Main five functions of the roots are as follow:
1.Anchorage of the plant
2. Absorption of water
3. Absorption of minerals or food
4. Preventing soil erosion
5. Transportation of food.
Five function of the roots of the plants:
Anchorage : It helps to fix the root part of the plant to the soil and help to grow the aerial shoot system of the plant or tree. Absorption of water : It helps to absorb water through the roots of the plants from the soil . Absorption of Minerals : it helps to absorbs salts and mineral from the soil to the roots of the plants. Preventing Soil Erosion : Root help to prevent the soil by binding the soil to the roots of the plants.Transport : Roots helps to transport salt , water , and mineral from the soil to the shoot part of the plant.Therefore, the five functions of the roots of the plants are
1.Anchorage of the plant
2. Absorption of water
3. Absorption of minerals or food
4. Preventing soil erosion
5. Transportation of food.
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What is 4 called in math?
In mathematics 4 is called a numerical term or a number.
What are numerical terms?A mathematical expression is a combination of two or more terms along with operator or symbols. Here, term defines the numbers and variables. variables are denoted by alphabets. When an expression contains only numbers and symbols then it is called numerical expression.
As example 1024 + 234 is a numerical expression.
What is 4 called in math?4 is a whole number. In a mathematical expression 4 is a numerical term.
A numerical term can be acted as a constant or coefficient depending on the types of expression given.
Suppose we have an expression 2x + 3Y - 4 in where 4 is a number act as a constant term. In the other hand, we imagine an expression
16z- 3y + 4x -10 in where 4 is a number accompanied by variable x so 4 is the coefficient of x.
If we write a linear equation, y = 4X + 5
here, 4 is the slope of equation
Whenever we write a square root of √16
we get 4
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Answer question pls, ixls
14. In the figure (not drawn to scale), MO bisects LMN, mZNMO = (6x + 19), and m
14). Solve for x and find ZLMN.
L
M
A. x= 11, m LMN = 198°
B. x= 11, m ZLMN = 170°
N
C. x=8, m ZLMN = 25°
D. x=8, m ZLMN = 54°
The value of x is 11 and ∠LMN = 190°
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable of the form ax + b = 0 are solved using simple algebraic techniques.
Solution:
Since, MO bisects the angle
we can say that, ∠LMO = ∠OMN
6x + 19 = 9x - 14
3x = 33
x = 11
so, ∠LMO = 66 + 19 = 85°
Therefor the ∠LMN = 190°
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What will be the nature of roots of quadratic equation 5x² 4x 5 0?
The nature of roots of quadratic equation 5x²- 4x +5= 0
are unreal.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Nature of Roots of the Quadratic Equation
The symbols alpha () and beta () are typically used to denote a quadratic equation's roots. Here, we'll learn more about how to identify a quadratic equation's nature without locating the equation's roots. Additionally, look at the formulas for calculating the product and sum of the equation's roots.
Without actually locating the roots (, ) of the equation, the nature of the roots of a quadratic equation can be determined. By using the discriminant value, which is a component of the quadratic equation solution formula, this is made achievable. The discriminant of a quadratic equation is denoted as "D" and has the value b2 - 4ac. Using the discriminatory value as a basis, the nature of the roots of the quadratic equation can be predicted.
Discriminant: D = b2 - 4ac
D > 0, the roots are real and distinct
D = 0, the roots are real and equal.
D < 0, the roots do not exist or the roots are imaginary.
From the given quadratic equation, we can observe that:
a = 5
b = -4
c = 5
On finding discriminant, we get:
D = b² - 4ac
D = (-4)² - (4 × 5 × 5)
D = 16 - 100
D = -84
We can notice that, D(-84) < 0, which means the roots are unreal. Therefore, no roots exist!
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The nature of roots of quadratic equation 5x²- 4x +5= 0
are unreal.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Nature of Roots of the Quadratic Equation
Discriminant: D = b2 - 4ac
D > 0, the roots are real and distinct
D = 0, the roots are real and equal.
D < 0, the roots do not exist or the roots are imaginary.
From the given quadratic equation, we can observe that:
a = 5
b = -4
c = 5
D = b² - 4ac
D = (-4)² - (4 × 5 × 5)
D = 16 - 100
D = -84
We can notice that, D(-84) < 0, which means the roots are unreal. Therefore, no roots exist!
Explain how to find the value of a line's y-intercept using its point-slope equation.
Answer:
Given the point-slope form of a line, y = mx + b, to get the y-intercept of a line, you first have to solve for b by setting x = 0. This gives you the b-value of y = 0 + b = b. We see that b is the y-intercept.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
The point-slope form of a line looks like
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
The number that is the place of the 'm' is the slope.
For example:
If we had the equation
y - 3 = 12(x +4)
The slope would be 12.
Throughout the reflection, make sure you have a copy of the student guide. in your experiment, you tested this prediction:
prediction: rna determines the sequence of amino acids in proteins and polypeptides by a two-step process: transcription of dna produces mrna in the nucleus, then translation of the mrna to trna takes place in the ribosome in the cytoplasm. you transcribed dna to make and built a sequence of amino acids through:____.
The two-step process of how RNA determines the sequence of amino acids in proteins and polypeptides begins with transcription.
During transcription, DNA is copied into messenger RNA (mRNA) in the nucleus. mRNA consists of codons that are read in triplets to code for specific amino acids. The codons are then translated into transfer RNA (tRNA) in the ribosome located in the cytoplasm. tRNA is made up of anticodons, which are complementary to the codons of mRNA. The anticodons of tRNA bind to the codons of mRNA, forming a codon-anticodon pair. This codon-anticodon pair carries the amino acid that corresponds to the codon of mRNA. This carried amino acid is then added to a growing polypeptide chain.
The process is summarized by the following formula: DNA → mRNA → tRNA → Polypeptide. DNA is first transcribed into mRNA. The codons of mRNA are then translated into the anticodons of tRNA, which carry the corresponding amino acid. Finally, the amino acid is added to the polypeptide chain, forming a protein. This two-step process of transcription and translation is how RNA determines the sequence of amino acids in proteins and polypeptides.
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Answer: mRNA, Translation
Step-by-step explanation: trust me bro
What are the first 3 consecutive odd numbers?
The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.
Consecutive numbers are those that always appear in the same order, from smallest to largest.
For instance:
The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.
consecutive odd numbers:
Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."
Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.
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find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48
The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.
In the given question, we have to find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48.
Cut by a plane at x = x(0) = constant, then z= 48-6x-8y while you are moving with y at x=x(0) constant
At this plane (x = x(0)), an element of area will be dA = z dy and an element of volume dV = dA dx
So , V = [tex]\int\int zdydx[/tex]
v = [tex]\int_{0}^{8}\int_{0}^{(48-6x)/8}(48-6x-8y)dy.dx[/tex]
v = [tex]\int_{0}^{8}[48y-6xy-4y^2]_{0}^{(48-6x)/8}dx[/tex]
v = [tex]\int_{0}^{8}[48\times((48-6x)/8)-6x\times((48-6x)/8)-4((48-6x)/8)^2-0]dx[/tex]
v = [tex]\int_{0}^{8}[9/4(x-8)^2]dx[/tex]
Let u = x-8
v = [tex]9/4\int_{0}^{8}(u)^2[/tex]
v = [tex]9/4\left[\frac{(u)^3}{3}\right]^{8}_{0}[/tex]
v = [tex]3/4[(x-8)^2]_{0}^{8}[/tex]
v = 3/4[(8-8)^3+(0-8)^3]
v = 3/4[0-(-512)]
v = 384
The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.
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f(x) = x² + 6x + 7; Find f(0)
Answer: f(0) = 7
Step-by-step explanation:
f(x) = x² + 6x + 7
f(0), we just need to put 0 in for all the x
f(0) = 0^2 + 6(0) +7
f(0) = 0 + 0 + 7
f(0) = 7
Is there a mode formula?
There is a mode formula, that is Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] * h
Where,
l = lower limit of the modal class
h = size of the class interval
f₁ = frequency of the modal class
f₀ = frequency of the class preceding the modal class
f₂ = frequency of the class succeeding the modal class
What is mode?The value that consistently appears in a given set is the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.
A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is this one.
To find the mode we use the formula Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] * h
Where,
l = lower limit of the modal class
h = size of the class interval
f₁ = frequency of the modal class
f₀ = frequency of the class preceding the modal class
f₂ = frequency of the class succeeding the modal class
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Solve the systems of equations graphed on the coordinate axes below. y=-4x-1 y=2x-1
jason was riding his bicycle, making deliveries on his newspaper route. He had no less than 12 newspapers left to deliver. Which number line represents this scenario?
number line with closed circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the right
number line with closed circle at point 12, shaded to the right
Answer:
number line with a closed circle at point 12, shaded to the left
Step-by-step explanation:
Because it say he had no less than 12 newspapapers
Which mean he had smaller than or equal to 12 nnewspapapers
Because there is equal, so it will be a close circle, and shaded to the left because it is less than !
#8: Donovan publishes a magazine of short stories. He keeps
track of the number of copies (y) of the magazine he has sold
after each of the first x days. After 1 day,
Donovan had sold 20 copies of his magazine. After 2 days, he
had sold 32 copies of his magazine. He connects these two
points with a straight line to estimate his
future sales. What is the equation of the line Donovan drew?
A.Y-20= 12(x - 2)
B.Y-32= 12(x - 20)
C.Y-2012(x - 1)
D.Y-2 = 12(x - 1)
The equation of the line would be y - 20 = 12(x - 1).
Option (C) is correct.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
Let's suppose on the y-axis there will be a number of copies sold and on the x-axis, there will be a number of days.
On day 1, he sold 20 copies so point would be (1, 20)
On day 2, he sold 32 copies so point would be (2, 32)
Slope of the line = (y2 - y1)/(x2 - x1)
= (32 - 20)/(2 - 1)
m = 12
By using the slope-point form of the line,
y - y1 = m(x - x1)
y - 20 = 12(x - 1)
Hence, the equation of the line would be y - 20 = 12(x - 1).
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Write the equation of the line represented by y=−2/3x+4 in standard form.
The equation y = (-2/3)x + 4 in standard form is 2x + 3y = 12.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = (-2/3)x + 4
The equation of a line in standard form is ax + by = c
Now,
y = (-2/3)x + 4
3y = -2x + 12
Adding 2x on both sides.
2x + 3y = 12
Thus,
The equation in standard form is 2x + 3y = 12.
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Is the 3x 1 conjecture?
The gradient of 3x+ 1 is conjecture states that this function can be iterated over and over until it yields the number 1, starting from any positive integer n.
Describe conjecture.A conjecture turns into a theorem when it is rigorously proven. A conjecture is not merely a tool for professional mathematicians; it is an essential step in problem-solving. It is extremely uncommon for a problem's solution to be immediately obvious while tackling problems on a daily basis. Instead, establishing a conjecture about the answer and then proving it through evidence are steps in the problem-solving process that include reviewing cases and the problem's structure. When one observes a pattern that holds true in numerous instances, hypotheses start to form. A pattern may be true in many instances, but that does not guarantee that it will be true in all instances. For a mathematical observation to be fully accepted, conjectures must be proven.
Given
The 3x + 1
Conjecture states that this function can be iterated over and over until it yields the number 1, starting from any positive integer n.
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What will be the location of point ′ F ′ if the triangle wa dilated by a cale factor of 3
If the coordinates of point F are (x,y), then the coordinates of point F' after the dilation will be (3x, 3y).
To find the location of point F' after the triangle is dilated by a scale factor of 3, you need to multiply the coordinates of point F by the scale factor.
For example, if the coordinates of point F are (x,y), then the coordinates of point F' after the dilation will be (3x, 3y).
It's important to note that the dilation will change the size of the triangle, but not its shape. The angles of the triangle will remain the same, and the ratios of the side lengths will also remain the same.
If you have a specific triangle and the coordinates of point F, I can provide more detailed guidance on finding the coordinates of point F' after the dilation.
∴ If the coordinates of point F are (x,y), then the coordinates of point F' after the dilation will be (3x, 3y).
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approximately 12,000 years ago, people began to domesticate grain in what we now call the middle east. this involved a process that slowly spread around the world over the next 6,000 to 7,000 years. in 1984, 8 percent of u.s. households had a computer, but that number was above 70 percent in 2008. how do these two things relate to social change?
From the examples given in the question, we can say that Both are illustrations of social change that is taking place at various rates.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given data,
Approximately 12,000 years ago, people began to domesticate grain in what we now call the Middle East. And it spread around the world over 6,000 to 7,000 years.
In this, it is taking a lot of time, which means that the rate is slower.
But on the other hand,
In 1984, 8 percent of u.s. households had a computer, but that number was above 70 percent in 2008.
But in this case, in around 24 years there are 70% of households have computers, which means that the rate is higher.
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How do you use slope to determine if a line is parallel or perpendicular and solve problems?
Lines that have the same slope are said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are merely intersecting lines.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A construction company can remove 1/2 metric tons of dirt from a construction site in 1/4 hours. What is the unit rate in metric tons per hour?
Answer: 2 metric tons per hour
Step-by-step explanation:
We know that to get from 1/4 hour to 1 hour we have time 4
So we take 1/2 times 4 = 4/2 = 2 metric tons per hour!
What is the example of Triangle Inequality theorem 2?
The example of Triangle inequality theorem 2 is 4 + 8 = 12, which is less than 15 in total. Triangle Inequality Theorem is not satisfied by this set of side lengths.
What is meant by triangle inequality ?According to the triangle inequality, the lengths of any two sides of any triangle must add up to at least the length of the third side. Triangle inequality, often known as a + b c, is a theorem in Euclidean geometry that states that the sum of any two triangle sides must be greater than or equal to the third side. The basic tenet of the theorem is that a straight line connects any two places. That is what the Triangle Inequality Theorem says.To learn more about triangle inequality refer to:
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man runs for an hour and a half at 8 miles an hour due south. he then continues south on a bus traveling at 55 miles an hour for 24 minutes. how far d
A man runs for an hour and a half at 8 miles an hour due south. he then continues south on a bus traveling at 55 miles an hour for 24 minutes. He will traveled 34 miles.
He covered 8 miles the first hour, and then half of that in his next half hour,
So, 8+4 = 12 miles.
The bus took 24 minutes, which is [tex]\frac{2}{5}[/tex] of an hour.
[tex]\frac{60}{5} = 12[/tex]
So, after 12 minutes on the bus, he travelled [tex]\frac{55}{5} = 11[/tex] miles
And after 24 minutes, 22 miles.
In total 12+22=34 miles.
Speed(v) is related to distance(d) and time(t) by
v= [tex]\frac{d}{t}[/tex].
Equivalently, d= v×t
So, d= 8×1.5+55×24×[tex]\frac{1}{60}[/tex]
= 34 miles.
Therefore, he traveled 34 miles.
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What is the value of the discriminant in the quadratic equation 2x² 5x 3 0?
The value of the discriminant in the quadratic equation 2x² 5x + 3 = 0 is 1.
The discriminant of a quadratic equation is the expression under the square root sign in the quadratic formula. It is used to determine the number and type of solutions for the equation. In the case of the equation 2x² 5x + 3 = 0, the discriminant can be found by using the quadratic formula and substituting the values for a, b, and c. The formula is given by b² - 4ac, where a = 2, b = 5 and c = 3. So the discriminant is then 5² - 4(2)(3), which is equal to 1. This means that the equation has a single real solution, which is -1.
Discriminant = b² - 4ac
= 5² - 4(2)(3)
= 1
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Which factor mut a producer conider when deciding what good to upply? check all that apply
Factors that are needed to be considered by producer when deciding on the kind of good to supply are :
1) The supply of a good's flexibility.
2)There is rivalry in the market.
3)The capacity to efficiently generate the good
What is the importance of supply of goods in market?
Supply is crucial because it ensures that there is sufficient production of the items needed to keep up with consumer demand. Typically, the price of that commodity will rise if supply is less than demand. This supply schedule, or curve, establishes the quantity of an item that is produced at a given price.
Applies to be checked are:
1) A producer must first conduct market research by taking into account a number of Factor before he can supply a good.
2) One of the most important factors to take into account is competition because when there is a lot of it, sales may not be as high.
3) Reliable production How are you going to stand out if the goods, given that there are so many competitors?
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Supply is crucial because it ensures that there is sufficient production of the items needed to keep up with consumer demand. Typically, the price of that commodity will rise if supply is less than demand. This supply schedule, or curve, establishes the quantity of an item that is produced at a given price.
Applies to be checked are:
A producer must first conduct market research by taking into account a number of Factor before he can supply a good.
One of the most important factors to take into account is competition because when there is a lot of it, sales may not be as high.
Reliable production How are you going to stand out if the goods, given that there are so many competitors?
Enter the equation of the following using line in slope-intercept form.
slope = 0; y-intercept is 4
Answer:
y=4
Step-by-step explanation:
slope doesn't exist
so y=0x+4 >>>>> y=4
maddy had a piece of ribbon that was 3 1/2 yards long each bow was made from a piece of the ribbon that was 3/4 yard long how many bows can Maddy make
Step-by-step explanation:
this is answered by "how often does 3/4 fit into 3 1/2 ?".
and that is what division is for :
3 1/2 / 3/4
(3×2 + 1)/2 / 3/4
7/2 / 3/4 = (7×4)/(2×3) = 28/6 = 14/3 = 4 2/3
Maddy can make 4 bows.
and she has some tape left, but not enough to make a 5th.
the average daily rainfall for the past week in the town of hope cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. if the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall?
The percentage of data that falls between 1.9 inches and 2.3 inches of rainfall is roughly (D) 68% if the distribution is normal.
What is the percentage?In essence, percentages are fractions with 100 as the denominator.
We place the percent symbol (%) next to the number to indicate that the number is a percentage.
For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
So, we determine each's z-score:
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
Then, the percentage we want to determine is:
P(-1<x<1)
For this, we utilize the normal scoring table:
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269
= 68%
Therefore, the percentage of data that falls between 1.9 inches and 2.3 inches of rainfall is roughly (D) 68% if the distribution is normal.
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Complete question:
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Which system is equivalent to startlayout enlarged left-brace 1st row y = negative 2 x squared 2nd row y = x minus 2 endlayout?.
The required inverse of the given function is expressed as [tex]y=\sqrt{\frac{x+10}{7} }[/tex]
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
Replacing y with x
x = 7y² – 10
Making y the subject of the formula:
7y² = x+ 10
Dividing both sides by 7
7y²/7 = (x+10)/ 7
y² = (x+10)/ 7
Taking the square root of both sides
[tex]\sqrt{y^{2} } =\sqrt{\frac{x+10}{7} }[/tex]
[tex]y=\sqrt{\frac{x+10}{7} }[/tex]
Hence the required inverse of the given function is expressed as [tex]y=\sqrt{\frac{x+10}{7} }[/tex]
Complete question:
Which equation is the inverse of y = 7x² – 10
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suppose that for a certain coastal city, in any given year the probability of a major hurricane hitting is 0.5, the probability of flooding is 0.3, and the probability of both a major hurricane and flooding is 0.2. what is the probability of flooding given that a major hurricane hits?
Using the concept of conditional probability and using the values provided, The answer is 0.4.
What do you mean by probability?Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes.
What do you mean by 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 of the subsequent, or conditional, occurrence to determine the conditional probability.
p(h)=0.5
p(f)=0.3
p(h ∩ f) = 0.2
p(f/h) = p(h ∩ f) / p(h)
=0.2/0.5
=0.4
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What does it mean when you regroup?
Solve by completing the square : x^2+4x-7=0 and 2x^2+8x-1=0
By completing the squares we will see that the solutions are:
a) For 2x^2 + 8x - 1 = 0:
x = -2 ±√4.5
b) For x^2+4x-7 = 0
x = ±√11 - 2
How to complete squares?Remember that the perfect square trinomial is:
(a + b)^2 = a^2 + 2ab + b^2
The first quadratic equation is:
2x^2 + 8x - 1 = 0
Dividing by 2 we get:
x^2 + 4x - 1/2 = 0
We can rewrite this as:
x^2 + 2*2*x - 1/2 = 0
Adding and subtracting 2^2 = 4, we get:
x^2 + 2*2*x + 4 - 4 - 1/2 = 0
(x + 2)^2 - 4 - 1/2 = 0
(x + 2)^2 = 4.5
Now we can solve this:
x + 2 = ±√4.5
x = -2 ±√4.5
These are the two solutions.
The other quadratic equation is:
x^2+4x-7 = 0
We can rewrite this as:
x^2 + 2*2*x - 7 = 0
Again, add and subtract 4 to get:
x^2 + 2*2*x + 4 - 4 - 7 = 0
(x + 2)^2 = 11
Solving this we get:
x = ±√11 - 2
Learn more about quadratic equations:
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