Answers
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
What is the discriminant?The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given as,
2(c² + d²)x² + (c - d)x + 9 = 0
Then the discriminant is given as,
D < 0
(c - d)² - 4 × 2(c² + d²) × 9 < 0
(c - d)² > 72 (c² + d²)
The expresssion (c - d)² must be positive. Then we have
(c - d)² > 0
c - d > 0
c > d
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
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Related Questions
3. A television screen has a 50-inch diagonal. If the aspect
ratio of the sides is 24:7, what are the dimensions of the
television
Answers
Answer:
48×14 in.
Step-by-step explanation:
[tex]50^{2} =48^{2} +14^{2}[/tex]
[tex]2500=2304+196[/tex]
[tex]2500=2500[/tex]
The TV screen is 48 inches long and 14 inches high.
Hope this helps.
Which set of ordered pairs represents a function?
Answers
The set of ordered pairs represents a function would be; {(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We need to know that to be a function each x value (first component) has to have one only y value (second component).
In the option 1 the first component 1 has two different y values (-1 and 0),
In option 3 the x value 5 has two different y values (-5 and 9) and in option four the x value -3 has three different y values (1, 2 and -3).
Then, the correct option is the second one.
{(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.
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Joe deposits $500 in an account
with 3% interest compounded
quarterly for a period of 5 years.
What expression would you type
into the calculator to calculate the
total amount of money Joe will
have after the 5 year period?
500 e(-03)(5)
500(1+.03)4(5)
500(1+3)5
500(1+.03/4)(4)(5)
Answers
Answer:
D) 500(1 +.03/4)^(4(5))
Step-by-step explanation:
You want to know the expression you would input to a calculator to find the money Joe will have in his account from a $500 deposit earning 3% interest compounded quarterly for 5 years.
Account valueThe value of the account is given by the formula ...
A = P(1 +r/n)^(n·t)
where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, you would want your calculator to evaluate ...
500(1 +.03/4)^(4(5)) . . . . . . . matches choice D
__
Additional comment
The attachment shows a couple of different calculator inputs that could be used to find the account value. Note that the product (4)(5) is the exponent of the base (1 +.03/4). This calculator uses the caret (^) key to open the exponent expression.
The calculator also has a "future value" function that will compute the same result.
The value in the account will be $580.59.
<95141404393>
HELP DUE IN 20 MIN
Write an expression that represents the height of a tree that begins at 8.4 feet and increases by 3.5 feet per year. Let t represent the number of years.
___+___t
Answers
Answer:
8.4+3.5t
Step-by-step explanation:
8.4+3.5t
Square 1 ABDC square 2 FGEH. AD= 18 DC=12 FE= 15 how do I find the square factor?
Answers
Using the similarity rectangle theorem, the value of FG is approx 23.
We determine the value of FG using the using the similar rectangle theorem.
Two rectangles must have proportional sides in order for them to be identical (form equal ratios). The two shorter sides should be proportionately equal to the two longer sides.
The rectangle ABCD and FGEH are both have same shape.
As we know that the rectangle same two sides equal. So
FG/EF = AD/DC
FG/15 = 18/12
Multiply by 15 on both side, we get
FG = 18/12 * 15
FG = 3/2 * 15
FG = 22.5
FG = 23 (approx)
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The complete question is:
Square 1 ABDC square 2 FGEH. AD= 18 DC=12 FE= 15. How do I find the square factor FG?
exercise 4. exercise 2 on page 65 on the textbook. suppose the world population today is 7 billion, and suppose this population grows at a constant rate of 3% per year from now on. (a) what would be population equal 100 years from now? (b) compute the level of population for t
Answers
Answer: A: what would be population equal 100 years from now?
Step-by-step explanation: I hope this helps!
On number 6.. would I divide 52 by 2??
Answers
Answer:
yes
Step-by-step explanation:
they are perpendicular so you can use 52/2 =26
26² + 33² = LM²
Relative frequency distributions are generally more useful than frequency distributions when?
Answers
Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of the same size.
The frequency (or absolute frequency) of an event in statistics is the number of times the event occurred in an experiment or research. Histograms are frequently used to graphically show these frequencies.
The absolute frequency of an occurrence normalized by the total number of events is referred to as its relative frequency (or empirical probability). A frequency distribution can be created by plotting the values of all events.
A histogram is a graphical representation of tabulated frequencies that is displayed as consecutive rectangles erected at discrete intervals (bins) with an area equal to the frequency of the observations in the interval.
The frequency density of the interval, i.e. the frequency divided by the width of the interval, is also equal to the height of a rectangle.
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Is w = 6 a solution to the inequality below?
8 > W
Answers
W = 6 is a solution to the inequality.
Solutions of an inequality expression:In mathematics, Inequality is an unequal comparison between two or more algebraic terms or expressions. The solution of an inequality is a numerical value that will satisfy the given expression.
The signs that we use in Inequality expression are
'>' - greater than
'<' - less than
'≥' - greater than or equal to
'≤' - less than or equal to
Here we have
Inequality 8 > W
Where the symbol '>' less than indicates 8 is greater than W
or the value of W is less than 8
As we can see that 6 < 8
Therefore,
W = 6 is a solution to the inequality.
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Marshawn ran with the football for a 24 yard gain.
Given that 1 yard = 3 feet, enter the distance Marshawn ran in feet.
Answers
Suppose the first class in a frequency table of quantitative data is 0-4 and the second class is 5-9. What is the class midpoint of the first class
Answers
The class midpoint of the first class in the case of table of quantitative data is 0-4 and the second class is 5-9 is 2.5
When you want to make a histogram to see the values in a frequency table, you frequently use class midpoints.A histogram shows the classes along the graph's x-axis while using bars to show how frequently each class occurs along the y-axis. At the midpoint of each class, each bar is centered.When you want to make a histogram to see the values in a frequency table, you frequently use class midpoints. A histogram shows the classes along the graph's x-axis while using bars to show how frequently each class occurs along the y-axis. At the midpoint of each class, each bar is centered.To know more about midpoint here
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If the neighborhood holds 13 total games and all 50 athletes participate, how many 6-player games and how many 2-player games are played?
Write a system of equations to represent this situation.
Equation for "There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").
Equation for "If the neighborhood holds 13 total games and all 50 athletes participate"
How many 6 player games?
How many 2 player games?
13 points
Answers
The total 7 two-player games and 6 six-player games were played.
Here the total games = 13
And the total number of athletes participated = 50
Let us assume that x represents the total 2-player games played and y represents the total 6-player games played.
The neighborhood holds 13 total games.
So, we get an equation,
x + y = 13 ................(1)
There are 50 athletes signed up for a neighborhood basketball competition.
So, we get an equation,
2x + 6y = 50 .............(2)
From equation (1)
x = 13 - y ..........(3)
substitute above value of x in equation (2)
2(13 - y) + 6y = 50
26 - 2y + 6y = 50
4y = 24
y = 6
Substitute above value of y in equation (3)
x = 13 - 6
x = 7
Thus, we can conclude that the total 7 two-player games and 6 six-player games were played.
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help it s due tomorrow!!!! PLS!! I don't want to fail
Answers
The two rational numbers that result in the lowest product are given as follows:
18.5 and -12.4.
How to obtain the lowest product?For the product of two rational numbers, we have that their signal is given as follows:
Negative: different signals.Positive: equal signals.For the lowest product, we want a negative number, with the highest absolute value, hence we take the lowest negative and highest positive, as follows:
18.5 and -12.4.
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9
Select the correct answer from each drop-down menu.
The edge of a cube is 4 Inches.
The area of a cross section perpendicular to one face is
square Inches, and its perimeter is
Inches.
Reset
Next
Answers
The area of a cross section perpendicular to one face is 16 square Inches and its perimeter is 16 inches.
The term perimeter in math is known as the total distance around the respective shape.
Here we know that the edge of a cube is 4 Inches.
Here we have to draw a sketch of a cube with side = 4 in as shown below..
Here we have to know that the shaded area is perpendicular to the right and left vertical faces of the cube, then the cross section is a square with each side equal to 4 in.
Hence the value of the area of the cross section is calculated as
=> 4*4 = 16 in²
And the value of the perimeter of the cross section is
=> 4+4+4+4 = 16 in.
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what is the measure of the acute angle formed by the hands of a clock at $4:20$ a.m.? express your answer as number of degrees.
Answers
The acute angle formed by the hands of a clock at 4:20a.m is 10°.
For the minute hand, we can compute that, for its every move, it covers 6 degrees. And for the hour hand, each move covers 30 degrees.
A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.
The angle between the hour's hand and the minute hand when the clock shows 4:20 pm can be calculated by using the formula:
Angle=|11/2 M-30H|
where M= minute H= hour's
Here M=20 H=4
Therefore we get the angle |11/2(20)- 30*4|=|110-120|=|-10°|=10°
Hence, 10° is the correct answer.
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Lauren and Shayla have ½ pound of Skittles. They want to share the Skittles between themselves and 2 friends.
How many pounds of Skittles will each of them receive?
Answers
Using division we know that each person will have 1/4 pound of Skittles.
What is division?In mathematics, the division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.
For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
The division sign, "," or occasionally "/," is used in computer code.
So, we know that:
Lauren and Shayla have 1/2 pound of Skittles
They will share it with 2 more people.
Then, each will have:
(1/2)/2
1/2 / 2
1/2 * 1/2
1/4
Therefore, using division we know that each person will have 1/4 pound of Skittles.
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18. For which of the following conditions will the sum of integers m and n always
be an odd integer?
F. m is an odd integer
G. n is an odd integer
H. m and n are both odd intrgers
OJ. m and n are both even integers
K. m is an odd integer and n is an even integer
Answers
Have a great day
13 is a odd number
Here is a number pyramid puzzle.
Each number is the product of the two numbers directly below it.
Complete the pyramid.
Answers
Complete the pyramid with the corresponding values
How to complete the pyramid?
Since each number is the product of the two numbers directly below it. Then the pyramid can be completed as follows:
Check the attached image for labeling.
j = -1 × -1 = 1
h = -2 × j = -2 × 1 = -2
y = h × -1 = -2 × -1 = 2
j × n = -1
1 × n = -1
n = -1
n × m = 2
-1 × m = 2
m = -2
w = -1 × 2 = -2
t = y × w = 2 × -2 = -4
-1 × k = n
-1 × k = -1
k = 1
k × l = m
1 × l = -2
l = -2
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The drama club holds a cast party at a local cafe.All 12 of the cafes tables are used to full capacity.Small tables seat 2 people and large tables seat 4 people.How many tables of each size are there?
Answers
With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.
What is algebraic expression?Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are performed on variables and constants. Let's imagine that while playing with matchsticks, James and Natalie came up with the idea to arrange the sticks into patterns that represented numbers.
James drew a four in the air with four matchsticks. Natalie was able to make a pattern with two 4s by putting three more matchsticks on the board. They realised they could proceed to add three matchsticks each round until they had a total of four. This led them to the conclusion that, in general, 4+ 3(n-1) sticks are needed to make a pattern with n numbers of 4s. This sentence makes reference to the algebraic expression 4+ 3(n-1).
The total no. of tables are 32
Let x be the no. of Small tables = 2x
And y be the no. of Large tables = 4y
Total no. of tables = 12
2x + 4y = 32
And
x + y = 12
x = 12 - y
Putting the value of x in first equation
2(12 - y) + 4y = 32
24 - 2y + 4y = 32
4y - 2y = 32 - 24
2y = 8
y = 4
And Putting the value of y in 2nd equation
x = 12 - (4)
x = 8
Thus, With the help of algebraic expression, there were 8 small tables and 4 large tables in the local cafe.
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What is the domain and range
Answers
Answer:
Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The domain of a function is the set of values that we are allowed to plug into our function. While a functions range, is the set of values that the function can take.
To be more precise, he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
A relation's domain can also be discussed, where one element in the domain may be mapped to more than one element in the range.
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What is the value of x?
Answers
x = 1
Answer:
-----------
3x + 1 = 4x
4x = 3x + 1
4x - 3x = + 1
x = 1
The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.
Which equation should she use?
k = 2Px2
k = k equals StartFraction one-half EndFraction P x squared.Px2
k = k equals StartFraction 2 P Over x squared EndFraction.
k = k equals StartFraction P Over 2 x squared EndFraction.
Answers
She should use the equation k = P/x². The correct answer would be an option (D).
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The potential energy, P, in spring is represented using the formula, as follows:
P = kx²
Solve for variable k and we get the equation:
k = P/x²
When we compare this equation to the provided possibilities, we can easily see that it corresponds to the last option.
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parallel to the line y =-3x + 5; passes through (-4,5)
Answers
Answer:
Step-by-step explanation:
ham 3.45x
when the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the . a. subjective method b. classical method c. relative frequency method d. posterior method
Answers
The method used to assign probabilities when the results of experimentation or historical data are used to assign probability values is referred to as the relative frequency method.
The relative frequency method is a way to assign probability values to events based on how often they have occurred in the past.
The probability of an event is determined by counting the number of times the event has occurred in a given set of observations, and dividing that number by the total number of observations. For example, if a certain event has occurred 20 times out of 100 total observations, the probability of that event would be 0.2 (20/100). This method is based on the idea that the probability of an event is related to its frequency of occurrence in a large number of trials.
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A jet takes off at a 15 degree angle of elevation. The jet’s air speed is 300 ft/sec.
What is the horizontal distance that the jet has traveled in 10 seconds? What is the jet’s altitude at this time?
Answers
The horizontal distance that the jet has traveled in 10 seconds will be 3000feet and the jet’s altitude at this time is 6.44 minutes
Given: A plane flies off at a 15-degree angle and 350 feet per second.
Find The time needed to ascend to a height of 35,000 feet.
Imagine a right triangle with a 15-degree angle at the origin at Q1.
The plane's flight route is the hypotenuse.
speed = distance/time
speed * time = distance
distance = 300*10 = 3000feet
Sin(15) = opposite / hypotenuse
Sin(15) = 35000 / (350*t)
350*t = 35000 / Sin(15)
t = 35000 / (350 * Sin(15)
t = 100 / Sin(15)
t = 100 / .25882
t = 386.37 seconds
t = (386.37 sec) * (1 min. / 60 sec) = 6.44 minutes
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Function Notation Worksheet #2
Use the functions below to evaluate at the given value.
f(x) = 4x - 7
g(x) = 4*
1. f(-2) =
4.j(-1) =
7. k(-1)-5=
10. f(a - 1) =
j(x) = 2x² - 3
2. g(3) =
5.k(-2) =
8. f(0) + 7 =
11. j(3a) =
k(x) = |x - 3|
h(x) = √x
3. h(25) =
6. g(-2) =
9. g(0) =
12. f(2p - 3q) =
Answers
the value of functions f(-2)=-15, g(3) =12.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(x) = 4x - 7
g(x) = 4*x
f(-2) = 4(-2)-7 = -8-7 = 15
g(3) = 4*3 = 12
Hence the value of functions f(-2)=-15, g(3) =12.
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it's election day for a student organization. if a president and vice-president are elected, how many different combinations can be made among six people?
Answers
30 different combinations can be made among six people.
The total number of arrangements is called Permutations.
According to the question,
There are 6 members to choose from.
And there are 2 posts to be filled. i.e, President, Vice-President.
Let's assume each position is a blank. Here each blank represents a placeholder.
The first position can be filled in 6 ways (because any one of the students can get that position)
The second position can be filled in 5 ways (as one person already got the first position, he can't get the second position).
The total number of ways all three positions can be filled in
= 6 * 5 = 30
So, the total number of ways in the combination = 30.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 436 gram setting. is there sufficient evidence at the 0.05 level that the bags are underfilled? assume the population is normally distributed.
Answers
Alternative Hypothesis is sufficient evidence at the 0.05 level that the bags are underfilled.
In the given question, we have to explain that there is sufficient evidence at the 0.05 level that the bags are underfilled or not assuming that the population is normally distributed.
We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). Or else, we are not able to rule out the null hypothesis.
The claim in the alternative hypothesis that you anticipate or hope to be accurate.
The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.
Since, bag filling machine works correctly at the 436 gram setting. Test the alternative hypothesis in place of the claim that the true mean is less than 436. This test has a left tail.
The null and alternative hypothesis are
H(0): μ = 436
H(a): μ < 436
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Determine whether the data described below are qualitative or quantitative and explain why.
The types of food served by restaurants (Italian, Chinese, fast, etc.) Choose the correct answer below.
A. The data are quantitative because they consist of counts or measurements.
B. The data are quantitative because they don't measure or count anything.
C. The data are qualitative because they don't measure or count anything.
D. The data are qualitative because they consist of
Answers
As per the statement the data are qualitative because they don't measure or count anything.
The term measurement in math is known as the process of associating numbers with physical quantities and phenomena.
Here we have the statement the types of food served by restaurants Italian, Chinese, fast, etc.
As we looking into the statement we have identified that the statement is defines the characteristics of the restaurant which is also defines that there is no value for counting in it.
So, this refers the quality of the product instead of quantity.
Which also defined that there is no measurement value in it.
Therefore, the correct option is (c).
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A car is 150 inches long. A truck is 75% longer than the car. How long is the truck?
Answers
Answer:
Hi, my name is Za'Riah! I will gladly help you with your problem. (see explanation)
Step-by-step explanation:
There really isn't much to explain or step out with this problem.
60% of 150 is 90
150 + 90 = 240 inches
The truck is 240 inches long.
Answer:
240