The nature of the roots of a quadratic equation is described by the discriminant calculated by seeing the equation and comparing it with the standard equation which is given by -
[tex]ax^{2} + bx+c[/tex] , where a , b , c are real numbers .
The root of the equation is given by -
x= (-b )± [tex]\frac{\sqrt{b^{2} - 4ac}}{2a}[/tex]
Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .
This discriminant is the defining factor of the nature of the roots.
Now, here arise three cases-
(i) If (b^2 - 4ac) > 0, the roots are real and distinct .
(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.
(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.
Hence, it is the discriminant which determines the nature of roots.
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Dalton built a linear model to show the height of a meteor falling to the Earth. The meteor starts at 100 km above the Earth's surface and falls at a rate of 20km per second. The x values represent the time in seconds and the y values represent the height of the meteor. What does the domain represent in context of the model?
Answer:
The domain represents the time of motion of the meteor as it falls from 100 km height above the Earth's surface at a speed of 20 km
Step-by-step explanation:
The given parameters from the question are;
The elevation of the meteor above the Earth's surface = 100 km
The rate at which the meteor falls = 20 km per second
The 'x' values represent the time in seconds and the 'y' values represent the meteor's height
Therefore, we have;
y = 100 - 20·x
The domain of a function is the set of inputs to the function
Therefore, the domain represent the time it takes the meteor to reach the given 100 km height above the Earth's surface
At the start x = 0 seconds
On the Earth's surface, y = 0, therefore;
0 = 100 - 20·x
x = 100/20 = 5
When the meteor just touches the Earth's surface x = 5 seconds
Therefore, the domain is 0 ≤ x ≤ 5.
Please help ~ You will get 50 points ~ I will be reporting answers that send links, just want to get points, etc. ~ Angles ~ Math ~ Pictures ~ Multiple Choice
Answer:
28, x , 62, 156
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Answer:
false
Step-by-step explanation:
a parallelogram is defined as a four sided figure with opposing sides parallel. So, a rectangle counts as a parallelogram, but all of its sides aren't equal
Which critical thinking skill is based on logic and reason?
Answer:
the ability to objectively analyze information and draw a rational conclusion
Step-by-step explanation:
The critical thinking skill that is based on logic and reason is "Logical reasoning" or "Logical thinking."
Critical thinking is the process of actively and skillfully analyzing, evaluating, and synthesizing information to make reasoned judgments and decisions.
Among the various critical thinking skills, "Logical reasoning" plays a fundamental role in the process.
Logical reasoning involves using principles of logic and reason to assess arguments, statements, and evidence.
It aims to identify the validity and soundness of claims and draw logical conclusions based on available information.
Hence, logical reasoning is the critical thinking which is based on logic and reason.
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ASAP PLASE GIVING BRAINLEST
Answer:
answer C
Step-by-step explanation:
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant.
A diameter is also a chord.
Alice is a good gambler and always knows when to stop. Suppose in a game, in each round she has a winning probability of 0.8 and she will stop at the first loss. Try to find the upper bound on the probability that she can win at least 10 rounds using Markov's inequality.
Answer:
The answer is "0.500".
Step-by-step explanation:
The chance that round will be won, [tex]P (win) =0.8[/tex]
The likelihood of losing round by complementary law
[tex]P(loss) = 1 -P(win)\\\\[/tex]
[tex]=1-0.8\\\\=0.2\\\\[/tex]
Let X be the number of rounds to the first loss played.
Here, [tex]X \sim Geometric (p=0.2)[/tex]
The PMF of X is the following:
[tex]P(X=x)=p(1-p)^x\\\\[/tex]
[tex]=(0.2)(1-0.2)^x\\\\=(0.2)(0.8)^x, \ \ \ \ \ x=1,2,.....[/tex]
The mean of X is the geometric random variable property, [tex]E(X) =\frac{1}{P}= \frac{1}{0.2}=5\\\\[/tex]
Markov's Inequality:
Suppose X is any random variable that has no negatives. So,
[tex]P(X \geq s)\leq \frac{E(X)}{s} for s >0\\\\[/tex]
Find the upper bound of [tex]P (X \geq 10)[/tex]
[tex]P(X \geq 10) \leq \frac{E(X)}{10}[/tex]
[tex]=\frac{5}{10}\\\\=\frac{1}{2}\\\\=0.5\\\\[/tex]
The highest probability is, therefore, that Markov's inequality will win at least ten rounds: 0.500
At a garage sale, Samuel purchased used books and DVDs. He bought a total of 18 items and spent $11. Each book cost $0.50 and each DVD cost $0.75. How many books did Samuel purchase?
Answer: 10 books
Step-by-step explanation:
Let the number of books bought be represented by x.
Let the number of dvds bought be represented by y.
The information given in the question can be formed into an equation as:
x + y = 18 ........ i
0.50x + 0.75y = 11 ....... ii
Multiply equation i by 0.75
Multiply equation ii by 1
0.75x + 0.75y = 13.50 ........ iii
0.50x + 0.75y = 11 ........ iv
Subtract iv from iii
0.25x = 2.50
x = 2.50/0.25
x = 10
Samuel bought 10 books
A cylindrical pool is leaking at a rate of 32 ft3 per minute. Determine how long it will take for all of the water to leak out? Round to the nearest whole number.
Answer:
Step-by-step explanation:
No dimensión? What are the dimensions?
At a state fair, every go-kart goes at most 40 mi/h.
1) Let s represent the speed of a go-kart.
Which inequality represents the situation?
A. 8 > (line underneath) 40
B. s < (line underneath) 40
C. s > 40
D. s < 40
Answer: s _< 40
Step-by-step explanation:
The correct inequality which represents the situation is,
⇒ s ≤ 40
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
At a state fair, every go-kart goes at most 40 mi/h.
Now, Let s represent the speed of a go-kart.
Hence, The correct inequality which represents the situation is,
⇒ s ≤ 40
Since, Symbol used for at most is, less than or equal to.
Thus, The correct inequality which represents the situation is,
⇒ s ≤ 40
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Tanya has a $50 gift card to spend on Amazon. She wants an airpod case cover for $12.
She also wants to buy some bracelets for $9.50 each. How many bracelets can she buy
without going over?
Answer:
4
Step-by-step explanation:
She can buy 4 bracelets because 4 x 9.50 = 38 + 12 = 50. So 4 would fit her budget perfectly without going over. LEt me know if you find any fault in my answer! Thanks! Have a good day! Hope this helps!
Select the ordered pair that is a solution to the function. (A point on the line.)?
A) 5
B) -5
C) -7
D) 7
Answer:
-7
Step-by-step explanation:
first you plug in f(3) in the x so -2(3)= -6
then -6 - 1 = -7
What is the value of s in 7 = -10s - 3
Answer:
-1 = s
Step-by-step explanation:
7 = -10s - 3
Add 3 to each side
7+3 = -10s - 3+3
10 = -10s
Divide each side by -10
10/-10 = -10s/-10
-1 = s
Cato's older brother took out a 4-year loan for $28,000 to buy a car If the simple interest rate was 8%, what will be the total cost he pays for the car, including interest?
Interest=$__
Total Price=$__
Please help me no links or files!!!!
Find the value of x.
Answer:
4x+8x = 180 degrees, so x=15
Step-by-step explanation:
Answer:
sum of 4x and 8x is 180°
( straight line )
4x + 8x = 180°12x = 180°x = 15°I'll mark u brainiest if you answer it.
Answer:
Step-by-step explanation:
3
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Jonathan's piggy bank contains 20 nickels, 30 quarters, and 50 one-dollar coins. He picks 20 coins from the bank at random; 12 of these coins are one-dollar coins. The theoretical probability of picking a one-dollar coin from the piggy bank before the draw is ---%, but the experimental probability, based on the draw, is ---%.
Answer:
First box is 50%
Second box is 60%
Step-by-step explanation:
Took the test and I got it right :)
The theoretical probability of picking a one-dollar coin from the piggy bank before the draw is 50%, But the experimental probability, based on the draw, is 60%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Jonathan's piggy bank contains 20 nickels, 30 quarters, and 50 one-dollar coins.
He picks 20 coins from the bank at random; 12 of these coins are one-dollar coins.
The total number of one-dollar coins = 50
Total number of coins the piggy bank contains = 100
The theoretical probability of picking a one-dollar coin from the piggy bank before the draw = 50/100
= 1/2
But the experimental probability, based on the draw, is 60%.
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What is the length of side PQ in this figure?
A. 4
B. 14
C. Square root 52
D. Square root 161
Answer:
The answer is D. I believe
Answer:
its 52
Step-by-step explanation:
Can someone please give me a answers on page 409? For 6th grade made and its in chapter 10
Answer:
We would need to know what school you go to or what textbook you are using. I don't think you want to share any of that online
Step-by-step explanation:
Polling organizations regularly collect data on the public’s opinions and habits. A question on a recent survey asked, “How often do you purchase coffee from a coffeehouse?” There may be differences in how people respond to this question based on whether the person is a full-time student. Suppose a polling organization uses random digit dialing of local phone numbers to take a poll and asks respondents whether they are full-time students. In addition, they ask respondents to identify how often they purchase coffee from a coffeehouse (never, once a week, two to three times a week, daily, more than once a day). The data are collected in a 5-by-2 table of counts. Which of the following is the appropriate null hypothesis when conducting a chi-square test for the data?
Answer:
there is an association between how often a person purchases coffee from a coffee house and whether a person is a full time student.
Step-by-step explanation:
Answer:
C) H0 : How often a person purchases coffee from a coffeehouse is not associated with whether a person is a full-time student.
Step-by-step explanation:
This represents a chi-square test for independence because one sample was taken and two variables were observed. This is an appropriate null hypothesis for a chi-square test for independence in this study as it hypothesizes no association between coffee-purchasing habits and full-time student status.
..........................................l
Answer:
It's the B ,
B y=3x-1
hope this help you
Answer:
b
Step-by-step explanation:
Each x value in the table is multiplied by 3 and then subtracted by 1
Please give me the answer please
Answer:360
Step-by-step explanation:
Answer:
area =
[tex] \frac{1}{2} \times (10 + 6) \times 6 [/tex]
=
[tex]3 \times 16[/tex]
=
[tex]48 \: ft {}^{2} [/tex]
Will give brainliest. A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (4x + 8) units and a width of 10 units. What will be the perimeter of both the rectangle and the square?
Which of the following is not used to classify biomes?
a.
weather patterns
b.
continent
c.
dominant plant life
d.
geographical terrain
Answer:it’s B on edge bro
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
continent
Susie is looking for butterflies in an area where: 15% of the butterflies are of type A 30% of the butterflies are of type B 55% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies
Answer:
the probability that the two butterflies she spots will both be type A butterflies is 0.0044
Step-by-step explanation:
The computation of the probability that the two butterflies she spots will both be type A butterflies is shown below:
= 1 ÷ Type A × 1 ÷ Type A
= 1 ÷ 15 × 1 ÷ 15
= 1 ÷ 225
= 0.0044
Hence, the probability that the two butterflies she spots will both be type A butterflies is 0.0044
I'll give u a brainliest to answer this<3
Answer:
762
Step-by-step explanation:
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Answer:
C
Step-by-step explanation:
You have 2 totals so the number of males + females = 127 so x + y = 127
Then there are 23 more males than females, it did not say 23 times more so B is out, so the female number + 23 = male number so y + 23 = x
Therefore letter C is the answer.
Hiiii!
What's 100 X 1,000,000?
Just answer so that this doesn't get deleted, please.
Do any boys wanna talk on discord, remind, or pad let?
Any gender is fine as long as you are from the ages 13-17.
Answer:100000000
Step-by-step explanation:
Find the value of x. If necessary, write your answer in simplest radical form.
12
Answer:
x = 13Step-by-step explanation:
According to Pythagoras Theorem,
[tex]{(height)}^{2} + {(base)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] = > {12}^{2} + {5}^{2} = {x}^{2} [/tex]
[tex] = > {x}^{2} = 144 + 25[/tex]
[tex] = > {x}^{2} = 169[/tex]
[tex] = > x = \sqrt{169} [/tex]
=> x = 13 (Ans)
Answer: 73 will be your answer hope this helped
Step-by-step explanation:
PLSSSSSSSS HELPPPPPPPPPPPP IT WOULD MAKE ME SO HAPPY
Answer:
i think it is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the answer to this one, answer it and no wrong answers.
Answer:
A
Step-by-step explanation: