Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.
Quadratics representing repeated roots has discriminant equals to zero.
Standard quadratic equation is:
ax² + bx + c = 0
Discriminant 'D' = b² - 4ac
option a. -x²+ 18x + 81
Discriminant
'D' = 18² - 4(-1)(81)
= 324 + 324
= 648
D>0 has distinct roots.
option b. 3x²- 3x - 168
Discriminant
'D' = (-3)² - 4(-3)(-168)
= 9 - 2016
= -2007
D< 0 has distinct roots.
option c. x²- 4x - 4
Discriminant
'D' = (-4)² - 4(1)(-4)
= 16 + 16
= 32
D>0 has distinct roots.
option d. 25x²- 30x + 9
Discriminant
'D' = (-30)² - 4(25)(9)
= 900 - 900
= 0
D = 0 has repeated roots.
Repeated roots are:
x = ( -b ±√D ) / 2a
= [-(-30)±√0 ]/ 2(25)
= 30/ 50
= 3/5.
option e. x² - 14x + 24
Discriminant
'D' = (-14)² - 4(1)(24)
= 196 - 96
= 100
D>0 has distinct roots.
Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.
The above question is incomplete, the complete question is:
One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
a. -x²+ 18x + 81
b. 3x² - 3x - 168
c. x² - 4x - 4
d. 25x² - 30x + 9
e. x² - 14x + 24
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Solve -11x - 7y = -56 in slope intercept form
Answer:
the slope of the line is -11/7 and the y-intercept is 8.
Step-by-step explanation:
First, we'll add 11x + 7y to both sides:
-11x - 7y + 11x + 7y = -56 + 11x + 7y
0 = -56 + 11x + 7y
Then, we'll add 56 to both sides:
0 + 56 = -56 + 11x + 7y + 56
56 = 11x + 7y
Finally, we'll divide both sides by 7:
56/7 = (11x + 7y)/7
8 = (11x + 7y)/7
Now we have the equation in slope-intercept form:
y = -(11/7)x + 8
So in this case, the slope of the line is -11/7 and the y-intercept is 8.
roxanne bought 7 packs of bottled water and 9 boxes of soda. there were 10 bottles of water in each pack and 6 cans of soda in each box. how many drinks did roxanne buy in all? drinks
The total number of drinks Roxanne buy is 124
Roxanne bought 7 packs of bottled water and 9 boxes of soda. There were 10 bottles of water in each pack and 6 cans of soda in each box.
Roxanne bought 7 pack of bottled water.
1 pack of water bottle contains 10 bottles of water,
Hence 7 pack of water bottle contains. [tex]$7 \times 10=70$[/tex] water bottles
Roxanne bought 9 boxes of soda, 1 box of soda contain 6 cans of soda, then 9 boxes of soda contains. [tex]$x=$[/tex] cans of soda,
Then the total number of drinks Roxanne buy[tex]$=70=1$[/tex]
The total number of bottles calculate by the Multiplication of number of packet of bottles and per packet bottles.
Therefore, the total number of drinks Roxanne buy = 124
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What is the probability that you pull a card at random from a regular 52 card deck and it is either a 3 or a heart?
The probability that you pull a card at random from a regular 52 card deck and it is either a 3 or a heart is,
⇒ 17/52
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We know that;
In a regular 52 card deck,
Number of 3 cards = 4
And, Number of heart cards = 14
Hence, The probability that you pull a 3 cards = 4 / 52
And, The probability that you pull a heart = 13/52
Thus, The probability that you pull a card at random from a regular 52 card deck and it is either a 3 or a heart is,
⇒ 4/52 + 13/52
⇒ 17/52
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1. The dark triangles are outliers.
When the outliers in the data were omitted, the correlation coefficient (r) changed to 0.86.
Why did omitting the outliers change the correlation between the variables?
2.) how do the outliers affect the data?
1) Note that the dark triangles are outliers.
2) Omitting the outlines changed the correlation between the variables because outliers can skew the data and make the relationship between the variables appear stronger or weaker than it actually is.
3) Outliers can greatly affect the data by distorting the overall relationship pattern between the variables.
What are Outliers?An outlier in statistics is a data point that deviates considerably from other observations.
It is correct to state that an outlier can be caused by measurement variability, a hint of new data, or an experimental mistake; the latter is sometimes eliminated from the data set.
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explain how we can use the eigenvalue decomposition to define the square root of a diagonalizable matrix.
It appears to be a constant connection that the square matrix has n eigenvalues, where n is the dimensions (not dimensions as in Rank, but as in # of Column values) of the square matrix.
similar to: a 3x3 matrix square, which has 3 Eigenvalues and only permits eigenvalue decomposition in the event that the matrix is diagonasible.
I think it has to do with how mirror-reflective and inverse the dimensional features of the Matrix can be, and how its linear structure is strong enough to support a dimensional cube.
When it comes to interaction, eigenvalue decomposition can be used to systematically eliminate it.
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Calculate the ratio of AB to BC and the ratio of AD to DC. Round your answers to the hundredths place. What do you notice about the ratios?
The ratio of AB to BC is 4.3 : 5 and the ratio of AD to DC is 2 : 2.3
How to calculate the ratio of AB to BC and the ratio of AD to DCFrom the question, we have the following parameters that can be used in our computation:
A = (0, 4)
B = (-5, -3)
C = (5, -3)
D = (2.4, 0.8)
Next, we calculate the distance between the points using
Distance = √[(x2 - x1)² + (y2 - y1)²]
So, we have
AB = √[(0 + 5)² + (4 + 3)²] = 8.6
BC = √[(5 + 5)² + (-3 + 3)²] = 10
AD = √[(0 - 2.4)² + (4 - 0.8)²] = 4
DC = √[(2.4 - 5)² + (0.8 + 3)²] = 4.6
The ratios are then represented as
AB : BC = 8.6 : 10
AD : DC = 4 : 4.6
Simplify the ratios
AB : BC = 4.3 : 5
AD : DC = 2 : 2.3
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
A) 2.3p – 10.1 = 6.4p – 4
B) 2.3p – 10.1 = 6.49p – 4
C) 230p – 1010 = 650p – 400 – p
D) 23p – 101 = 65p – 40 – p
E) 2.3p – 14.1 = 6.4p – 4
Answer: Multiplying both sides of the original equation by 100 gives the same
the solution as follows;
100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)
230·p - 1010 = 650·p - 400 - p
Step-by-step explanation:
A parallelogram has an area of 48 m2. If the base is 12 m long, what is the height?
4 m
8 m
36 m
12 m
According to the area of parallelogram, the value of height is 4m.
In math the term parallelogram is defined as a special kind of quadrilateral in which the opposite sides are parallel and equal.
And the general form to calculate the area of parallelogram is written as,
=> A = base x height,
Here we know that the area of the parallelogram is 48 m² and the base is 12 m.
Then the value of height is calculated as,
=> 48 = 12 x height.
When we simplify this one then we get the value of height as,
=> height = 48/12
=> height = 4.
Therefore the correct option is A.
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what is order of the likelihood of the following events, from most to least likely : winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5). most likely. guessing a 64-bit key on the first try. second most likely. guessing a 128-bit key on the first try. third most likely. being hit by lightening this year (the probability is 1/105)
Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.
1) Being hit by lightning this year (probability is 1/105) - The probability is the lowest because the odds of being hit by lightning in a given year are relatively low.
2) Guessing a 128-bit key on the first try - The probability of guessing a 128-bit key on the first try is very low because of the large number of possible key combinations.
3) Guessing a 64-bit key on the first try - The probability of guessing a 64-bit key on the first try is lower than guessing a 128-bit key, but still relatively low because of the large number of possible key combinations.
4) Winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5) - The probability of winning a lottery with such large number of contestants is relatively low, but it is still much higher than the first three events.
So the order is:
1) Being hit by lightning this year
2) Guessing a 128-bit key on the first try
3) Guessing a 64-bit key on the first try
4) Winning a lottery with 1 million contestants five times in a row,
Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.
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the density of an object with mass m and volume v is m/v . abigail has a diamond stone that her grandmother gave her. the diamond's mass is 70 grams, and its volume is 20 cubic centimeters. what is the density of the diamond?
Answer: 3.5
Step-by-step explanation:
70/20=3.5
Okay, it says “write each mixed number as an improper fraction” and ignore the letters, for 1,2,3,4,5,6,7 do I just add/subtract the mixed numbers or make the answer as an improper fraction?
The value of the improper fraction will be:
1. 2 2/3 = 8/3
2. 4 1/2 = 9/2
3. 1 7/10 = 17/10
4. 2 3/8 = 19 / 8
5. 5 5/9 = 50/9
6. 1 7/12 = 19/12
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
The improper fraction will be:
1. 2 2/3 = (2 × 3 + 2) / 3 = 8/3
2. 4 1/2 = (4 × 2 + 1) / 2 = 9/2
3. 1 7/10 = (1 × 10 + 7) / 10 = 17/10
4. 2 3/8 = (2 × 8 + 3) / 8 = 19 / 8
5. 5 5/9 = (5 × 9 + 5) / 9 = 50/9
6. 1 7/12 = (1 × 12 + 7) / 12 = 19/12
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the number of seconds in a year is seconds. what is a rounded form of this number of seconds in scientific notation?
The number of seconds in a year in scientific notation is 31,536,000 seconds or [tex]3.154 * 10 ^{7}[/tex]
In one hour [tex]60 \ sec * 60\ min = 3600 \ sec[/tex]
For one day we have to multiply [tex]3600 * 24 = 86400\ sec[/tex]
For one calendar year (365 days) = [tex]86400 * 365 = 31536000 \ sec[/tex]
It Can be written as : [tex]3.154 * 10 ^{7}[/tex]
∴ In a year, there are 31,536,000 seconds.
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation.
We must adhere to the following rule in order to calculate the power or exponent of 10:
The base must always be 10.Exponents that are non-zero integers must be either positive or negative in order to be used.The coefficient's absolute value is more than or equal to 1, but it must be less than 10.Positive and negative numbers, including whole and decimal values, can be coefficients.The remaining significant digits of the number are represented by the mantissa.For such more question on seconds:
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The following question may be like this:
Express the number of seconds in a year in scientific notation (1year= 365days)
The number of seconds in a year is 31,536,000 seconds. Rounded to three significant figures, the number of seconds in a year can be written as 3.15 x 10^7 seconds in scientific notation.
Scientific notation is a way to represent numbers as a decimal multiplied by a power of 10. The decimal part is always between 1 and 10, and the power of 10 gives the number of zeros or decimal places in the original number. For example, the number of seconds in a year can be written as 31,536,000 seconds in scientific notation as 3.1536 x 10^7.
The number of seconds in a year is 31,536,000 (60 seconds x 60 minutes x 24 hours x 365 days).
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What is the value of m in this proportion? 1/7/3/4=1/6/m Enter your answer as a fraction in simplest form in the box. M =
A fraction in simplest form M = 3/4
Part A is 1/4 of the whole
Part B is 3/4 of the whole
Assuming there are no other parts,
the Whole = A + B is the denominator:
Whole = 3 + 9 = 12
Part A = 3 and Part B = 9 are numerators for each fraction.
The fractions are then:
3/12 and 9/12
Meaning:
Part A is 3/12 of the whole
Part B is 9/12 of the whole
Reducing the fractions, it is also true that:
Part A = 1/4 of the whole
Part B = 3/4 of the whole
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3x - 9 (if x = 6) I need some help on this
PLS HELP! Asap
I need helppp!
Answer:
The first option (angle 2 and 5)
Step-by-step explanation:
Vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent, meaning that they have the same angle measure.
In this case, angle 2 and angle 5 are vertical angles. So, the measure of angle 2 is equal to the measure of angle 5. Angle 6 and angle 3 are also vertical angles. So, the measure of angle 6 is equal to the measure of angle 3.
whats 2848x3848 + 575x848 / 48583 x 4848 + 828382
(who just wants to take a break from school and just relax and talk about things?)
Me. I definitely want to take a break
as the number of rainy days increases, so does the height of all of the tomato plants in liz's garden. there appears to be a(n) correlation between number of rainy days and tomato plant height.
There appears to be positive correlation between number of rainy days and tomato plant height.
This can be said because a positive correlation is a relationship between two variables that if one moves in a direction the other moves in the same direction. In this situation the rain increases so the tomato plant height increases, therefore there is a positive correlation.
A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
A correlation reveals the nature and magnitude of a link between two variables. In other words, it illustrates the degree to which measurements of two or more variables are comparable throughout a dataset.
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can you pls solve this i need help
2 apples is equivalent to 6 bananas.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here; Scale1 as 20 bananas equal to 4 pineapples
Scale 2 as 2 pineapple equals 4 bananas and 2 apple
Let the weights of pineapple, bananas , apple as x,y,z respectively
Thus 20y=4x
or x=5y
Again 2x=4y+2z
or 10y=4y+2z
6y=2z
z=3y
Thus 2 apples or 2z=6y that is 6 bananas
Hence, 2 apples is equivalent to 6 bananas.
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occurs when the effects of two or more explanatory variables are not separated. therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.
The complete statement would be, confounding in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.
We know that an extraneous variable is a variable that has the potential to affect the results and it is not a independent variable.
A confounding variable is nothing but a type of extraneous variable which is related to a study’s independent and dependent variables.
These variables (confounding variables) are also known as confounders or confounding factors.
Any variable must follow following conditions to be a confounding variable:
1) A variable must be correlated with the independent variable.
2) It must be related to the dependent variable.
Thus, confounding occurs when the effects of two or more explanatory variables are not separated. therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.
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The complete question is:
__________ in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.
find the equation of the exponential function represented by the table
The equation of the exponential function in the table is
f(x) = 0.2(3)ˣHow to write the equation of the exponential functionExponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, as in the table
the starting = is f(0) = 0.2
Solving for the base
f(x) = a(b)^x at x = 1
0.6 = 0.2(b)^1
0.6 = 0.2b
b = 0.6 / 0.2
b = 3
hence the equation is f(x) = 0.2(3)ˣ
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Answer:
I DONT KNOW SORRYStep-by-step explanation:
I KNOW ALOT OF MATH BUT NOT THIS ONE :| LIFE IS LIFEI GOT MY PONITS I'M HAPPY :) :) :) :) :) :) :) :) :) :) :) :)
true or false: the curve of a distribution has thicker tails than the curve of the standard normal distribution.
Therefore, the given statement that the t-distribution has more area in the tails than the standard normal distribution
SO ITS TRUE
Answer: true
Step-by-step explanation:
To better understand the website builder market, Clutch surveyed individuals who created a website using a do-it-yourself (DIY) website builder. Respondents, categorized by the type of website they built—business or personal, were asked to indicate the primary purpose for building their website. The following table summarizes the findings:
As the importance of having a powerful online presence continues to grow, many people are chosen to build their own websites using do-it-yourself (DIY) tools.
These tools, also known as website builders, are relatively easy to use and inexpensive. Examples include Wix, Square Space, Weebly, and more.
Web builder users lean to create two various types of websites, either personal sites a creative display, blog or portfolio or business sites for online ecommerce, sales, or an online business presence.
Understanding what users of web builders design with the DIY tools is an important step in pick out what makes these tools stand out.
While the mass of users is familiar with the techniques needed to build a site, the actual types of websites being built vary. Nearly half of respondents (48%) specify that their website was built for personal purposes, while 42% said that their website is for business.
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How can I know when
to place a zero in the quotient?
Answer:
See below
Step-by-step explanation:
Your question lacks context, but zero would be in the quotient if the dividend is 0 and the divisor is some natural number (all integers but 0).
Given f(x)=x^2 +2x - 6 and the values of the linear function g(x) in the table, what is the range of (f+g)(x)?
The range of the function will exist on all real numbers. Option D is correct.
what is the Range?
The range gives an idea of how spread out the values in a dataset are and it's a simple measure of dispersion.
The formula for range is:
Range = Maximum value - Minimum value
Given the function f (x) = x^2 + 2x – 6,
The function of the table will also give a quadratic function of degree two.
The sum of the functions will also lead to a quadratic function and since for all input values of the function, there will be a corresponding output, hence the range of the function will exist on all real numbers.
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Find the length of side a in simplest radical form with a rational denominator.
The length of side x is √2 units. The solution has been obtained by using the trigonometry formulas.
What is trigonometry?
The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulas, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in calculations are 0, 30, 45, 60, and 90 degrees.
We are given a right-angled triangle with hypotenuse 2units.
We know that sin theta = opposite side/hypotenuse
Also, sin 45° = 1/√2
So,
⇒sin 45° = x/2
⇒1/√2 = x/2
⇒2/√2 = x
⇒√2 = x
Hence, the length of side x is √2 units.
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Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c.15, 11, 11, 16, 16, 9
Which of the data sets from Exercise 2 are skewed?
Answer:
Answers are in bold
Data set A:
Mean: 7
Median: 7
Mode: 7
Range: 11
Data set B:
Mean: 78
Median: 95
Mode: No mode or all the numbers (85, 105, 95, 90, 115)
Range: 30
Data set C:
Mean: 13
Median: 13
Mode: 11 and 16
Range: 7
Step-by-step explanation:
I just answered this but you're welcome.
Does this table represent a function why or why not?
The table of values is not a function
How to determine if the table is a functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
The general rule of functions is that
Each y value must have different x values
In the table of values, the y values 2 and 5 all have the same x value
Hence, it is not a function
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A lump of butter has a mass of 250 g and a volume of 290 cm³. Find its density in g/cm³. Give your answer to 3 decimal places.
The density in butter has a mass of 250g and volume of 290cm³ is 0.862 g/cm³.
What is meant by density?Density is a physical property of matter that is defined as the amount of mass per unit of volume. It is measured in units of kilograms per cubic meter (kg/m^3) and is usually represented by the Greek symbol ρ (rho).
Density is a measure of how tightly the particles of a substance are packed together. The denser a substance is, the more mass it contains in a given volume.
Most commonly, density is used to compare different substances, such as solids, liquids, and gases.
In general, solids are more dense than liquids, and liquids are more dense than gases.
The density of a substance can change based on temperature, pressure, and other factors. For example, water has a greater density at 4°C than at any other temperature, and the density of a gas increases with increasing pressure.
Density is an important factor in many physical and chemical processes, including buoyancy, diffusion, and surface tension.
Density is also used in many calculations, such as calculating the volume of a container or the mass of an object.
Density, p = m/v
Where, m is mass of butter and v is volume of butter.
p = 250/290
p = 0.862 g/cm³
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Which is a correct solution for the following system of Inequalities
Answer:
I believe the answer is C... I might be wrong but I hope it helps you!!
Step-by-step explanation:
Answer:
I think the answer is b
-1,2
Simplify. (w15th power/ w5th power) 4
Answer:
the answer is to the question is 12