a) For two distinct real roots: x > 0 or x > m
b) For two distinct real roots: x > 0 or x > 2m
c) For two distinct real roots: x > 0 or x > 4
This is based on the quadratic equation.
What is a quadratic equation?Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.
a) Quadratic equation: x² - 4x + m = 0
The discriminant: Δ = b² - 4ac
Δ = (2x)² - 4.x.(m)
Δ = 4x² - 4mx
Δ = 4x (x - m)
For two distinct real roots: Δ > 0
4x (x - m) > 0
x > 0 or x > m
For two real roots: Δ ≥ 0
4x (x - m) ≥ 0
x ≥ 0 or x ≥ m
For a repeated root: Δ = 0
4x (x - m) = 0
x = 0 or x = m
(b) Quadratic equation: mx² + 3x + 2 = 0
The discriminant: Δ = b² - 4ac
Δ = (3x)² - 4.mx.(2)
Δ = 4x² - 8mx
Δ = 4x (x - 2m)
For two distinct real roots: Δ > 0
4x (x - 2m) > 0
x > 0 or x > 2m
For two real roots: Δ ≥ 0
4x (x - 2m) ≥ 0
x ≥ 0 or x ≥ 2m
For a repeated root: Δ = 0
4x (x - 2m) = 0
x = 0 or x = 2m
(c) Quadratic equation: x² - mx + 1 = 0
The discriminant: Δ = b² - 4ac
Δ = (x)² - 4.x.(1)
Δ = x² - 4x
Δ = x (x - 4)
For two distinct real roots: Δ > 0
x (x - 4) > 0
x > 0 or x > 4
For two real roots: Δ ≥ 0
x (x - 4) ≥ 0
x ≥ 0 or x ≥ 4
For a repeated root: Δ = 0
x (x - 4) = 0
x = 0 or x = 4
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Which of the following problems would NOT have a solution? Group of answer choices 10 divided by 2. 10 divided by 5. 10 divided by 0. 0 divided by 10.
10 divided by 0 problem would NOT have a solution.
Given:
a. 10 divided by 2
b. 10 divided by 5
c. 10 divided by 0
d. 0 divided by 10
We know that ,
Integer divided by an integer is an integer
Therefore (a) and (b) will have a proper solution
We also know that ,
Zero divided by anything is Zero
Therefore (d) also have a unique answer that is zero
Now , We know that
Any numeric value divided by Zero tends to infinity .
Hence, 10 divided by 0 problem would NOT have a solution.
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Translate this sentence into an equation. The sun of 15 and Delia’s age is 65. Use the variable d to represent Delia’s age
The translation of the sentence 'The sum of 15 and Delia’s age is 65'
is 15 + d = 65.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The age of Delia be 'd'.
Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65' can be expressed as,'
15 + d = 65.
d = 65 - 15.
d = 50.
So, The age of Delia is 50 years.
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the average of senators in the 108th congress was 61 years, if the standard deviation was 15 years find the z-scores corresponding to the oldest and youngest senators of age 86% and 41. round z scores to two decimal places.
Therefore , the solution of the given problem of test statistic comes out to be rounding to two decimal places, the z-score is -0.26.
What is the test statistic?The Z-statistic, which demonstrates that the ordinary ordinary neutral hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the variable results show that you got a 2.5 R t. (also Z-value). The p-value for this Z-value is 0.0124.
Here,
To find the z-scores corresponding to the oldest and youngest senators of age 86% and 41%, respectively, we can use the standard normal distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
For the oldest senators of age 86%, we can find the corresponding z-score as follows:
z = (x - μ) / σ
z = (0.86 - 0.5) / 0.3413
z = 1.055
Rounding to two decimal places, the z-score is 1.06.
For the youngest senators of age 41%, we can find the corresponding z-score as follows:
z = (x - μ) / σ
z = (0.41 - 0.5) / 0.3413
z = -0.264
Rounding to two decimal places, the z-score is -0.26.
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From 15 men and 11 women how many committees of 10 persons can be chosen is each committee is to have exactly 8 men
There are 353925 committees of 10 persons that can be chosen with exactly 8 men.
How to determine the number of waysFrom the question, we have the following parameters that can be used in our computation:
People = 15 men and 11 women
Committee = 10 persons (8 men)
The number of ways is then calculated as
Ways = Men * Women
So, we have
Ways = C(15, 8) * C(11, 2)
Evaluate the products
Ways = 353925
Hence, the number of committee is 353925
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a cylindrical tank is 18 feet high with a diameter of 8.5 feet. if the tank is filled to the top, how many gallons will it hold
I believe its 44,880
The effect of the time of day a science class is taught on test scores is being
studied in an experiment. Which of these is most likely to be an extraneous
factor that could also affect test scores?
O A. Color of the school hallways
B. Principal of the school
OC. Difficulty of test questions
OD. Student clothing
In linear equation, The effect of the time of day a science class is taught on test scores being studied in an experiment will be the length of the class period.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
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the domain of the function given below is the set of all real numbers greater than 1/2.
F(x) =(1/2)^x
A. True
B. false
Answer:
B. False
Step-by-step explanation:
The domain is the set of values of x.
There is no restriction on the value of x.
x can be any real number.
Answer: B. False
how many 3/5 are in two as a tape diagram
The number of the 3 / 5 in a tape diagram is 3.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator. Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.
Given that the fraction is 3 / 5. When we add the fraction three times we will get the value that is closest to 2.
E = 3 / 5 + 3 / 5 + 3 / 5
E = ( 3 + 3 + 3 ) / 5
E = 9 / 5
E = 1.8 ≅ 2
Hence, in a tape diagram, the 3/5 is represented by the number 3.
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Five years ago, a father was six times as old as his son. Two years hence, the age of the father will be 1 year more the three times then age of his son. Find their present ages.
Answer:
84
Step-by-step explanation:
Let's call the father's present age "F" and the son's present age "S".
Five years ago, the father's age was F - 5 and the son's age was S - 5.
According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.
Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.
According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.
We can now substitute the first equation into the second:
3S + 7 = 6S - 28,
3S - 6S = -35 - 7 = -42,
-3S = -42,
S = 14.
Finally, the father's present age is F = 6S - 35 = 84.
Answer:
The dad is 35 and the son is 10
Step-by-step explanation:
Let f = the father's age
let s - the son's age
In the equations f-5 and s-5 represents the father and son's ages 5 years ago. f + 2 and s +2 represent the father and son's ages two years in the future.
Consider a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3. Calculate the z-score given that x = 79.8. Round your answer to two decimal places.
For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555
We know that the formula for calculating a z-score is :
z = (x - μ) / σ
where z is the standard z - score
x is the observed value
μ is the mean of the sample
σis the standard deviation of the sample
here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3
i.e., μ = 83.3, σ = 6.3
We calculate the z-score for x = 79.8
Using above formula,
z = (x - μ) / σ
z = (79.8 - 83.3) / (6.3)
z = (-3.5) / (6.3)
z = -0.555
Therefore, the z-score is: -0.555
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Deandre rented some movies and video games last month. He did the same this month. The table below shows the number of movies and video games he
rented each month. It also shows the total cost (in dollars).
A) the picture…
B)How much did it cost(in dollars) to rent each movie and each video game?
Rental cost for each movie:?
Rental cost for each video game:?
Answer:
Step-by-step explanation:
We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.
For the movies:
Rental cost for each movie = Total cost of movies rented / Number of movies rented
= $33 + $24 = $57
= $57 / 6 = $9.50 per movie
For the video games:
Rental cost for each video game = Total cost of video games rented / Number of video games rented
= $18 + $24 = $42
= $42 / 4 = $10.50 per video game.
Select the expression that matches subtract three from 4/9 of 20
Answer: The answer is D
the data set shows the january 1 noon temperatures in degrees Fahrenheit for a particular day in each of the past six years. 28 34 27 42 52 15 the five number summary of the data set is15 27 28 34 42 52 the mean of the data set is 33 what is the sum of the squares of the differences between each data value and the mean? use the table to organize your work
The sum of the squares of the differences between each data value and the mean is given as follows:
828.
How to obtain the sum of the squares?The mean of the data-set in this problem is given as follows:
33.
The data-set is given as follows:
28, 34, 27, 42, 52 and 15.
Hence the sum of the squares of the differences between each data value and the mean is obtained as follows:
(28 - 33)² + (34 - 33)² + (27 - 33)² + (42 - 33)² + (52 - 33)² + (15 - 33)² = 828.
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suppose that a is an upper bound for the set S and that there is a sequence of elements xn that exists in S such that xn-->a. Prove that a is the least upper bound.
a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
What is the difference between the least upper bound and upper bound?
An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.
To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:
a is an upper bound of S, meaning that for every element x in S, x <= a.
If there is another upper bound b for S, then a <= b.
First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.
Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.
Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
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please save me ASAP !
Answer:
40h = e
Step-by-step explanation:
40 x 11 = 440
In a small rectangular wallet photo, the width is 5 cm less than the length. If the border (perimeter) of the photo is 22 cm, find the length and width
As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.
what is perimeter ?
An enclosed line that surrounds, distinguishes, or incorporates a two-dimensional contour or a three-dimensional length is referred to as a boundary. The edge of an ellipse or circle refers to its broadest area. The perimeter calculation has many useful properties. The rim of a form is its edge's radius. Understand how to determine the perimeter by adding the lengths of such sides of various forms. You can always measure the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At your house, any enclosed terrace is one illustration. The border of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.
given
let the length of the rectangular wallet be x
the width be x - 5
perimeter = sum of all the sides = 22
x + x - 5 = 22
2x - 5 = 22
2x = 17
x = 8.5
length is 8.5 and width is 8.5 - 5 = 3.5
As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.
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Suppose X has a Poisson distribution with a mean of 7. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654) (a) P(X= 1)i (b) PIXs 2)=i (c) PIX= 4)- (d) PIX-8)
The probabilities are obtained as -
a) P(X = 1) = 0.006377
b) P(X ≤ 2) = 0.0296075
c) P(X = 4) = 0.091137
d) P(X = 8) = 0.130251
What is Poisson Distribution?
The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.
The mean of the Poisson distribution is given by λ.
The cumative distribution function is -
P(X = π) = (e^(-λ)λ^π) / π!, where π = 0,1,2,...
a) So, putting π = 1, λ = 7 in the above formula -
P(X = 1) = (e^(-7)7^1) / 1!
P(X = 1) = (0.000911 × 7) / 1
P(X = 1) = 0.006377
Therefore, the value is P(X = 1) = 0.006377.
b) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (e^(-7)7^0) / 0! + (e^(-7)7^1) / 1! + (e^(-7)7^2) / 2!
P(X ≤ 2) = 0.000911 + 0.006377 + 0.022319
P(X ≤ 2) = 0.0296075
Therefore, the value is P(X ≤ 2) = 0.0296075.
c) So, putting π = 4, λ = 7 in the above formula -
P(X = 4) = (e^(-7)7^4) / 4!
P(X = 4) = (0.000911 × 2401) / 24
P(X = 4) = 0.091137
Therefore, the value is P(X = 4) = 0.091137.
c) So, putting π = 8, λ = 7 in the above formula -
P(X = 8) = (e^(-7)7^8) / 8!
P(X = 8) = (0.000911 × 5764801) / 24
P(X = 8) = 0.130251
Therefore, the value is P(X = 8) = 0.130251.
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Solve The Following System Of Equations For Z And For Y: System Of Equations: y= 10+2zy=38-5z
For the system of equations, y = 10 + 2z and y = 38 - 5z the value of y and z are 18 and 4 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is : y = 10 + 2z
The second equation is : y = 38 - 5z
Subtract equation (1) and (2) -
y - y = 10 + 2z - (38 - 5z)
0 = 10 + 2z - 38 + 5z
Collect the like terms -
2z + 5z = -10 + 38
7z = 28
z = 28/7
z = 4
Substitute the value of z in equation (1) -
y = 10 + 2(4)
y = 10 + 8
y = 18
Therefore, the value of y = 18 and z = 4.
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The digit in the units place of a 2 digit number is 4 times the digit in the tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.
A. 28B. 32C. 15D. 25
The number in question is 28.
To make solving this problem easier, we need to consider the number.
Let the number is ab.
So that,
4 × a = b
4a = b
We spread the numbers on the options.
28
(4 × 2 = 8) → True
32
(4 × 3 = 2) → False
15
(4 × 1 = 5) → False
25
(4 × 2 = 5) → False
We prove what number of 28 is when the digits is reversed to be greater than 54.
28 ⇄ 82
It is proved that the number 82 is greater than the number 54.
So, the number in question is 28.
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Determine which of the lines are skew
The lines are skew is Lines AD and BF.
Definition of Skew lineSkew lines are two lines that do not intersect, are not parallel, and are not coplanar. This means that the skew lines never cross and are not parallel to each other. For lines to be two-dimensional or coplanar, they can intersect or be parallel. This property does not apply to diagonal lines, which are always non-coplanar and exist in three or more dimensions.
Skew line exampleIn real life, cities have different types of roads, such as highways and overpasses. These streets are supposed to be on different levels. Lines drawn on such roads never intersect, creating skew lines instead of being parallel to each other.
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1. Given the image of the circle, identify the length of the radius, diameter, and circumference. Also, find the area. Make sure to show work (area and circumference) to receive credit. Choose a number for the diameter.
Answer:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
Step-by-step explanation:
i choose diameter.
Let's say the diameter of the circle is 10 units.
The radius of the circle can be found by dividing the diameter by 2:
Radius = Diameter / 2 = 10 / 2 = 5 units
The circumference of the circle can be found using the formula:
Circumference = 2πr = 2π * 5 = 10π units
The area of the circle can be found using the formula:
Area = πr^2 = π * 5^2 = 25π square units.
So, for a circle with a diameter of 10 units:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
Morgan is shipping boxes at a package center. She is shipping x small boxes that weight 2 pounds each and y large boxes that weigh 10 pounds each. She is shipping 17 boxes altogether and the combined weight of all the boxes she ships is 74 pounds. Write an equation in standard form to model this scenario.
A system of equations in standard form to model this scenario include the following:
2x + 10y = 74.
x + y = 17.
How to write the system of equations for this system?In order to write a system of linear equations that could be used to model the situation and determine the number of small boxes shipped and the number of large boxes shipped, we would assign variables to the number of small boxes that were shipped, the number of large boxes that were shipped respectively as follows:
Let the variable s represent the number of small boxes.Let the variable l represent the number of large boxes.Next, we would translate the word problem into system of linear equations as follows:
Since x small boxes weigh 2 pounds each and y large boxes weigh 10 pounds each and all the boxes she ships is 74 pounds;
2x + 10y = 74.
Additionally, she is shipping 17 boxes altogether;
x + y = 17.
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Alexa plans to join a members-only speaker series for $50. As a member, she will pay just $12.50 for each event she attends. Alexa has budgeted $100 to become and member and attend these events. How many events can she afford to attend?
Answer:
4 events
Step-by-step explanation:
you divide 12.50 by 50 then you get 4
why did brainly get me so up someone help
Answer:
we on top
Step-by-step explanation:
Answer:
Step-by-step explanation:
you gotta be kidding me right now b r u h. Aint no way bro is posting this hahahha get it i guess
Practice
Solve for x.
1.x³ = 64
2.x² = 49
3.x³ =25
4.x²=125
The solutions for all the equations are:
1) x = 4
2) x = ±7
3) x = 5²´³
4) x = ±5³´²
How to solve the equations for x?The first equation is:
x³ = 64
If we apply the cubic root in both sides we will get:
∛x³ = ∛64
x = ∛64 = 4
2) now we have:
x² = 49
If we apply the square root:
√x² = ± √49
(remember the plus minus sign when you use a even degree root)
x = ±7
In this case we have two solutions.
3) x³ =25
Like in the first case:
x = ∛25 = ∛5² = 5²´³
Now we can't simplify this, so we leave it in this way.
4) x² = 125
Remember that 125 = 5³, then:
x² = 5³
x = ±√5³ = ±5³´²
These are all the solutions.
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On Friday, Thomas the clown sells 16 balloons at the circus. Due to demand, Thomas charges three dollars more per balloon on Saturday. On Saturday, he sells 40 balloons. Let f represent the price of a balloon on Friday and let t represent the total amount he earns on both days combined.
a Write an equation to describe the relationship between the price of a balloon on Friday and the total amount earned.
b Determine the price of a balloon on Saturday if Thomas earns 400 dollars on Friday and Saturday.
The relationship between the price of balloons and the amount earned is 56f + 120 dollars
The price of the balloons if 400 dollars is earned on friday and saturday is 5 dollars on friday and 8 dollars on saturday
How to solve for the pricea) If f is the price of a balloon on Friday, then the price of a balloon on Saturday would be f + 3 dollars. The total amount Thomas earns on Friday would be 16 balloons * f dollars/balloon = 16f dollars. The total amount Thomas earns on Saturday would be 40 balloons * (f + 3 dollars/balloon) = 40f + 120 dollars. Hence, the total amount earned on Friday and Saturday would be 16f + 40f + 120 dollars = 56f + 120 dollars.
Therefore, the equation to describe the relationship between the price of a balloon on Friday and the total amount earned is: t = 56f + 120 dollars.
b) We are given that Thomas earns 400 dollars on Friday and Saturday, so we can set t = 400 dollars in the equation derived above:
400 = 56f + 120
Solving for f, we have:
280 = 56f
f = 5 dollars
The price of a balloon on Friday is $5, and the price of a balloon on Saturday would be f + 3 = 5 + 3 = $8.
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A fully inflated professional basketball has a circumference of 78 centimeters. What is the radius of a circular cross section through the center of the ball? use 3.14 for pi?
A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.
what is circle ?A circle is created when almost every point there in plane that is a specific distance away from another point does so (center). As a conclusion, it is a curve made up of segments that are spaced from each other in the plane. It is rotationally homogeneous about the centre in anyway angles. All pair of points in the grid that make up a circle are evenly spaced away from the "centre" and create a closed, two-dimensional object. A specular parity line is generated by a line that passes through circle. It is rotationally symmetric about just the centre at all angles.
given
The football's circumference is 12.42 cm.
Football's circumference is 78 cm.
The formula for the football's circumference is C = 2pir
= 78 r
= 78/2pi r
= 12.42 cm.
A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.
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7. For a dropped object, the function t(h)=√ h/16 can be used to find the distance, h, in feet,
that the object has fallen after a time, t, in seconds. How far has the object fallen after 1.6
seconds?
Answer: To find the distance fallen after 1.6 seconds, we simply plug this value into the function and solve for h:
h = t^2 * 16
h = 1.6^2 * 16
h = 2.56 * 16
h = 40.96 feet
So, the object has fallen 40.96 feet after 1.6 seconds.
Step-by-step explanation:
Answer the questions below
The triangle is congruent by the Angle side Angle property.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.
The three parameters that are congruent are:-
BV ≅ BV ( common side)
∠1 ≅ ∠2 ( Bisector)
∠3 ≅ ∠4 ( Bisector)
Hence, the two triangles are congruent with each other.
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2-1=1 explain how you get 1
Answer:
Step-by-step explanation:
you take away 1 from 2 and that leaves you with 1
Answer:
Let's say I have two apples. You want one too! I give you one, and how many do I have left? 1
What I am explaining here is that if you take one away from two, it becomes one.