The slope of the line is 3 and the y-intercept is -5.
The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.
The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.
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The frequency distribution of birthweights in human infants is bell shaped with most birthweights in the middle of the range. What type of selection does this demonstrate
On solving the provided question, we can say that stabilizing selection type of selection does this demonstrate is shown by frequency distribution.
what is frequency distribution?In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,
stabilizing selection type of selection does this demonstrate is shown by frequency distribution.
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Complete question: The frequency distribution of birthweights in human infants is bell shaped with most birthweights in the middle of the range of birthweights. What type of selection does this exemplify?
One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.
(Assume that the computers do not back up at the start of the 24-hour period.)
The number of times which the two computers back up at the same time in twenty four hours as required is; 144.
How many times does the computers back up at the same time in 24 hours?It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.
On this note, the least common multiple of both backup times represents when the two computers back up at the same time.
Hence, since the LCM of 5 and 2 is; 10.
It follows that the two computers back up at the same time after every ten minutes.
Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;
= ( 24 × 60 ) / 10
= 24 × 6
= 144 times.
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what must be true for (m+p) so that the value of the expression below is negative? Explain.
-2 + (m + p)
For the expression to be negative (m + p) < 2.
What is an expression?An expression is a group of terms and mathematical symbols which can be evaluated to a given value.
How to determine what must be true for (m+p)?Since we have the expression -2 + (m + p), we need to determine the value of (m + p) for which the value of the expression is negative.
This implies that the value of the expression is less than zero.
So, we proceed as follows.
Since the expression is -2 + (m + p), for it to be negative, it must be less than zero.
So, -2 + (m + p) < 0
⇒ -2 < -(m + p)
Dividing both sides by -1, we have that
-2/-1 < -(m + p)/-1
2 > (m + p)
(m + p) < 2
So, for the expression to be negative (m + p) < 2.
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An art store manager buys easels for 10.20 each. He marks up the cost by 75% to get the selling price. What is the selling price of each easel
Answer:
17.85
Step-by-step explanation:
175% * 10.20 = 17.85
Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true? A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. C. $a-b$ is a multiple of $6$. D. $a-b$ is a multiple of $2$. List the choices in your answer separated by commas. For example, if you think they are all true, then answer "A,B,C,D".
The statements that are true, based on the multiples of 3 and 6 are:
A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. How do multiples relate ?When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.
This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.
It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.
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How to do log2 in Excel?
The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.
For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
Next, since we have the multiplication sign, we use the addition law:
The power of the number becomes the product of the log, so we have:
When you have the same base and number, the result is always 1.
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An ancient human tribe had a hierarchical system where there existed one chief with $2$ supporting chiefs (supporting chief A and supporting chief B), each of whom had $2$ equal, inferior officers. If the tribe at one point had $10$ members, what is the number of different ways to choose the leadership of the tribe? That is, in how many ways can we choose a chief, $2$ supporting chiefs, and two inferior officers reporting to each supporting chief?
The number of different ways is 7560 ways
How to determine the number of different waysFrom the question, we have the following parameters that can be used in our computation:
Chiefs = 1
Supporting chiefs = 2
Members = 10
Inferior officers = 2
There are 10 members.
So, the number of ways to select a chief is 10
Now, there are 9 members left
The number of ways to select a supporting chief is then represented as
Supporting chief = ⁹C₂
Now, there are 7 members left
The number of ways to select an inferior officer is then represented as
Inferior officers = ⁷C₂
So, the total number of ways is
Ways = 10 * ⁹C₂ * ⁷C₂
Evaluate
Ways = 7560
Hence, the number of ways is 7560
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The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:
For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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The two smaller angles of a right triangle have equal measures. find the measure of all three angles.
Answer:
Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.
Angle 1: (right angle) 90 degrees
Angle 2: 45 degrees
Angle 3: 45 degrees
A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.
The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.
Suppose you choose a red/black card:
The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].
Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].
Suppose you choose a red/red card:
The probability of choosing red and red card is 2/6.
Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .
Considering we see a single side of the card we have the following probability:
[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]
The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].
The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].
So, the conditional probability of both red sides is given as:
[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]
Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
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What is the degree of 3x³?
Answer:
3x³ is a polynomial of degree
The degree of the polynomial 3x³ is 3
Ben's mom is 22 years older than ben. In 5 years she will be 3 times as old as he will be. How old are they now?
In linear equation, Ben is 9 years old currently.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. 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.
Ben's mom = 22 years
Ben is 9 years old currently.
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1. What is the measure of angle ABE?
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2. Select all true statements about the figura
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The solution is 40°
The measure of the angle ∠ABE = 40°
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the angle be represented as ∠ABE
Now , let the line be EBC and the total angle of a straight line = 180°
And , the measure of ∠CBD = 40°
Since , ∠ABE and ∠CBD are vertically opposite angles ,
The measure of ∠ABE = measure of ∠CBD
Therefore , the value of ∠ABE = 40°
Hence , the measure of vertically opposite angle ∠ABE = 40°
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3: 5 and 2:10 is are equivalent . explain
The ratios are not equivalent.
How do you solve a 3 sided triangle?
It is impossible to solve a 3-sided triangle because triangles require 3 sides and 3 angles in order to be solved.
A triangle is a three-sided polygon, and the sum of its angles is always 180 degrees. In order to solve a triangle, you must know the length of all three sides and the measure of all three angles. If you know two sides and the angle between them (the angle opposite to one of the sides), you can use the Law of Sines to determine the other angle. If you know two angles and a side, you can use the Law of Cosines to determine the other two sides. With all three sides and angles known, you can use the Pythagorean Theorem to check your work. However, if you only have three sides, it is impossible to solve the triangle because you do not have enough information.
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How do you graph the equation y = 1x / 2 + (-5)
To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.
To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.
For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.
You can then plot these points on the coordinate plane and connect them with a line to graph the equation.
Im really sorry that I was unable to provide a picture. I hope this helped!
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
1/2
y-intercept: (0,−5)
x y
0 −5
2 −4
Step-by-step explanation:
Write an equation in slope-intercept form for the line that passes through the given
point and is perpendicular to the graph of the equation.
24. (−5, 2), y = ¹⁄2x − 3
Please explain how to get the answer too.
Answer:
Step-by-step explanation:
perp. -2
y - 2 = -2(x + 5)
y - 2 = -2x - 10
y = -2x - 8
Help with question 3
Answer:
All real numbers for both Range and Domain
R
or
(−∞,∞)
(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC) An ice cream shop serves chocolate milkshakes that are made with ice cream and milk. There is a proportional relationship between the number of scoops of ice cream and the amount of milk needed to make them. For every 1 scoop of ice cream, cup of milk is needed, and for every 5 scoops of ice cream, cups of milk are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many cups of milk are needed for 18 scoops of ice cream? (2 points)
The constant of proportionality is 2
The equation of the relationship is s = 2mThe number of cups for 18 scoops is 9 cupsHow to determine the constant of proportionalityFrom the question, we have the following parameters that can be used in our computation:
1 scoop of ice cream = 1/2 cup of milk
5 scoops of ice cream = 2.5 cups of milk
The constant of proportionality (k) is then calculated as
k = Scoop of ice cream/Cup of milk
So, we have
k = 5/2.5
Evaluate
k = 2
The equation of the relationshipIn (a), we have:
k = 2
A proportional relationship is represented as
s = km
Where
s = scoop of ice cream
m = cup of milk
So, we have
s = 2m
How to graph the relationshipIn (b), we have
s = 2m
To graph the relationship, we start by generating a table of values and then plot the points
Number of cups for 18 scoopsRecall that
s = 2m
So, we have
18 = 2m
Divide by 2
m = 9
Hence, the number of cups is 9
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The rectangular floor of a classroom is 36 feet in length and 27 feet in width.A scale drawing of the floor has a length of 12 inches.What is the area, in square inches, of the floor in the scale drawing?
The area of the scale drawing is 108 square inches.
I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108
HIJK is a square and KI = 6√2. Find HI
The length of HI will be;
⇒ 6 units.
What is Pythagoras theorem?The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
HIJK is a square.
The length of KI = 6√2
Now,
Since, HIJK is a square.
Hence, There are all sides are equal.
Let the side of square = x
So, By Pythagoras theorem, we get;
⇒ KI² = HI² + HK²
Substitute the given values, we get;
⇒ (6√2)² = x² + x²
⇒ 72 = 2x²
⇒ x² = 36
⇒ x = √ 36
⇒ x = 6
Thus, The length of HI = 6 units
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What is 2 polynomials called?
Binomial is the referred to the polynomial algebraic expression that has two terms.
What is Binomial?An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.
An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.
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Which simplified ratio correctly compares 5 meters to 100 centimeters?
A. 5:1
B. 20:1
C. 1:5
D. 1:20
The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A
How to determine the ratioRatio is simply described as the non equal comparison of two numbers, variables, or events.
It shows how many times a number or variable contains another.
The comparison is also based on size.
From the information given, we have;
5 meter to 100 centimeters
It is important to note that;
100 centimeters = 1 meters
Also, 1 meter= 100 centimeters
5 meters = x centimeters
cross multiply
x = 100(5)
Multiply the values
x = 500 centimeters
Then,
5 meters = 1 meter
Hence, the ratio is 5:1
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Sara put her dog on a diet and kept track of his weight. At the end of 4 weeks,
she recorded her dog's weight change as -3 1/2 pounds. She noticed her dog lost
the same amount of weight each week. What is the dog's weight change each
week of the diet?
Answer:
Weight change per week = -0.875 or -7/8
Step-by-step explanation:
Sara recorded her dog's weight change as -3.5 pounds after 4 weeks of dieting. We know the weight loss is consistent each week, so we need to find out how much the dog loses in one week.
To find out the weight change per week, we can use the formula:
Weight change per week = Total weight change / Total number of weeks
Plugging in the known values:
Weight change per week = -3.5 / 4
Weight change per week = -0.875
The dog loses 0.875 pounds each week.
or -0.875 pounds is the weekly weight change of the dog during the dieting period.
What is simple negation give 5 examples?
Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .
Examples of negation are ,
The negation of P is ∼P.The negation of A ^ B^ C is ∼( A ^ B ^ C ).The negation of A is ∼( A ).The negation of Y ^ VB is ∼( Y ^ VB ).The negation of 6 ^ 7is ∼( 6 ^ 7).Logical operations are performed to check the trueness of an expression.
These are generally Boolean expressions or algebraic functions.
A negation of a basic assertion is made by inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.
Under negation, what was true becomes false and the vice - versa.
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PLEASE PLEASE HELP I WILL MARK THE BRAINIEST (the little crown thingy)
Answer: A
Step-by-step explanation: They both go up but they have diffrent patterns
hopes this helps any
Answer:
A.
Step-by-step explanation:
the 'x' slot is going up two and the 'y' slot is going up one every change.
Twelve eggs cost $2.04. How much will 18 eggs cost
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
WILL MAKE BRAINLIEST!!Match the radical to its simplified form.
1. 9i
2. 5i√2
3. 12√6
4.6i√7
A. √-81
B. 4√54
C. √-50
D. √-252
After simplification the correct matching is
1) 9i - A)[tex]\sqrt{-81}[/tex]
2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]
3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]
4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Here to convert radical to simplified form we need to simplify them then
A)=> [tex]\sqrt{-81}[/tex] = [tex](\sqrt{i*9*9} })[/tex] = 9i
B) => [tex]4\sqrt{54} = 4\sqrt{9*6}= 4\sqrt{3^2*6}= 4*3\sqrt{6} = 12\sqrt{6}[/tex]
C) => [tex]\sqrt{-50} = \sqrt{i^2*25*2}=\sqrt{i^2*5^2*2}=5i\sqrt{2}[/tex]
D) => [tex]\sqrt{-252} = \sqrt{i^2*36*7}=6i\sqrt{7}[/tex]
Hence the correct matching is
1) 9i - A)[tex]\sqrt{-81}[/tex]
2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]
3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]
4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]
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To simplify a square root, simply factor the number and extract the roots of any perfect squares found from the radical sign.
What is meant by simplification?To simplify means to make something easier. Simplifying an equation, fraction, or problem in mathematics means taking it and making it simpler. Calculations and problem-solving techniques help to simplify the situation.Simplify a radical expression that use the Product Property.
Find the radicand's largest factor that is a perfect power of the index. Using that factor, rewrite the radicand as a product of two factors.Rewrite the radical as the product of two radicals using the product rule.Simplify the perfect power's root.To convert radicals to simplified forms, we must first simplify them.
A) = [tex]\sqrt{-81}[/tex]
= ([tex]\sqrt{i*9*9}[/tex] )
= 9i
B) = 4[tex]\sqrt{54}[/tex]
= 4[tex]\sqrt{9*6}[/tex]
= 4[tex]\sqrt{3^{2}*6 }[/tex]
= 4*3√6
= 12√6
C) = [tex]\sqrt{-50}[/tex]
= [tex]\sqrt{i^{2}*25*2 }[/tex]
= [tex]\sqrt{i^{2}*5^{2}*2 }[/tex]
= 5i√2
D) = [tex]\sqrt{-252}[/tex]
= [tex]\sqrt{i^{2}*36*7 }[/tex]
= 6i√7
As a result, the correct match is
1) 9i - A) [tex]\sqrt{-81}[/tex]
2) 5i - C) [tex]\sqrt{-50}[/tex]
3) 12 - B) 4[tex]\sqrt{54}[/tex]
4) 6i - D)[tex]\sqrt{-252}[/tex]
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Frank is going to plant n vegetable seeds in one garden and 2n +9 vegetable seeds in another. How many seeds is Frank
going to plant?
The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
What is meant by algebraic expressions?An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.
Like terms with the same variables are added together.
Let the equation be n + 2n + 9
simplifying the above equation, we get
3n + 9
Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
What is meant by algebraic expressions?An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.
Like terms with the same variables are added together.
Let the equation be n + 2n + 9
simplifying the above equation, we get
3n + 9
Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
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y-int coordinates of y=x^2-5x+6, please explain
The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
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
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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