Answers
The explanation is shown below:
1. To solve the problem shown in the figure above, you must apply the following proccedure:
2. You have that the roots of the quadratic equation shown in the figure attached in the problem are:
x=-1±i
3. Then, you know the quadratic formula to solve quadratic equations, which is:
(-b±√(b^2-4ac))/2a
4. You can see in the figure that a=1 and c=2; then, by analizing this, you can conclude that the coefficient b is:
b=-2
5. Therefore, you can conclude tha the quadratic equation is:
x^2-2x+2=0
6. If you want to verify it, apply the quadratic formula to the quadratic equation shown above and you will obtain the roots shown in the figure.
To form a quadratic equation, let α and β be the two roots.
Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).
According to the problem, roots of this equation are α and β.
Therefore,
α + β = - baba and αβ = caca.
Now, ax22 + bx + c = 0
⇒ x22 + babax + caca = 0 (Since, a ≠ 0)
⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]
⇒ x22 - (sum of the roots)x + product of the roots = 0
⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)
Formula (i) is used for the formation of a quadratic equation when its roots are given.
Given the roots: (-1+-i)
where; i=sqrt(-1)
Thus, the answer is (2x)
You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)
Related Questions
PLEASE HELP ME!!!!!!!! ASAP
Answers
A
The A choice is that the y intercept of g(x) < y intercept of f(x). Remember, a y intercept occurs when x = 0
g(x) = 2 * sqrt(x) - 8
g(0) = 2*0 - 8
g(0) = - 8
=======
f(x) = - 4 when x = 0 (you just read it.) - 4 is greater than -8. That's a true statement. Think money. Would you rather be 4 dollars in debt or 8 dollars in debt?
A: True <<<<<< answer for A.
B
y intercept occurs when x = 0 The values of f(x) and g(x) have been found in part A.
Are they equal?
The y intercept of g(x) = g(0) = 2*sqrt(0) - 8 = - 8
The y intercept of f(x) = f(x) = - 4 when x = 0
Conclusion
They are not equal and B is not the answer.
C
The x intercept occurs when y = 0
g(x) = 0
0 = 2*sqrt(x) - 8
8 = 2*sqrt(x)
4 = sqrt(x)
x = 16
======
When f(x) = 0, x = 16.
Conclusion
The x intercepts are both 16. This statement is true.
C: True <<<<<< answer.
D
If the condition is anything but equal, the statement is false. g(x) is not greater then f(x).
D <<<<<< False.
in a city of 88,000 people, there are 33,000 people under 25 years of age. What percent of the population is under 25 years of age?
Answers
A hotel has $504 to buy new pillows. If the cost of each pillow is $6, how many pillows will the hotel be able to buy? A) 78 B) 84 C) 88 D) 96
Answers
You can use the equation:
504 ÷ 6
84
The hotel can buy 84 pillows.
Hope this helped! :D
504 ÷ 6 = 84
Therefore, the hotel can buy 84 pillows
Hope this helps!
Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a two or a three. what are the expected winnings?
Answers
somebody please help so I can pass, please
Rewrite the following equation in the form y = a(x - h)2 + k. Then, determine the x-coordinate of the minimum.
y=2x^2 - 32x + 56
The rewritten equation is y = ____ (x - _____ )2 + ____ .
The x-coordinate of the minimum is _____
Answers
We now from our quadratic that [tex]a=2[/tex] and [tex]b=-32[/tex], so lets use our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-(-32)}{2(2)} [/tex]
[tex]h= \frac{32}{4} [/tex]
[tex]h=8[/tex]
Now we can evaluate our quadratic at 8 to find [tex]k[/tex]:
[tex]k=2(8)^2-32(8)+56[/tex]
[tex]k=2(64)-256+56[/tex]
[tex]k=128-200[/tex]
[tex]k=-72[/tex]
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
[tex]y=2(x-8)^2+(-72)[/tex]
[tex]y=2(x-8)^2-72[/tex]
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is [tex]y=2(x-8)^2-72[/tex]
The x-coordinate of the minimum is 8
Answer:
y = 2 (x - 8 )2 + (-72)) .
The x-coordinate of the minimum is 8.
Step-by-step explanation:
I just took this test on plato and I got it correct.
Determine whether the given equation has one solution, no solution, or infinitely many solutions. x+4/4=x+3/3
A. one solution
B. no solution
C. infinitely many solutions
D. cannot be determined
Please explain what you did to get the answer (it'll help me learn better)
Answers
Check the attachment.
Hope it helps you :)
Answer:
There can be only one solution
Step-by-step explanation:
The only soution is zero, because anything else is unequal.
Mr. Smith earns 6% commission on every house he sells. If he earns 9,000, what was the price of the house?
Answers
Add it to 9000
Total sum is your answer
$9000/0.06 = sale price . . . . . . . . .. divide by 0.06
150,000 = sale price . . . . . . . . . . . . . evaluate
The price of the house was $150,000.
PLEASE HELP ***What is the length of AC??? Please help me understand how to find this
Answers
AC and CE have the same ratio as BA and DE. So you can get the answer by getting their proportions.
84 = 7
156-x x
Cross multiply, transpose, and simplify to get the variable x.
84x = 1092-7x
84x + 7x = 1092
91x = 1092
x = 12
To get AC, substitute.
AC = 156 - x
AC = 156 - 12
AC = 144
What equation results from completing the square and then factoring? x^2-8x=39
Answers
x²-8x=39
Group terms that contain the same variable
(x²-8x)=39
Complete
the square. Remember to balance the equation by adding the same constants
to each side
(x²-8x+16)=39+16
Rewrite as perfect squares
(x-4)²=55-------> (x-4)²-55=0(+/-)]x-4]=√55
(+)]x-4]=√55--------> x=4+√55
(-)]x-4]=√55-------> x=4-√55
the answer is
(x-4)²-55=0
Answer: (x-4)²=55
Step-by-step explanation:
This is apex answer
A six-sided die in which each side is equally likely to appear is repeatedly rolled until the total of all rolls exceed 400
Answers
Approximately 0.2266, or 22.66%, is the probability that rolling the die more than 140 times is needed to exceed a total of 400.
To approximate the probability that rolling the die more than 140 times is needed to exceed a total of 400, we can use a normal approximation to the binomial distribution since the number of rolls is large.
First, let's calculate the mean (μ) and standard deviation (σ) of the number of rolls needed to exceed 400:
[tex]\[ \text{Mean (μ)} = \frac{\text{Total target}}{\text{Expected value per roll}} = \frac{400}{\frac{7}{2}} \][/tex]
[tex]\[ \text{Standard deviation (σ)} = \sqrt{\frac{\text{Total target} \times (\text{Sides}^2 - 1)}{12}} = \sqrt{\frac{400 \times (6^2 - 1)}{12}} \][/tex]
Now, we'll use the normal approximation and the z-score formula to find the probability:
[tex]\[ z = \frac{\text{X} - \text{μ}}{\text{σ}} \][/tex]
[tex]\[ z = \frac{140 - \text{μ}}{\text{σ}} \][/tex]
Then, we look up the z-score in a standard normal distribution table or use a calculator to find the probability associated with that z-score.
Let's calculate these values.
First, let's calculate the mean (μ) and standard deviation (σ):
[tex]\[ \text{Mean (μ)} = \frac{400}{\frac{7}{2}} = \frac{800}{7} \approx 114.29 \][/tex]
[tex]\[ \text{Standard deviation (σ)} = \sqrt{\frac{400 \times (6^2 - 1)}{12}} = \sqrt{\frac{400 \times 35}{12}} \approx \sqrt{\frac{14000}{12}} \approx \sqrt{1166.67} \approx 34.16 \][/tex]
Now, let's find the z-score for rolling the die more than 140 times:
[tex]\[ z = \frac{140 - \text{μ}}{\text{σ}} = \frac{140 - 114.29}{34.16} \approx \frac{25.71}{34.16} \approx 0.75 \][/tex]
Using a standard normal distribution table or calculator, we find the probability associated with a z-score of 0.75, which represents the probability that rolling the die more than 140 times is needed to exceed a total of 400.
The Correct Question is :
A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. Approximate the probability that this will require more than 140 rolls.
The approximate probability that it will require more than 140 rolls for the total to exceed 400 is 0.005.
To find the approximate probability that it will require more than 140 rolls for the total to exceed 400, we can relate it to the probability that the sum of the first 140 rolls is less than 400.
Let X be the random variable representing the sum of the rolls. We want to find P(X > 400), which is the probability that it will require more than 140 rolls.
We can calculate this by finding the complement of the event that the sum of the first 140 rolls is less than 400.
Let A be the event that the sum of the first 140 rolls is less than 400. Then, P(A) is the probability that we're interested in.
Now, we calculate P(A):
Since each side of the die is equally likely, the expected value of the roll is [tex]\( \frac{1+6}{2} = 3.5 \)[/tex].
The expected value of the sum of the first 140 rolls is [tex]\( 140 \times 3.5 = 490 \)[/tex].
Therefore, P(A) can be approximated using the normal distribution, since the sum of the rolls follows approximately a normal distribution due to the Central Limit Theorem.
Using the properties of the normal distribution, we can standardize the value:
[tex]\[ Z = \frac{400 - 490}{\sqrt{140 \times \left(\frac{1}{12}\right)}} \][/tex]
Here, [tex]\( \frac{1}{12} \)[/tex] is the variance of a single roll of the die.
Now, we find P(A) using the standardized value of Z:
P(A) = P(X < 400) = P(Z > z)
We can then find the probability from a standard normal distribution table or calculator.
[tex]\[ P(A) \approx P(Z > -2.589) \][/tex]
From a standard normal distribution table, we find that [tex]\( P(Z > -2.589) \approx 0.995 \)[/tex].
So, the approximate probability that it will require more than 140 rolls for the total to exceed 400 is 1 - 0.995 = 0.005.
The probable question may be:
A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. What is the approximate probability that this will require more than 140 rolls? (Hint: Relate this to the probability that the sum of the first 140 rolls is less than 400.)
When s is the open hemisphere x 2 + y 2 + z 2 = 1, z ≤ 0 , oriented by the inward normal pointing to the origin, then the boundary orientation on ∂s is clockwise. true or false?
Answers
Therefore, the answer above False
3 times as much as the sum of 3/4 and 2/6
Answers
The result of 3 times as much as the sum of 3/4 and 2/6 is; 13/4
Fraction and ArithmeticsFirst, we must evaluate the sum of 3/4 and 2/6; we have;
3/4 + 2/6Using the lowest common multiple; 12
We have; (9 +4)/12 = 13/12.
Therefore, 3 times 13/12 = 39/12 = 13/4
Read more on fraction addition;
https://brainly.com/question/11562149
What is the cube root of 216x^9y^8
Answers
Please, see the attached file.
Thanks.
(216x^9y^8)^(1/3)
216^(1/3) = 6
9/3 = 3
8/3 = 2 2/3
(216x^9y^8)^(1/3) = 6 x^3 y^2 y^(2/3)
Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with mu equals100 and sigma equals 15. explain your reasoning. (a) p(90less than or equals x overbarless than or equals110) for a random sample of size nequals 10 (b) p(90less than or equals x overbarless than or equals110) for a random sample of size nequals 20
Answers
hey can you please help me posted picture of question
Answers
Vertical translation is obtained by adding or subtracting a number from the function. Addition of a number brings about upward translation and subtraction of a number brings downward translation.
So, the answer to this question is option A
what is the median for the set of data shown? 26,34,38,49,65,75,81
Answers
Answer: 49
Step-by-step explanation:
We need to remember that the median of a set of data is the middle value in the set.
To find the median of a set of data the first step is to arrange the data in order from least to greatest, but, in this case, the set of data given is already arranged from least to greatest:
26,34,38,49,65,75,81
Therefore, you can oberve that the middle value in the set is the following:
26,34,38,49,65,75,81
Then, the median for this set of data is: 49
The answer is provided in the image attached.
PLZ HELP NOOWWWWWWW!!!
The diameter of a certain planet is approximately 3x10^7 meters (aka 30000000 meters). The length of a certain city is approximately 5x10^4 meters (aka 50000 meters).
How many times greater is the diameter of the planet compared to the length of the city?
Answers
You divide the diameter of the planet by the length of the city
30000000 / 50000 = 600
The diameter is 600 times greater than the length of the city
The answer is 600
Hope this helps!
What is the difference between 2386 and 7000?
Answers
Suppose that a sample of size 44 is drawn from a population with mean 36 and standard deviation 47, find the standard deviation of the distribution of sample means
Answers
Answer:
Standard deviation of the distribution of sample means = 7.0855
Step-by-step explanation:
We are given that a sample of size 44 is drawn from a population with mean 36 and standard deviation 47.
Using Central Limit Theorem, it is stated that;
Standard deviation of the distribution of sample means = [tex]\frac{Population S.D.}{\sqrt{n} }[/tex]
= [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{47}{\sqrt{44} }[/tex] = 7.0855
Please help me with this
Answers
The explanation is shown below:
1. By definition, a geometric sequence is a sequence of numbers each number, after the first one, is the result of multiply the previous number by a common ratio.
2. The Option B has the following common ratio:
(2/3) / (4/9)=1.5
1/(2/3)=1.5
r=1.5
3. The Option E has the following common ratio:
-15/3=-5
75/-15=-5
r=-5
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch apothem
A = sq. in
Answers
a is the apothem and A is area:
A=√3/4(6)²
A= 9√3
Answer: 12√3 square inches
Step-by-step explanation:
By the property of equilateral triangle,
Apothem = √3/2 × Side
⇒ Side = 2/√3 × Apothem
Here, apothem = 6 inches
Thus, the side of the given equilateral triangle = [tex]\frac{2}{\sqrt{3}}\times 6[/tex]
= [tex] \frac{12}{\sqrt{3}}[/tex]
= [tex]4\sqrt{3}[/tex] unit
Since, For an equilateral triangle,
[tex]\text{ Area} = \frac{\sqrt{3}}{4}\times (\text{ side})^2[/tex]
⇒ The area of the given equilateral triangle = [tex] \frac{\sqrt{3}}{4}\times (4\sqrt{3})^2[/tex]
[tex]=\frac{\sqrt{3}}{4}\times 48[/tex]
[tex]=12\sqrt{3}[/tex] square inches
The polygon circumscribes a circle find the perimeter of the polygon
Answers
Polygons that encircle a circle contain tangents of similar length, as such the perimeter of the polygon that circumscribes the circle is 76 cm.
The act of circumscribing a circle inside a polygon involves the process of drawing a circle that perfectly fits in the polygon by bisecting two arcs on each side of the polygon and then drawing a circle where all the sides meet in the middle of the polygon.
Polygons that encircle a circle contain tangents of similar length that originate at the same vertex, which explains the computation of the dimensions.
Taking a look at the figure attached, we have:
Two tangents with a length of 19 cmTwo tangents with a length of 9 cmTwo tangents with a length of 4 cmTwo tangents with with a length of 6 cmThus, the perimeter of the polygon can be calculated as:
= (19 + 19 + 6 + 6 + 4 + 4 + 9 + 9) cm
= 76 cm
Learn more about the perimeter of a polygon here:
https://brainly.com/question/15387363
What is the median of the data set: 50, 54,62,48,49,52
Answers
First, sort the data from least to greatest:
48, 49, 50, 52, 54, 62
The median lies between the number 50 and 52
The median is 51
On a bulletin board, the principal, Ms.Gomez, put 115 photos of the fourth grade students in her school. She put the photo in 5 esqueleto rows. How many photos did she put in each row?
Answers
23 photos per row. Got it? Good.
1. WHAT DOES IT MEAN TO SOLVE A RIGHT TRIANGLE?
2. HOW CAN YOU SOLVE RIGHT TRIANGLES USING SIMILARITY? THE PYTHAGOREAN THEOREM?
3. WHAT IS THE RELATIONSHIP BETWEEN THE SIDES AND ANGLES MEASURES OF RIGHT TRIANGLES THAT
DESCRIBE TRIGONOMETRIC FUNCTIONS?
4. WHAT ARE THE INVERSE TRIGONOMETRIC FUNCTIONS? HOW ARE THE INVERSE FUNCTIONS USED WHEN
SOLVING RIGHT TRIANGLES?
5. WHAT IS THE RELATIONSHIP BETWEEN THE ANGLE OF ELEVATION AND THE ANGLE OF DEPRESSION?
GIVE AN EXAMPLE OF AN APPLICATION USING THE ANGLE OF ELEVATION OR THE ANGLE OF DEPRESSION.
Answers
1) Solving a right triangle means finding the values of the unknown {most likely a variable}
2) The picture is for the Similarity in Right Triangles, I couldn't explain it.
How you can use Pythagorean Theorem: The formula for that is (a^2 + b^2 = c^2). The longest side of a triangle is called the hypotenuse, and the other sides are called legs. You usually use Pythagorean Theorem when you are trying to find an angle of a side. A and B in the formula are the legs and C is the hypotenuse, it makes sense because the hypotenuse is the longest side of the triangle, which means that it has a greater angle than the legs. So say you have a triangle with a leg of 5, a leg of 7, and the hypotenuse is unknown. (If you're a visual person, I also drew it on paint and put it in :P) The formula is a^2 + b^2 = c^2. The ^2 is an exponent, which means that we have to multiply the base by itself that many times. For example, if we had 3^4, we'd have to multiply 3 4 times. (3*3*3*3=81) So 5*5=25 and 7*7=49. It would be better it fill in the formula as you go. So now you have (25+49=c^2). You wouldn't multiply c^2, because we don't know the base yet, it's an unknown, so we keep it at that for a while. So now we just continue with the problem which is basically 25+49 which is 74. (74=c^2) But that's not the answer. We have to find the square root of 74 in order to get the answer because we have to multiply with an exponent, the opposite is square rooting which is what we have to do. (((what sucks is that I reached the max of files to enter for you so your just gonna have to read the rest. sorry))) So the square root of 74 is 8.6. And that's your answer. The legs are 5 and 7, and your hypotenuse is 8.6. But what if you need to find one of the legs. The formula would be a= [tex] \sqrt{c^2-b ^2} [/tex] ( I hope the insert thing works if it doesn't I said a= square root of c^2-b^2)
I hope you can solve that because I have to go to a testing Class Connect, and I don't think I've learned the other questions yet. I'm sorry, and I hope I've helped!!
whats 70/100 as a decimal
Answers
percentage:70%
An analogy makes a comparison between objects based on their similar qualities. Cassidy wanted to create an analogy for the motion of atoms in solids, liquids, and gases, so she compared them to marbles in a tray. Which best compares the phases of matter to marbles in a tray? A solid is like the tray being shaken and the marbles moving around it, and a liquid is like the tray being shaken slowly and all the marbles moving in their positions. A solid is like the tray being shaken slowly and all the marbles moving in their positions, a liquid is like the tray being shaken and the marbles moving around it, and a gas is like the tray being shaken hard and the marbles moving vigorously around it. A gas is like the tray being shaken slowly and all the marbles moving in their positions, and a solid is like the tray being shaken hard and the marbles moving vigorously around it. A liquid is like the tray being shaken hard and the marbles moving vigorously around it, and a gas is like the tray being shaken slowly and all the marbles moving in their positions.
Answers
Answer:
B
Step-by-step explanation:
Can anyone help ME? PLEASE HELP IF I DONT TURN THIS IN BY TOMMOROW I DONT GET TO GO TO NEW YORK AND THAT IS MY DREAM
Answers
∠b = 180 = 25 -25 = 130 (Angles in a triangle)
∠c = 180 - 130 = 50 (Adjacent angles on a straight line)
∠d = ∠b = 130 (Vertically opposite angles)
∠e = ∠c = 50 (Vertically opposite angles)
∠f = 180 - 90 - 50 = 40 (Angles in a triangle)
∠g = 180 - 65 - 50 = 65 (Angles in a triangle)
∠h = 90 - 65 = 25 (Complementary angles)
*Enjoy your trip to New York!
what is 30% of 250 =
Compute with percents
Answers
0.3(250) = 75
30% of 250 is 75. Is this what you mean by "compute with percents?"
250*0.3=75
30% of 250 is 75
exponential function for 2,6,18,54
Answers
y = A * (b) ^ x
Where,
A: initial amount
b: growth rate
x: domain of the function.
We have then that the function is:
y = 2 * (3) ^ x
For example,
for x = 0:
y = 2 * (3) ^ 0
y = 2
for x = 1:
y = 2 * (3) ^ 1
y = 6
for x = 2:
y = 2 * (3) ^ 2
y = 18
for x = 3:
y = 2 * (3) ^ 3
y = 54
Answer:
y = 2 * (3) ^ x