7[/tex]
We know that the sum of the length of two sides of the triangle must be greater than the length of the third side.
Hence, none of the triangles is formed.
Thus, option A is correct.
More about the triangle link is given below.
https://brainly.com/question/25813512
Answer:
A
Step-by-step explanation:
The circumference of a circle is 20 cm. What is the approximate radius of the circle?
1.5 cm
3.2 cm
7.0 cm
8.5 cm
Answer:
3.2 cm
Step-by-step explanation:
This is the answer becuase when doing the math you get 3.1831cm but rounded you get basically 3.2cm
help ASAP
x-(-25)=
also if ya'll need help with spanish don't worry im a fluent mexican who
Samantha owes her brother fifty dollars. Each week she pays off 2 dollars of the debt to her brother repeats the amount owed as a positive number.
After how many weeks did Samantha owe her brother fourth four dollars
Answer:
It take her 25 weeks
Step-by-step explanation:
2÷50
Which binomial is a factor of 9x2 – 64? 3x – 8 9x – 32 3x 32 9x 8.
Answer:
Step-by-step explanation:
9x^2 - 64 = (3x - 8)(3x + 8)
3x - 8 is a factor
Darius buys a shirt for $15. 25. The next month , the store increases the price of the shirt to $18. 75. What is the percent increase in the price of the shirt
Answer:
23%
Step-by-step explanation:
Step 1. Find increase of price amount
18.75 - 15.25 = 3.50
Step 2. Find the percentage increase
- Since we are finding the percent increase, we know that we need to find 3.50 is ____% of 15.25. We can simply do 3.50/15.25, which can be simplified to approximately 0.23.
- Note that percentage = 100 times decimal
100 x 0.23 = 23
The answer is 23%
Hope this helps :)
Have a nice day!
What is the value of x in this proportion?
Choose one of the choices below
2/7=−5x+3
x=−20 1/2
x=−19
x=−16
x=−14 1/2
Answer:
(a) -20 1/2
Step-by-step explanation:
The proportion can be solved using "cross multiply" as the first step. This eliminates the fractions and turns it into a linear equation.
2/7 = -5/(x +3) . . . . . given
2(x +3) = -35 . . . . . . multiply by 7(x +3)
2x = -41 . . . . . . . . . simplify, subtract 6
x = -20 1/2 . . . . . . divide by 2
Anyone know the answer to this?
Answer:
lmk if something doesnt add up
Step-by-step explanation:
I hope it helps
In which graph does line L have a negative slope?
Graph 1.
You have to look at the graph from left to right. If the starting point of the graph is higher than the endpoint, that means that the slope is negative. If the starting point is lower than the end point, it means the slope is positive.
Gabriella needs 120 meters of fence to surround a rectangular garden.
The length of the garden is three times its width, w.
How wide is the fence?
To fence a rectangular garden, we need to fence the length 2 times, and the width 2 times.
So, it will take 120 : 2 = 60 meters of fence to fence 1 length and 1 width
-> The length = 60 : (3+1)x3 = 45 (meters)
-> The width = 60 - 45 = 15 (meters)
Recheck : (45+15) x 2 = 120 and 45:15 = 3
(If it's wrong you can tell me, I don't really know what do you mean by how wide is the fence)
The width of the rectangular garden, for which Gabriella needs 120 meters of fence to surround it is 15 units long.
What is the perimeter of a rectangle?The measure of the boundary of the sides of a rectangle is called its perimeter. The perimeter of a rectangle is twice the sum of its length and width.
[tex]P=2(l+w)[/tex]
Here, (l) is the length of the rectangle and (w) is the width of the rectangle.
Let suppose the length of the garden is l units long. The length of the garden is three times its width, w. Thus,
[tex]l=3w[/tex]
Gabriella needs 120 meters of fence to surround a rectangular garden. This fencing is equal to the perimeter of the rectangular garden. Thus,
[tex]P=2(l+ w)\\120=2(l+ w)[/tex]
Put the value of length from equation 1 to this equation,
[tex]120=2(3w+ w)\\3w+w=\dfrac{120}{2}\\4w=60\\w=\dfrac{60}{4}\\w=15\rm\; units[/tex]
Thus, the width of the rectangular garden, for which Gabriella needs 120 meters of fence to surround it is 15 units long.
Learn more about the perimeter of the rectangle here;
https://brainly.com/question/19819849
Help me with this please I need this done today
Answer: See below
Step-by-step explanation:
Rewrite in vertex form
f(x) = 2x^2-8x+1
f(x) = 2(x^2-4x) + 1
f(x) + ? = 2(x^2 -4x +?) + 1
To find ?, calculate (b/2)^2, in this case, b is 2
(2/2)^2
= 4
f(x) + 4 = 2(x^2 -4x +4) + 1
f(x) + 2*4 = 2(x^2 -4x +4) + 1
f(x) = 2(x-2)^2 -7
Vertex: (2, -7)
Minimum: (2 -7) - Same as the vertex
A professor compares the number of absences for each student in his class with the student's final grade. The table below lists the absences and grade for each student.
Number of Absences (x) Final Grade (y)
10 55
2 80
7 68
7 65
3 90
6 72
15 38
8 74
1 85
5 80
3 85
4 90
The professor determines that the line of best fit for this data has the equation y=−3.68x+95.25.
Part A:
Explain what the slope of this line means in terms of the context.
Part B:
Explain what the y-intercept of this line means in terms of the context.
Answer:
Slope is 3.68
Y intercept is 95.25
Step-by-step explanation:
Slope is the rate of increase and it is the number next to X.
Y interecept is when X is 0 so if we put 0 to x we get 95.25
Please mark as brainliest if this helped
Identify the key features of the parabola that is formed by the equation
the y-intercept
the vertex
Is the vertex a maximum/minimum?
Round your answers to the nearest whole number.
Answer:
y-intercept: 58vertex: (2, 78) -- a maximumStep-by-step explanation:
The negative leading coefficient tells you this parabola opens downward, so the vertex will be a maximum. The constant is the y-intercept, which is 58.
__
The vertex is nicely found using a graphing calculator, but can also be found algebraically. The x-value is ...
x = -b/(2a) = -19.8/(2·(-4.9)) = 19.8/9.8 = 99/49 ≈ 2.02041
The value of f(99/49) is ...
f(99/49) = (-4.9(99/49) +19.8)(99/49) +58 = (9.9)(99/49) +58 ≈ 78.002
The location of the vertex is approximately ...
(x, y) ≈ (2.0204, 78.002) ≈ (2, 78)
The usual price of a bottle of champagne was $52. Stanley sold the bottle of champagne to Eugene for $59.80.
Find the percentage increase in price.
Answer:
u get 59.08 divide by 52 multiply by 100% u get da answer
3 tomatoes cost $1.29
How much will 5 tomatoes
cost?
Answer:
$2.15
Step-by-step explanation:
Since 3 Tomatoes cost $1.29
Then let's first find how much is 1 Tomatoes.
To do that we have to divide Cost by # of Tomatoes
3/1.29 = 0.43
Thus, 1 Tomatoes Cost 0.43
Now, the question is: How much will 5 tomatoes cost?
Therefore, 0.43 * 5 =2.15
Hence, 5 Tomatoes cost $2.15
[RevyBreeze]
Factor completely x3 6x2 8x 48. (x − 6)(x2 − 8) (x − 6)(x2 8) (x 6)(x2 − 8) (x 6)(x2 8).
By takin common we got that factorization of [tex]x^3+6x^2+8x+48[/tex] is [tex](x+6)(x^2+8)[/tex]
What is factorization ?
factorization is writing a expression as a product of several factors.
Given polynomial
[tex]x^3+6x^2+8x+48[/tex]
We can factorize it as
Taking [tex]x^2[/tex] common from first two terms and 8x common from last two terms
[tex]x^2(x+6)+8(x+6)[/tex]
Taking (x+6) common
[tex](x+6)(x^2+8)[/tex]
By takin common we got that factorization of [tex]x^3+6x^2+8x+48[/tex] is [tex](x+6)(x^2+8)[/tex]
To learn more about factorization visit :
https://brainly.com/question/11579257
Answer:
The answer is D (x+6)(x^2+8)
Step-by-step explanation:
im not the best at explaning but this is the only answer that makes sense have a good day! :)
simplify (2x-2y)(2y + 8)
Answer:
=4xy−4y2+16x−16y
Step-by-step explanation:
(2x−2y)(2y+8)
=(2x+−2y)(2y+8)
=(2x)(2y)+(2x)(8)+(−2y)(2y)+(−2y)(8)
=4xy+16x−4y2−16y
=4xy−4y2+16x−16y
Answer:-4y^2+4xy+16x-16y
Step-by-step explanation: Hi there.
For this answer I will show you the FOIL method.
Form: (ax-by)(cy-d)
1. Multiply ax and cy
2x*2y=4xy
2. Multiply ax and d
2x*8=16x
3. Multiply by and cy
-2y*2y=-4y^2
4. Multiply by and d
-2y*8=-16y
Add all of them together and you get:
-4y^2+4xy+16x-16y
Have a nice day! :)
Find the value of x
Answer:
23 degrees
Step-by-step explanation:
5: 100 = 2x + 3 + 51
100 = 2x + 54
100 - 54 = 2x
46 = 2x
x = 23 degrees
Answer:
I hope you can understand this
1.
The expected probability of rolling an even number in 1 roll of a fair cube with faces numbered 1 through 6 is 1/2 When the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. When the same cube was rolled 100 times, an even number came up 51 times, or almost 1/2 the time. Why are the actual results closer to the expected probability of 1/2 when rolling the cube 100 times?
Using the Central Limit Theorem, it is found that a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
That is, the standard error is inverse proportional to the square root of the sample size, hence a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.
More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
Answer this math word bank:
alternate interior angles, alternate exterior angles, vertical angles, adjacent angles, linear pair corresponding angles use the word bank and fill in the blanks (words will only be used once) < a and < b are ______________________ and __________________ angles. < b and < f and 55° are ____________________ angles. < a
The relationship between the angles depend on their relative positions.
Response:
∠a and ∠c are Vertical angles∠a and ∠b are Adjacent angles and linear pair angles∠b and ∠h are Alternate interior angles∠f and 55° are Alternate exterior angles∠a and ∠e are Corresponding angles How can the different angles formed be identified?The possible drawing in the question created based on the relationship between the angles is attached.
∠a and ∠c;
Vertical angles: Opposite angles formed by intersecting lines∠a and ∠b
Adjacent angles: Angles that share a common sideLinear pair angles: Adjacent angles that sum up to 180° or form a straight line∠b and ∠h
Alternate interior angles: Angles formed on the opposite side of a transversal intersecting two coplanar lines, and in the interior region between the lines∠f and 55°
Alternate exterior angles: Angles formed on the exterior region between two lines having a common transversal and on the opposite sides of the transversal∠a and ∠e
Corresponding angles: Angles formed in similar positions relative to a transversal and the two lines intersected.Learn more about different types of angles here:
https://brainly.com/question/17006592
what is 5/6 ÷ 10/21 (show ur work)
Answer:
105/61 is the answer for 5/6 ÷ 10/21
Sabendo que 1 UA = 1,496 .10^11 metros e que a distância média entre a Terra e a Lua é 384 400 000 metros, podemos afirmar que essa distância em unidades astronômicas é: *
3,8917 x 10^(-2) 2,5695 x 10^(-3) 3,8917 x 10^2 2,5695 x 10^3
Answer:
The answer would be a because I checked my work and it shows to be A
i hope this work for you
and sory if im wrang
If a star is 17 light-years away, how long does the light from the star take to reach earth?.
Answer:
17 years
Step-by-step explanation:
a light year is a measurement of distance where each light year is equal to the distance light would travel in a year
answer quick please!
Answer:
B and C
Step-by-step explanation:
AND SHE SAID SHE SAID SHES FROM HAWAI ♀️DO U KNOW HOW TO ♀️SAY CUTE IN JAPANESE "KAWAII"
The area of the triangle is 11.02 square centimeters. What is the length of the base if the height is 2.9?
Answer:
7.6
Step-by-step explanation:
area of triangle=1/2(bxh)
make equation
11.02=1/2(2.9b)
solve
22.04=2.9b
7.6=b
Please help me, I'm so lost! If you can explain it to me, I will give brainliest!
Answer:
40
y = ----
3
Step-by-step explanation:
[tex]\\ \rm\rightarrowtail \dfrac{3y-8}{12}=\dfrac{y}{5}[/tex]
[tex]\\ \rm\rightarrowtail 5(3y-8)=12y[/tex]
[tex]\\ \rm\rightarrowtail 15y-40=12y[/tex]
[tex]\\ \rm\rightarrowtail 3y=40[/tex]
[tex]\\ \rm\rightarrowtail y=40/3[/tex]
Ben owns an ice cream shop. Last quarter's income was $9,000; his cost of goods was $575, and his total expenses were $5,000.
What is Ben's Gross Profit for the last quarter?
Click this link to open the Business Financials Part 2 Study Guide to view the formula used for this problem!
Type a comma to separate the digits and type the $ symbol when you enter your answer as shown below:
Example: $15,300
Answer: $8,425
Step-by-step explanation:
•Gross Profit = Income - Cost of Goods
- Ben's Income was $9,000 and his cost of goods were $575.
-Therefore, $9,000 - $575 = $8,425
Please help! The table shows the results of rolling a number cube with sides labeled 1 through 6 several times.
Answer: I think the answer is 3
Step-by-step explanation:
I need help
I will give BRAINLY and
FIVE STARS PLUS THANKS
Answer:
8 to 7
Step-by-step explanation:
5/7 to 5/8 = 40/56 to 35/56
We then have:
5/7 to 5/8 = 40 to 35
Now...
40 to 35 = 8 to 7
P.S: These colons ':' mean the same as 'to' in ratios
