The value of k in the quadratic equation is k = 0 or k = 8
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
2x² + kx + k = 0 be equation (1)
And , the roots of the equation are equal
So , when the discriminant is zero we get just one real solution
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
( b² - 4ac ) = 0
Substituting the values in the equation , we get
k² - 4 ( 2 ) ( k ) = 0
On simplifying the equation , we get
k² - 8k = 0
Adding 8k on both sides of the equation , we get
k² = 8k
So , when k = 0 , the equation satisfies
And ,
k = 8
Therefore , the value of k are 0 and 8
Hence , the value of k in the equation is 0 or 8
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Determine the domain of the following graph:
Answer: [-11, 11)
Step-by-step explanation:
Because the point is closed and shaded in at x = -11, we know that the value is included in the domain. So, in interval notation, we will use a "[".
Because the point is empty and not shaded in at x = 11, we know that values approaching x = 11 are included, but not x = 11 itself. So, in interval notation, we will use a ")".
A rectangle price of lawn i 55 m 98 m long find the length of the fence around it
Answer:
306m
Step-by-step explanation:
someone else asked the same question here! https://brainly.com/question/30091724
there are better explainations there :)
you're looking for the perimeter, so you need to add all the sides. that's 55+55+98+98, which is 306.
x=[ ? ]° PLEASE HELP I WILL BE MAKING MULTIPLE POST
Answer:
In a triangle, there are a total of 180 degrees.
Step-by-step explanation:
his is because the interior angles of a triangle always add up to 180 degrees. This is a property of triangles that can be proven using geometry.
Consider a triangle with three angles, A, B, and C. The sum of the angles in a triangle is equal to the sum of the angles in a straight line, which is 180 degrees. Therefore, the sum of the angles in the triangle is A + B + C = 180 degrees. This means that the three angles in a triangle always add up to 180 degrees.
It is important to note that this applies to all triangles, regardless of their size or shape. Whether the triangle is a right triangle, an isosceles triangle, an equilateral triangle, or any other type of triangle, the sum of its interior angles will always be 180 degrees.
Adrian and his children went into a grocery store and will buy apples and
mangos. Each apple costs $2.25 and each mango costs $2. Adrian has a total
of $25 to spend on apples and mangos. Write an inequality that would
represent the possible values for the number of apples purchased, a, and the
number of mangos purchased, m.
We can represent the number of apples purchased by Adrian as the variable "a" and the number of mangos purchased by Adrian as the variable "m". The total cost of apples can be represented as $2.25 * a, and the total cost of mangos can be represented as $2 * m. The inequality that represents the possible values for the number of apples and mangos that Adrian can purchase is $2.25 * a + 2 * m <= 25.
Lauren builds a sandbox shaped like an octagon. Each side of the sandbox is the same length.
The perimeter of the sandbox is 18.8 feet.
An octagon with 8 equal sides, all with unknown length, in feet.
Part A
How long is each side of the sandbox? Enter your answer in the box.
feet ( Input Answer )
Part B
The total cost of sand to fill the sandbox is $59.48. Lauren and 3 friends divide the cost equally.
How much does each person pay? Enter your answer in the box.
$ ( Amount??? )
Answer:
To solve this problem, we need to first find the length of each side of the sandbox. Since the sandbox is an octagon with 8 equal sides, we know that the perimeter of the sandbox is 8 times the length of each side. Thus, we can use the formula for perimeter to find the length of each side:
Perimeter = 8 * Side Length
Substituting the given values into this formula, we get:
18.8 feet = 8 * Side Length
Dividing both sides of the equation by 8, we get:
Side Length = 2.35 feet
Therefore, each side of the sandbox has a length of 2.35 feet.
________________________________________________________
To find the amount of money that each person pays to fill the sandbox, we need to divide the total cost by the number of people involved. In this case, there are 4 people in total, so each person pays 1/4 of the total cost. Thus, the cost per person is $59.48 / 4 = $14.87.
Ben has a cellphone plan where he pays $12 per month plus $.10 per minute of talk time. The equation y=0.1x+12 can be used to find his monthly phone bill y given the number of minutes x he is talking. Which of the following, in set builder notation, represents a reasonable range of the function.
Answer:
A reasonable range for the function y=0.1x+12 would be all real numbers greater than or equal to 12. This is because the minimum monthly phone bill that Ben could have would be $12 (if he does not use any minutes), and the monthly bill can increase to any higher value depending on the number of minutes he talks. In set builder notation, this range would be written as {y | y >= 12}.
Step-by-step explanation:
A truck hauls a car cross-country. The truck's mass is 5.00x10 kg and the car's mass is 1.60x10 kg. If the force of propulsion resulting from the truck's turning wheels is 2.50x10' N, then determine the acceleration of the car (or the truck) and the force at which the truck pulls upon the car. Assume negligible air resistance forces. 3. Find the net forces for Situation 1 & 2 in page 56 of the module. 4. Figure below shows a truck is hauling a trailer along a level road. Find the force D that moves the truck forward. Use the given free body diagram. *27000 8500 0.7 m/? Drawbar D Trailer Truck
The truck is propelled forward by force D of 2.769 * 10⁴ N and acceleration of 0.78 m/s2.
What is Force?The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Given, Mass of the truck = 5000 kg
Mass of car = 1600 kg
Force applied = 25000 N
As we know Force (F) =m.a
Where m = mass of the body
a = acceleration of the body
25000 = (5000 + 1600) * a
a = 25000/ 6600 = 3.7878.
a = 3.79 m/s²
According to diagram D = ma
m = 27000 + 8500 = 35500 kg
a = 0.78 m/s²
so D = 35500 * 0.78 = 27690N
Therefore, Force D that moves the truck forward is 2.769 * 10⁴ N, and acceleration is 0.78 m/s².
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What is the relationship between the area of the rectangle and its sides?
The relationship between area and sides of rectangle is Area = product of length and breadth.
what is rectangle?The geometrical shape which has four right angles and four straight sides. The identical sides are parallel to each other.
How to calculate the area of rectangle?the sides of rectangle which are situated along the horizontal axis and parallel to each other are called length. The other parallel sides which situated along the vertical axis are called breadth. The area of rectangle = length× breadth
hence, area of rectangle is the product of two unequal side length.
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1. A clock that strikes only the hours has just finished striking a total of 9 times in last 2.5 hrs. What hour did it just finish striking?
Answer:
I have solved it and attached a picture in the explanation part!
Step-by-step explanation:
Answer: 9:00
Step-by-step explanation:
You just solve it.
What are the 3 shortcuts to prove triangles are similar?
In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.
In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Here we have to find the 3 shortcuts to prove the triangles are similar.
According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).
Here we must know that the term similarity and congruent are similar terms.
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I need help with problem 11.
Answer: 12-pound bag of cat food
Step-by-step explanation:
12 pounds bag of cat food = $18
15 pounds bag of cat food = $24
Let's find the cost per pound of the 12-pound bag first
Take 18 divided by 12 = $1.50 per pound
Now find the cost per pound of the 15-pound bag
Take 24 divided by 15 = $1.60 per pound
So, buying a 12-pound bag of cat food is better because it is cheaper per pound.
What are the 5 discontinuities?
A removable discontinuity exists when a function is not defined at a certain point. An infinity discontinuity occurs when the function approaches infinity. A jump discontinuity occurs when the function has a finite jump in value at a certain point. An essential discontinuity exists when the limit of the function exists but the function is not defined at the point. A mixed discontinuity is a combination of the other discontinuities.
A removable discontinuity occurs when a function is not defined at a certain point. This means that the limit of the function as it approaches the point does not exist. However, if the function can be modified by adding or subtracting a constant to make the limit exist, then the discontinuity is removable. An example of this would be f(x) = 1/x, which is undefined at x = 0, but if we subtract 1 from both sides, the limit of f(x) as x approaches 0 is 0. An infinity discontinuity occurs when the function approaches infinity as it approaches a certain point. This means that the limit of the function as it approaches the point does not exist. An example of this would be f(x) = 1/x as x approaches 0, where the limit of f(x) is infinity. A jump discontinuity occurs when the function has a finite jump in value at a certain point. This means that the limit of the function from both sides of the point do exist, but they are not equal. An example of this would be f(x) = x + 1 for x >= 0 and f(x) = x for x < 0, where the function jumps from 0 to 1 at x = 0.An essential discontinuity exists when the limit of the function exists but the function is not defined at the point. An example of this would be f(x) = 1/x for x != 0, where the limit of f(x) as x approaches 0 is 0, but the function is not defined at x = 0. A mixed discontinuity is a combination of the other discontinuities. It occurs when the limit of the function as it approaches a certain point exists, but the value of the function at the point is undefined. An example of this would be f(x) = x^2 - 1 for x != 1, where the limit of f(x) as x approaches 1 is 0, but the function is undefined at x = 1.
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Michelle's class just held a class election. 24 out of the 30 students in the class voted in the election. What percentage of the students voted?
Answer:
80
Step-by-step explanation:
The total answers count 30 - it's 100%, so we to get a 1% value, divide 30 by 100 to get 0.30. Next, calculate the percentage of 24: divide 24 by 1% value (0.30), and you get 80.00% - it's your percentage grade
the side of the cube is increasing at a constant rate of 0.2 centimeters per second. in terms of the surface area s, what is the rate of change of the volume of the cube, in cubic centimeters?
The rate of change of the volume of the cube is 0.4s cm³/s
What is rate of change?Rate of change is the rate at which a quantity increases or decreases with time.
How to find the rate of change of the volume of the cube, in cubic centimeters?Since the side of the cube is increasing at a constant rate of 0.2 centimeters per second. Its volume is given by V = L³ where L = length of side of cube.
Now, to find the rate of change of its volume, we differentiate the equation with respect to time, t.
So, V = L³
Differentiating, we have
dV/dt = dL³/dt
= dL³/dL × dL/dt
= 2L² × dL/dt
Since the rate of increase of the side of the cube is dL/dt = 0.2 cm/s, we have that
dV/dt = 2L² × dL/dt
= 2L² × 0.2 cm/s
= 0.4L² cm³/s
We know that the area of a cube s = L². So, substituting this into the equation, we have
dV/dt = 0.4L² cm³/s
= 0.4s cm³/s
So, the rate of change is 0.4s cm³/s
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Q9 A ferris wheel can accommodate 54 people in 24 minutes . How many people can ride ferris wheel in 2 hours ?
What do we mean by equidistant?
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.
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Is 7 3x is a factor of 3x² 7x?
No, 7 3x is not a factor of 3x² 7x.
What is factor?Factor is an element that is used in mathematics and economics to describe the relationship between two or more variables. It is a numerical value that is multiplied by a given number to produce a product. Factors can also refer to the elements of a decision-making process, such as risk, cost, and potential reward. Factors are used to determine the potential outcome of a situation and to make decisions based on those outcomes.
A factor is a number that can be divided into another number without leaving a remainder. To test if 7 3x is a factor of 3x² 7x, it must be possible to divide 3x² 7x by 7 3x without leaving a remainder. However, this is not possible, as 3x² 7x is not divisible by 7 3x. Therefore, 7 3x is not a factor of 3x² 7x.
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What is 3rd binomial formula?
The third binomial formula is given by ( a + b )( a - b) = a² - b².
Binomial theorem in the standard form is given by :
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ
Binomial formula starts from n = 2
First binomial formula of the binomial theorem is given by :
( a ± b )² = a ² ± 2ab + b²
Second binomial formula is given by:
( a ± b )³ = a³ ± 3a²b + 3ab² ± b³
Third binomial formula is given by :
( a + b) ( a - b) = a² - b²
Therefore, the third binomial formula is equal to ( a + b )( a - b) = a² - b².
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Gil and Beth want to purchase a new marching band uniform for a friend. All uniforms at Brad's Band Supplies are 50% off. While shopping the store announces a special sale for an additional 20% off the discounted price for all items. The uniform Gil and Beth want to buy cost $45.00. Before any discounts are applied Beth claims uniforms are 70% now. Gil disagrees and claims the total discount is not 70% off. Who is correct?
The person that is correct is Beth because the total discount is 70% off before the discount took effect on the original price.
What is a discount sale?A discount sale is defined as the selling of items at a price that is below the normal price is a way to show appreciation or to encourage the customers.
The first discount announced by the shop = 50% off.
The second discount announced by the shop= 20% off.
The total discount by the shop = 50 + 20 = 70% off.
The original cost of the uniform = $45.00
Beth is correct because when the discounts were added, the total discount is 70%.
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What is SAS ASA SSS AAS?
SSS (Side-Side-Side) , SAS (Side-Angle-Side) , ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) are the four postulates that defines the Congruency of a triangle.
What is Congruence of triangles ?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.
In Mathematics , Four postulates are defined in order to judge the congruency of a triangle , they are as followed :
SSS which stands for (Side-Side-Side) : when all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.SAS which stands for (Side-Angle-Side) : when any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle.ASA which stands for (Angle-Side-Angle) : when any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle.AAS which stands for (Angle-Angle-Side) : When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.Learn more about Congruence of triangles at:
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of 5 employees, 3 are to be assigned an office and 2 are to be assigned a cubicle. if 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?
The probability that the offices will be assigned to 2 of the men and 1 of the women will be 3/5
Lets find all the combinations of 2 men and 1 woman that can be chosen
(men, men, women) m m w
3/5 x 2/4 x2/3
(men, women, men) m w m
3/5 x 2/4 x 2/3
(women, men, men) w m m
2/5 x 3/4 x2/3
then just add those probabilities together:
= 3/5x2/4x2/3+3/5x2/4x2/3+2/5x3/4x2/3
= 12+12+12/60
this simplifies to 3/5
Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics explains the examination of events that can occur subject to probability.
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Find the compositions for the given functions.
Answer:
x = 1
Step-by-step explanation:
f(x) = 5 - 6x g(x) = 3x -4
5 -6x = 3x - 4
5 = 9x - 4
9 = 9x
x = 1
Two friends argue over who brushes their teeth more often. To settle the
argument, they keep track of the number of mornings and nights they brush
and calculate a probability. These are shown in the table.
Probability of brushing
in morning
Probability of brushing
in evening
Braxton
0.72
0.85
Arabella
0.82
0.79
Who is more likely to brush both morning and evening? Assume all events are
independent.
Answer:
Arabella
Step-by-step explanation:
I am assuming the information in your table looks like this:
P(brushing in morning) P(brushing in evening)
Braxton .72 .85
Arabella .82 .79
Now, to find the probability either of Braxton or Arabella brushes in both the morning and evening (knowing they are independent), we multiply them together.
P(Braxton brushes in morning AND evening) = .72 × .85 = .612 = 61.2%
P(Arabella brushes in morning AND evening) = .82 × .79 = .6478 = 64.78%
Since 664.77% > 61.2%, we know that Arabella is more likely to brush her teeth in both the morning and evening compared to Braxton
Arabella is more likely to brush both morning and evening than Braxton, as her probability of brushing both morning and evening is higher.
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
To find out who is more likely to brush both morning and evening, we need to calculate the probability of each person brushing both morning and evening and compare the results.
For Braxton, the probability of brushing both morning and evening is:
P(Braxton brushes both morning and evening) = P(Braxton brushes in the morning) × P(Braxton brushes in the evening)
= 0.72 × 0.85
P ( B ) = 0.612
For Arabella, the probability of brushing both morning and evening is:
P(Arabella brushes both morning and evening) = P(Arabella brushes in the morning) × P(Arabella brushes in the evening)
= 0.82 × 0.79
P ( A ) = 0.6478
And , P ( A ) > P ( B )
Therefore, Arabella is more likely to brush both morning and evening than Braxton, as her probability of brushing both morning and evening is higher.
Hence , the probability is solved
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The complete question is attached below :
Two friends argue over who brushes their teeth more often. To settle the argument, they keep track of the number of mornings and nights they brushand calculate a probability. These are shown in the table.Who is more likely to brush both morning and evening? Assume all events are independent.
What value of b will cause the system to have an infinite number of solutions 6 3 3 6?
The value of b when the system has an infinite number of solutions is 12.
The Given equations are
y=6x-b ---(1)
6=3x+3y ----(2)
If the system has an infinite number of solutions, then equation 1 is equal to equation 2
If a pair of linear equations have unique or infinite solutions, then the system of equation is said to be a consistent pair of linear equations
Isolate variable y in equation 2
2=x+y
Multiply by 6 on both sides
y=6x-12 -----(3)
To find the value of b, equate equation 1 and equation 3
6x-b=6x-12
b=12
Thus the value of b=12.
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What is the standard form of quadratic equation class 10?
The standard form of a quadratic equation is ax² + bx + c = 0.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as it's degree is two.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where, 'x' is the variable and a, b, c are constants.
Suppose you are given to find the roots of a quadratic equation
2x² + 6x + 4 = 0.
It says two numbers that multiply to 8 and add to 6.
So,
2x² + 2x + 4x + 4 = 0.
2x(x + 1) + 4(x + 1) = 0.
(x + 1)(2x + 4) = 0.
(x + 1) = 0 Or (2x + 4) = 0.
x = - 1 Or x = - 2.
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How many more cups of orange juice than lemon-lime soda were in Martha's fruit punch the last time?
Answer:
There is no way to answer this question without more information about the amounts of orange juice and lemon-lime soda in Martha's fruit punch the last time.
Step-by-step explanation:
Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. Clear check integers rational numbers that are not integers irrational numbers.
As the question is incomplete, an integer, a rational number that is not an integer, and an irrational number are explained with examples.
Integer: An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. EXAMPLE: positive integer: 23, 76, 1, 54, etc.negative interger: -12, -6, -32 etc.
zero integers: 0
Rational numbers: A real number known as a rational number is represented by the formula p/q, where q is not equal to zero. A rational number is any fraction with a non-zero denominator. EXAMPLE: 3/4,1/2. 7/9, 0/4 etc.Irrational numbers: All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers. EXAMPLE: π=3⋅14159265…, √2 etc.A rational number that is not an integer would be a number that can be written as a ratio of 2 integers but cannot be represented as a single integer. EXAMPLE: 5/4 etc.To know more about rational numbers try the:
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Find the sale price after a discount of 30% offa snowboard that originally cost $529
Answer:
you pay 370.30
you saved 158.70
I believe
Answer:
$370.3
Step-by-step explanation:
If you need to find 30% of $529 you need to put 30% into a decimal. 30/100 =0.3 so if we do 0.3 x 529 we get the answer $158.7.
Then we subtract 529 by 158.7 to get 370.3 as the sale price.
(50/34.2)^1.5 = 10-t
(50/34.2)^1.5=10-t this equation is proved.
What is equation?An equation is a formula that is express the equality of two equation.
(50/34.2)^1.5=10-t
Covert decimal to integers
(500/342)^1.5 =10-t
Rearrange the variables to left side of the equation
t=10-(500/342)^1.5
Covert decimal to fraction
t=10(500/342)15/10
Simplify using a^n/m
Simplify using exponent rule with the same exponent(ab)^n=a^n.b^n
t=10-√250^3/171^3
Factor and rewrite the redicant in expotential form
T=10-√250^2×250/√171^2×171
Simplify the radical expression
t=10-1250√10×√19/513×19
Multiply number with radicals
t=1250√190/9747
Rewrite fraction using the latest common denominator
t=97470-1250√190/9747
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What is the slope of a line Y − 3x − 5?
Three is the slope of the line y= 3x + 5.
The slope of a line is a measure of its steepness or incline. It is defined as the change in the y-value of a point on the line divided by the corresponding change in the x-value.
In the equation y = 3x + 5, the coefficient of x (3) is the slope of the line. Therefore, the slope of the line y = 3x + 5 is 3.
A line's slope might be zero, positive, negative, or undefinable. Positive slope lines climb as they move from left to right. A negative slope line slopes downward as it moves from left to right. Zero slopes indicate that a line is horizontal. An arbitrary sloped line has a vertical component.
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