A quadratic polynomial can have 0, 1, or 2 real roots, including repeated roots. The roots are determined by the discriminant. Numbers 4, 5, or 6 are not possible numbers of real roots for a quadratic polynomial.
Explanation:In Mathematics, specifically in Algebra, a quadratic polynomial with real coefficients can have either 0, 1, or 2 real roots, including any repeated roots. The number of roots is determined by the discriminant (the value under the square root in the quadratic formula). If the discriminant is greater than 0, the quadratic has 2 real roots. If it equals 0, there is 1 real root (a repeated root), and if it is less than 0, there are no real roots (there are 2 complex roots instead). Consequently, the possible number of real roots for a quadratic polynomial is not 4, 5, or 6.
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A quadratic polynomial with real coefficients can have 0, 1, or 2 real roots. Only '0 real roots' is a valid choice. This is determined based on the discriminant of the quadratic equation.
A quadratic polynomial with real coefficients is of the form [tex]\( ax^2 + bx + c = 0 \)[/tex], where ( a, b, ) and ( c ) are real numbers.
The number of real roots of a quadratic polynomial can be determined by its discriminant, [tex]\( \Delta = b^2 - 4ac \)[/tex]:
1. If [tex]\( \Delta[/tex] > 0, the polynomial has two distinct real roots.
2. If [tex]\( \Delta[/tex] = 0, the polynomial has one real root (a repeated root).
3. If [tex]\( \Delta[/tex] < 0, the polynomial has no real roots (it has two complex conjugate roots).
Based on this, the possible number of real roots, including repeated roots, for a quadratic polynomial with real coefficients are:
- ( 0 ) (when the discriminant is negative, there are no real roots)
- ( 1 ) (when the discriminant is zero, there is one repeated real root)
- ( 2 ) (when the discriminant is positive, there are two distinct real roots)
Given the options:
- 0
- 4
- 5
- 6
The only valid number of real roots for a quadratic polynomial with real coefficients from the provided options is: 0
The following are two sets of class scores (you may consider these scores to be normally distributed). Julia received the two scores marked with an asterisk. Did she do better or worse on the second test? Why? (16 points) First Test 48 *56 61 60 39 49 5 57 52 51 Second Test 75 81 63 *74 59 88 77 79 76 69 67
First let’s find the mean and standard deviation for both test and then we can calculate the probability of getting that score in his respective test and compare.
First test
P(x < 56)
P(z < 56-47.80/16.38)
P(z<0.50) = 1 – 0.3085 = 0.6915 or 69 percentile
Second test
P(x < 74)
P(z < 74 – 73.45 / 8.37)
P(z<0.07) = 1 – 0.4721= 0.5279 or 53 percentile
The probability for this normal distribution also means the percentile, so we can say that in the first test she was in the 69 percentile while in the second test she was in the 53 percentile. Therefore, she did worse in the second test
Julia did better on the first test compared to the second test.
Explanation:To determine whether Julia did better or worse on the second test, we need to compare her score on the first test with her score on the second test. For the first test, Julia received a score of 56 and for the second test, she received a score of 74. To determine which score is better, we can compare their positions in the distribution of scores.
First, we can calculate the mean and standard deviation of the scores for each test. For the first test, the mean is 49.9 and the standard deviation is 12.8. For the second test, the mean is 73.6 and the standard deviation is 7.3.
Next, we can calculate the z-scores of Julia's scores on each test. A z-score represents the number of standard deviations a data point is from the mean. For the first test, Julia's z-score is 0.16, and for the second test, her z-score is -0.2538.
Since a higher z-score indicates a better performance relative to the mean, Julia did better on the first test than the second test.
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I NEED HELP ASAP WILL GIVE 50 POINTS!!!
This diagram shows a pre-image
△ABC, and its image, A′′B′′C′′, after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is rotated 180 degrees about the origin to become △A'B'C'. Then △A'B'C' is translated 3 units down to become △A"B"C". Because the transformations are both rigid, the pre-image and image are congruent.
In Euclidean Geometry, the mapping rule for the rotation of a geometric figure about the origin by 180° in a clockwise or counterclockwise direction can be modeled by the following mathematical expression:
(x, y) → (-x, -y)
Point A (1, -1) → Point A' (-1, 1)
Point B (4, -2) → Point B' (-4, 2)
Point C (7, 2) → Point C' (-7, -2)
Next, we would apply a translation 3 units down to the new figure (△A'B'C'), in order to determine the coordinates of its image as follows;
(x, y) → (x, y - 3)
A' (-1, 1) → (-1, 1 - 3) = A" (-1, -2).
B' (-4, 2) → (-4, 2 - 3) = B" (-4, -1).
C' (-7, -2) → (-7, -2 - 3) = C" (-7, -5).
Therefore, the resulting figure must be located in the third quadrant as illustrated in the diagram shown above.
What is the x and y intercept of the line -7/5x-4y=7
I don’t understand part B. Can someone please help me?!
Picture included
Ethan buys a video game on sale. If the video game usually costs $39.99, and it was on sale for 20% off, how much did Ethan pay?
Ethan paid $31.99 for the video game on sale.
How to calculate the discount?To calculate the discount that Ethan obtained in the price of his video game, we do the following operations:
We divide the total price by one hundred and multiply the result by the discount, in this case 20.
$39,99 ÷ 100 = $0,3999$0,3999 × 20 = $7,998Subsequently, we subtract the result of the previous operation (value of the discount) from the total value of the video game.
$39,99 - $7,998 = $31,992
According to the above, the value that Ethan paid for the video game was $31,992
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Answer: $31.99
Step-by-step explanation:
$39,99 ÷ 100 = $0,3999
$0,3999 × 20 = $7,998
$39,99 - $7,998 = $31,992
If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express your answer as a common fraction.
1/12 is the probability that a 5 is rolled on at least one of the two dice
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that two standard six-sided dice are tossed,
We need to find the probability that a 5 is rolled on at least one of the two dice.
When we roll two dice there is a possibiltiy of 36 outcomes.
In these 36 outcomes atleast one of the dice should show 5.
There are 36 possible rolls
(5, x), (x, 5) and (5, 5) are the possible outcomes with 5 on any of the dice.
x represents any number from one to five.
So the probability that a 5 is rolled on at least one of the two dice is 3/36
which is equal to 1/12.
Hence, 1/12 is the probability that a 5 is rolled on at least one of the two dice
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Please answer as soon as possible.
Eric downloads a coupon for 10% off. He bought a camera for 95 dollars and an extra battery for 15.99 dollars.
a: what is the total cost if the coupon is applied to the digital camera
b: What is the total cost if the coupon is applied to the extra battery
c: To witch item should Eric apply the discount? explain
d: Eric has to pay 8% sales tax after the coupon is applied. How much is his total bill?
Determine the graph
jacquie hired a contractor to install a tile floor in her laundry room which measures 10.5 feet by 8 feet. the contractor informed her that the tiles cost $4.75 a square foot, he would charge $22 per hour, and it would take him 7.5 hours to complete the job. when the job was done, jacquie received a bill in the amount of $659.12 from the contractor which included an 8% sales tax. is the amount on the bill correct?
An isosceles right triangle has leg lengths of 4 centimeters. What is the length of the altitude drawn from the right angle to the hypotenuse?
What two lines are parallel i 5y 3x 5 ii 5y=2x-5y 5y=4+3x 5y-3x=-1?
Easy points!!! Correct answer gets brainliest. :)
Lisa can run a mile in 7 minutes. at that rate of speed how long would it take her to run 2 kilometers
It would take Lisa approximately 8.669 minutes to run 2 kilometers at her rate of speed.
Explanation:To find out how long it would take Lisa to run 2 kilometers, we need to convert the distance she can run in a mile to kilometers. Since there are 1.60934 kilometers in a mile, we multiply the time it takes her to run a mile (7 minutes) by the conversion factor (1.60934 kilometers/mile). This gives us the time it would take her to run 1.60934 kilometers. To find the time it would take her to run 2 kilometers, we can set up a proportion:
Calculating this gives us x ≈ 8.669 minutes. Therefore, it would take Lisa approximately 8.669 minutes to run 2 kilometers at her rate of speed.
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How many ways are there to choose a dozen donuts from 21 varieties?
Look at ΔABC. Which triangle is congruent to ΔABC by the ASA criterion? triangle 1 triangle 2 triangle 3 triangle 4
Answer:
Triangle 4
Step-by-step explanation:
Congruent triangles are identical in all aspects. They have identical sides and angles.
The ASA the Angle Side Angle criterion.
Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.
The triangle ABC is made distinct by the lines on it.
The lines mark the different angles on the triangle.
By looking at the triangle and comparing, Triangle satisfies the ASA criterion
Every square is a rectangle.
always
never
sometimes
Winnie Pooh Boo Boo
Needs help
:P XD
YEEET im so hyper right know
Answer:
Always! I mean that is easy...
Step-by-step explanation:
john and brian work for a toy manufacturers putting stuffing in teddy bears. On average, john can stuff x teddy bears in one day and brian can stuff y in one day. They both the same number of days,t. What does the expression (x +y)t represent? A. the number of teddy bears John can stuff in t days B.the number of teddy bears Brian can stuff in t days C. the number of teddy bears John and Brian can stuff in t days D.the number of teddy bears John and Brian can stuff in one day
Answer:
C
Step-by-step explanation:
Because The Equation Represents how many of those thingy's were stuffed
can someone graph this equation? 3x-10=21+3x
Jenny Spent $200 at a gift shop. She bought 3 rings for $21 each and spent the rest on 4 equally priced bracelets. How much does each bracelet cost?
A car was moving 110 km/h how long did it take to go 25.5 miles?
How do you convert 0.45 (45 being repeated) to a fraction?
The basal energy rate is the daily amount of energy (measured in calories) needed by the body at rest to maintain body temperature and the basic life processes of respiration, cell metabolism, circulation, and glandular activity. As you may suspect, the basal energy rate differs for individuals, depending on their gender, age, height, and weight. The formula for the basal energy rate for men is 4072-01-02-03-00_files/i0270000.jpg, where B is the basal energy rate (in calories), W is the weight (in kilograms), H is the height (in centimeters), and A is the age (in years). A male patient is 70 years old, weighs 55 kilograms, and is 172 centimeters tall. A total daily caloric intake of 1000 calories is prescribed for him. Determine if his caloric intake is sufficient for his needs and explain why or why not.
Geometry help please, 4 questions.
Attachment 2 and 3 go together.
Are my guesses on 4 and five correct?
Thank you!!
Jack's mother gave him 505050 chocolates to give to his friends at his birthday party. He gave 333 chocolates to each of his friends and still had 222 chocolates left.
Write an equation to determine the number of friends (x)(x)left parenthesis, x, right parenthesis at Jack's party.
Find the number of friends at Jack's party.
16
This seems to have been miswritten. So I went ahead and just put it as 50, 3 and 2Okay, so Jack started with 50 chocolates and ended with 2.
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing 48÷3=16.
Using algebra, we substitute the value we want to find with x. Here what we want to find is the number of friends that were at Jack's party.
We know that he started with 50 chocolates, then distributed 3× the number of friends present (which is x).
We write that down as 50−3x
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)
We know that after this, there were only 2 chocolates left, so it's
50−3x=2
Then we proceed by moving all the numbers to the right until only x is left:
−3x=2−50
−3x=−48
x=−48−3
x=16
Conclusion: The number of people that attended the party was 16.
Answer:
The equation is 3x+2=50
There were 16 friends at Jack's party.
Step-by-step explanation:
I JUST TOOK THE TEST
A bracelet was marked up $50 from cost, which amounts to a 20% increase. Find the original cost of the bracelet.
Patrick has a 600-meter skin of your used to before 8.9 minutes of yarn to make a hat does he have enough yarn left to make a scarf that use 350 4.0 thing Renaissance explain
To determine if Patrick has enough yarn left to make a scarf, subtract the amount of yarn used for the hat from the total amount of yarn, and then compare it with the amount needed for the scarf.
Explanation:In this question, we are given that Patrick has a 600-meter spool of yarn. He used 8.9 minutes of yarn to make a hat. We need to determine if he has enough yarn left to make a scarf that uses 350 meters of yarn.
To solve this problem, we need to subtract the amount of yarn used for the hat from the total amount of yarn, and then compare it with the amount needed for the scarf.
Let's calculate:
Amount of yarn used for the hat: 8.9 minutesAmount of yarn left: 600 - 8.9 = 591.1 metersAmount of yarn needed for the scarf: 350 metersSince the amount of yarn left (591.1 meters) is greater than the amount needed for the scarf (350 meters), Patrick has enough yarn left to make the scarf.
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What is the quotient?
158÷(−135)
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
the answer is -1 1/64
Step-by-step explanation:
i have k12
Answer:
got 80 percent cuz i missed this :l
Step-by-step explanation:
15 3/4 is the right hope it help
Choose the graph of the function f(x) =1/2 x - 2. Click on the graph until the correct graph appears.
Answer with explanation:
The given function is
[tex]y=\frac{x}{2}-2[/tex]
→2 y = x-4
→x -2 y -4=0
The function represents Linear function.
To plot the linear function on x y plane, we will write function in the form of slope intercept form, which is as follows
[tex]\frac{x}{a}+\frac{y}{b}=1\\\\\frac{x}{4}+\frac{y}{-2}=1[/tex]
So, the graph will cut X axis at , (4,0) and (0, -2).
To draw a unique line we need two points . The unique line will pass through (4,0) and (0, -2).
A bag contains 3 yellow, 1 red, and 2 green beads. Charlene draws a bead, keeps it out, then draws another bead. What’s the probability that Charlene drew the red bead, then a green bead? Write your answer in simplified form.
The length of a rectangle is 4 inches greater than the width. The perimeter of the rectangle is 24 inches. What are the dimensions of the rectangle?
length = 12 in.; width = 8 in.
length = 8 in.; width = 6 in.
length = 8 in.; width = 4 in
length = 6 in.; width = 2 in.
By using the formula for the perimeter of a rectangle and substitution, it is determined that the dimensions of the rectangle are 6 inches for the length and 2 inches for the width.
Explanation:This is a traditional problem in algebra that we can solve using known formulas and principles.
The perimeter of a rectangle is calculated using the formula 2(l+w), where 'l' stands for length and 'w' stands for width. In this problem, we know the perimeter (P) is 24 inches, and we know the length (l) is the width (w) + 4 inches.
We can set up and solve an equation using these facts. Replace 'l' in the equation with '(w + 4)' and solve for 'w': 2[(w + 4) + w] = 24, which simplifies to 2w + 8 = 12, and finally, w = 2.
Having found 'w', we can find 'l' by substituting 'w' in our equation of 'l', l = w + 4 = 2 + 4 = 6.
Therefore, the length is 6 inches and the width is 2 inches.
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