Answer:
Step-by-step explanation:
Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.
a³/b³=1001/1024+45*sqrt(23)/1024*i
b³/a³=1001/1024-45*sqrt(23)/1024*i
Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!
If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.
It is -2c=-2*1001/1024=-1001/512, and
c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.
A recent survey was given to determine students favorite school subjects. 6 students chose Math, 3 students chose Science, 4 students chose English and 7 students chose History. Predict the number of students out of 400 that would pick math as their favorite subject
Out of 400 students, 120 students would pick math as their favorite subject.
Data provided to us
fav subject students
Math 6
Science 3
English 4
History 7
Hence the total becomes 20 students
we have to calculate students whose favorite subject is math from 400 students
students with math as fav subject out of 20 students = 6
students with math as fav subject out of 400 students = (6 / 20) x 400
= 120 students
we can verify it as
%age of students out of 20 , who like math = 6/20 x 100
= 30 %
similarly, %age of students out of 400, who like math= 120/400 x 100
= 30 %
As we can see both the percentages are same. and the answer is verified .
So 120 students would pick math as their favorite subject out of 400 students.
learn more about survey and percentage here :
https://brainly.com/question/17360321
#SPJ4
Choose the graph of g(x) = |x-1| and its parent function f. Then choose the description of the
transformation.
Bill Gutierrez drove 130 miles at a speed of 65 miles per hour on an expressway for 2 hours. He drove 67.5 miles for 1.5 hours at 45 miles per hours on a state highway. What is his average speed?
Bill's average speed throughout his journey is 55mi/hr
Average Speed
The average speed Bill drove can be calculated using the formula of speed which is given as
[tex]speed = \frac{distance}{time}[/tex]
Substituting all the values into the equation, we can find the speed.
130 miles at 65mi/hr, 67.5miles at 1.5 hours and 45mi/hr.
[tex]average speed = \frac{65 + 45}{2} = \\speed = \frac{110}{2} = 55mi/hr[/tex]
The average speed at the end of the journey is 55mi/hr
Learn more on average speed here;
https://brainly.com/question/6504879
#SPJ1
What is the equation of the line that is perpendicular to the line y = -5x - 12 and passes through the
point (10, 4).
Line's equation is y=(1/5)x + 2.
What does perpendicular mean?
In elementary geometry, two geometrical objects are perpendicular if they intersect at a right angle. The condition of perpendicularity can be graphically represented using the perpendicular symbol,. Any pair of lines, any pair of planes, or any pair of lines and planes can be used to define it.
The arrow
In slope-intercept form, y=-5x12
y=mx+b
where the slope m is.
Thus, the slope of this line is
m= -5
Slopes on perpendicular lines are reciprocally negative. In other words, modify the sign by taking the slope's reciprocal.
The reciprocal of (-5) in the negative is 1/5.
Plug in the point to determine b in the formula y = (1/5)x + b.
4 = (1/5)(10) + b
4 = 2 + b
b = 2
The perpendicular line passing through the indicated point is y= (1/5)x + 2.
Thus, the equation of the line that is perpendicular to the line y = -5x - 12 and passes through the point is y= (1/5)x + 2.
point (10, 4). (10, 4).
To learn more about Perpendicular click on the link
https://brainly.com/question/1202004
#SPJ9
What is the correct notation for a ray with endpoint E
Answer:
There isn't an image to go with your question. repost this question with an image to be able to receive an answer.
Have a nice day :)
Answer:
Step-by-step explanation: You don't have an picture for me to explain add a picture and I'll be able to help you.
The equation for line A is given by y = 1/2 x + 4 suppose line A is parallel to line B and line T is perpendicular to line A point (- 3, 1) lies on both lineB and liner T. Part A write an equation for line B Part B Write an equation for line T
We will find lines B &
suppose that, in the base period, a college student buys 20 gallons of gasoline at $2 per gallon, 2 mugs for $13 each, and 4 movie tickets for $7 each. in the next month, the price of gasoline is $2.25 per gallon, mugs cost $12.50 each, and the price of a movie ticket is $7.50. the change in the price level from the first to the second month is:
The change in the price level from the first to the second month is 106.4
What is meant by price index?Price index: Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places.
A college student purchases 4 movie tickets for $7 each, 2 CDs for $13 each, and 20 gallons of gasoline at $2 a gallon during the base period.
Gas will cost $2.25 per gallon in the upcoming month, CDs will cost $12.50 each, and cinema tickets will cost $7.50
The price index
=(price in current year/price in last year) x 100
=100/94 x 100
=106.38 or 106.4
The change in the price level from the first to the second month is 106.4
To learn more about Money problems visit:
brainly.com/question/19294126
#SPJ4
View the image to answer the question.
Considering the table of f ( x ) and graph of g ( x ), the value of the expression [tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex] is represented by 3
How to determine the value when x tends to 1 using the graph and the tableThe table represents the values of f ( x ). Using the table, checking the value of f ( x ) when x = 1 gives f ( x ) = 1
Using the graph, the value of g ( x ) when x = 1 is traced to give a value of -1
substituting the values of f ( x ) = 1 and g ( x ) = -1 into the equation
[tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex]
[tex]=\lim_{x \to 1} 2f(1)+g(1)^2[/tex]
[tex]=2(1)+(-1)^2[/tex]
= 2 + 1
= 3
This makes the third option the best choice and the value is 3
Learn more about graphs and tables for limits here: https://brainly.com/question/12746952
#SPJ1
23 out of 26 students want pancakes and the rest want waffles. What is the ratio of the number of students who want waffles to the total number of students?
Write your answer as two numbers separated by a colon (for example, 2:3).
please help asap!!!!
The ratio of the number of students who want waffles to the total number of students is 3 : 26 students
The ratio of the number of students who want waffles to the total number of students?Ratio refers to the number representing a comparison between two named things or quantities.
Total number of students = 26Number of students who wants pancakes = 23Number of students who wants waffles = Total number of students - Number of students who wants pancakes
= 26 students - 23 students
= 3 students
Ratio of the number of students who want waffles to the total number of students = 3 students : 26 students
So therefore, the ratio of the number of students who want waffles to the total number of students separated by a colon is 3 : 26
Read more on ratio:
https://brainly.com/question/2328454
#SPJ1
What value of n makes the equation true ?
8 × 0.25n = 2n
8 × -2 = -16
-0.5 × 8 = -4
-0.5 × -4n = 2n
2n - 16 + n= -4 + 2n
2n + n = 3n
3n - 16 = -4 + 2n
-2n -2n
n - 16 = -4
+16 +16
n = 12
Anya has 115 mangoes lauren has five times the the number of mangoes Anya has they put them together and sold them in the market at $450 to $15 the sold all the mangoes how much money was collected at the end of the sale
The total amount of money collected if Anya and Lauren sold their mangoes at $15 is $10,350
How to find total revenue made from selling the mangoes?Number of mangoes Anya has = 115 mangoesNumber of mangoes Lauren has = 5 × 115= 575 mangoes
Total number of mangoes = Number of mangoes Anya has + Number of mangoes Lauren has
= 115 + 575
= 690 mangoes
Amount each mangoes was sold = $15
Total amount of money collected = Total number of mangoes × Amount each mangoes was sold
= 690 × 15
= $10,350
So therefore, Anya and Lauren sold their total mangoes for $10,350
Read more on revenue:
https://brainly.com/question/23706629
#SPJ1
HELPPPP PLEASEEEE
If y varies directly with x, and y=18
when x=6
, find the value of y when x=4
.
Answer:
y=12
Step-by-step explanation:
1.Took the ratio between x and y value.
18:6 is the same as 3:1 ratio this means that our y value will be 3 times greater than our x value.
9 = 3y + 37 + 4y solve for y and simplify as much as possible
[tex]3y + 37 + 4y = 9 \\ 3y + 4y = 9 - 37 \\ 7y =- 28 \\ \frac{7y}{7} = \frac{-28}{7} \\ y = -4[/tex]
ATTACHED IS THE SOLUTION
Please help,
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Woozy Wheel and the Roller Rail.
A. 119 units
B. 11 units
C. 169 units
D. 13 units
Answer:
D. 13 units
Step-by-step explanation:
Woozy Wheel: (-14, 1)
Roller Rail: (-2, -4)
[tex] \sqrt{ { - 14 - ( - 2))}^{2} + {(1 - ( - 4))}^{2} } [/tex]
[tex] \sqrt{ {( - 12)}^{2} + {5}^{2} } [/tex]
[tex] \sqrt{144 + 25} = \sqrt{169} = 13[/tex]
The distance between the Woozy Wheel and the Roller Rail is D. 13 units
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is
D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given, A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
The point at which Woozy Wheel is (-14, 1) and the point at which Roller Rail
is (-2, - 4).
∴ The distance between the Woozy Wheel and the Roller Rail is,
D = [tex]\sqrt{(-2 + 14)^2 + (-4 - 1)^2}[/tex] units.
D = [tex]\sqrt{(12)^2 + (-5)^2}[/tex] units.
D = [tex]\sqrt{144 + 25}[/tex] units.
D = [tex]\sqrt{169}[/tex] units.
D = 13 units.
learn more about the distance formula here :
https://brainly.com/question/28956738
#SPJ2
Describe a series of transformations that takes triangle Q to triangle P.
ANSWER: Translation of Triangle Q to Triangle P
Horizontal shift 4 units left and Vertical shift 1 unit upward
Find the number which wohen added
to its square, makes 90..
Answer: -10 or 9
Step-by-step explanation:
Let the number be x. Then,
[tex]x^2 +x=90\\\\x^2 +x-90=0\\\\(x+10)(x-9)=0\\\\x=-10, 9[/tex]
can anyone help me pls?
1. Which kind of model do you think best represents the profit for each business?
2. Find a function that models the profit you can expect, based on your projections, for each business. You can round your values to the nearest thousandth, as needed.
Lawn care is kind of model do you think best represents the profit for each business.
What is profit?
The financial gain a business has when revenue exceeds costs and expenses is repeatedly alluded to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the drink. She made $1.75 in profit just on cup of lemonade.Dog walker = 5 + 12 + 23 + 50 + 62 + 82 = $234
House sitter = 11 + 19 + 29 + 38 + 50 + 73 = $220
Lawn care = 142 + 150 + 165 + 141 + 120 + 91 = $809
Lawn care is kind of model do you think best represents the profit for each business.
Learn more about profit
brainly.com/question/14281684
#SPJ13
Factorise:
x² + 6x - 16
Answer:
(x-2)(x+8)
Step-by-step explanation:
What is the volume of this sphere? Use : 3.14 and round your answer to the nearest hundredth. 9 yd cubic yards
3,058.08 cubic yards
Explanation:radius = 9 yd
π = 3.14
Volume of a sphere = 4/3 πr³
Volume of sphere = 4/3 × 3.14 × 9³
Volume of sphere = 3052.08
To the nearest hundredth, the volume 3,058.08 cubic yards
solve for w -5.36=10+w/6
An expression is a collection of variables and constants that are bound by some mathematical operation the value for w for the given expression w -5.36=10+w/6 is 18.432.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
w - 5.36 = 10 + w/6
Subtract w/6 both sides,
w - w/6 - 5.36 = 10 + w/6 - w/6
5w/6 = 10 + 5.36
w = 18.432
Hence "The value for w for the given expression w -5.36=10+w/6 is 18.432".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ1
Help please promise i'm Grade 2 and I don't know what is this but please help our teacher didn't teach us this.
Answer:
First one is 92
Step-by-step explanation:
Answer:
1. 9/2
2. 7 3/13
3. 3 13/15
4. 3 25/27
5. 2 1/4
6. 3 30/91
7. 2 5/21
8. 6 3/5
Step-by-step explanation:
When I put it like 2 5/21 I mean it's a mixed number.
Now I'll tell you the steps.
1. Find the common denominator (The denominator is the bottom number of the fraction. To find it you have to write out the multiplies of each number and once a number is the same that's the common denominator.)
2. Multiply the numerator by the amount of times it took to find the common denominator. (The numerator is the top number of the fraction. And the amount of times you'll have to multiply the numerator depends. I'll put an example below)
Example:
4/20 ÷ 7/2
2 goes into 20, 10 times so you have to multiply 7 by 10.
Then you'll get
70/20.
Now you can solve it.
4/20÷70/20
(I put random numbers so the answer may turn out funky this is just an example.)
3. Divide the fractions
4. Simplify answer if possible
I hope this helped!
Find m∠1 and m∠2. Tell which theorem can be used.
Answer:
m∠1 = 140 by the Alternate Interior Angles Theorem
m∠2 = 40 by the Consecutive Interior Angles Theorem
Step-by-step explanation:
What is the solution to the inequality x2 + 2x ≤ 24?
Answer:
-6 ≤ x ≤ ∨ x = 4
Step-by-step explanation:
x^2 + 2·x ≤ 24
x^2 + 2·x - 24 ≤ 0
-1 - √(1 + 24) ≤ x ≤ -1 + √(1 + 24)
-1 - 5 ≤ x ≤ -1 + 5
-6 ≤ x ≤ ∨ x = 4
Solve for X to the nearest tenth please help me asap
Answer:
10.4
Step-by-step explanation:
explanation in photos
What's the best food you could eat?
Answer:
It unexpected, but did you know you could live over 40 years on just pizza! Crazy! It's not so good tho because of all the salt in it, so that's not THE HEALTHIEST. I've looked it up and, fish seems to be the top choice when it comes to what's good for you. I've also have come across dark green vegetables too.
Step-by-step explanation:
I didn't notice you were just talking about what tastes good rather than whats healthiest.... eh! YOUR NOW EDUCATED!!!
Hope it helps! =D
Express (23)−2 using exponents
The expression as an exponent is 21^1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
(23) - 2
Open the bracket in the above expression
So, we have the following equation
(23) - 2 = 23 - 2
Evaluate the difference in the above expression
So, we have the following equation
(23) - 2 = 21
The above expression can be rewritten as
(23) - 2 = 21^1
Hence, the equivalent expression is 21^1
Read more about expressions at
https://brainly.com/question/723406
#SPJ1
What is Huangmei Opera, and where did Huangmei Opera originate?
Answer:
look at explanation!
Step-by-step explanation:
Huangmei Opera is a local opera of the Han nationality. Being one of Chinese big five operas, Huangmei Opera enjoy equal popularity with Beijing Opera, Yue Opera, Ping Opera and Yu Opera. It originates from Huangmei, a junction of Hubei, Anhui and Jiangxi.
is one of the five major opera genres in China. It is the main local opera in City, Anhui Province. The predecessor of Opera is and Anhui Opera. Also known as tune, in the middle and late Dynasty, tea picking tune was combined with local folk opera in Prefecture, Anhui Province, and sung and recited in dialect of , and gradually developed into a new type of opera, which was called at that time. This is the early stage The prototype of i Opera. Later, drew on the music, performances and repertoires of and , and began to perform "this opera". Later, with Town, County, Prefecture as the center, and after more than 100 years of development, it became an independent large-scale local drama - Anhui Opera, which was renamed " Opera" in the Opera is the main local opera variety in Anhui, and after spreading to the neighboring City, Jiangxi Province, and City, Hubei Province, it eventually became a well-known national opera variety. There are also professional and amateur performance groups of Opera in Taiwan and Taiwan, which are widely welcomed. After the founding of the People's Republic of China, it quickly developed into an influential opera genre in the whole of China and became famous overseas. In 2006, Opera was selected into the first batch of China's national intangible cultural heritage.
Step-by-step explanation:
please help
with answer
Answer: -20
Step-by-step explanation: 16 x 1/4 - 4x 6
Solve for x in the triangle. Round your answer to the nearest tenth.
20
X
52°
X =
Answer:
25.4
Step-by-step explanation:
use sine rule [tex]\frac{a}{sinA}[/tex]=[tex]\frac{b}{sinB}[/tex]
[tex]\frac{20}{sin(52)}[/tex] ×sin(90)
or
use sine rule [tex]\frac{opposite}{hypotenuse}[/tex] = sinФ
[tex]\frac{20}{h}[/tex]=sin(52)
rearrange-
20÷sin(52)=h
(h is x)
Last year, Raina had $10,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 6% simple interest per year. After one year, she received a total of $620 in interest. How much did she invest in each account?
If after one year, she received a total of $620 in interest. The amount that she invest in each account is 2,000 amount invested at 7% , 8,000 amount invested at 6.
Amount investedLet x represent the amount invested
Hence,
.07x + .06(10,000-x) =620
.07X+600-.06x = 620
Combine like terms
.01x =620-600
.01x=20
Divide both side by .01x
x=20/.01
x =2,000 amount invested at 7%
So,
10,000-2,000 = 8,000 amount invested at 6%
Check :
.07 × 2,000+.06× 8,000=620
150 + 480 = 620
620 = 620
Therefore we can conclude that $2,000 was invested at 7% and $8,000 was invested at 6%.
Learn more about amount invested here: https://brainly.com/question/25300925
#SPJ1