Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.
How do complimentary angles work?Two angles are considered complementary when their sum equals 90 degrees. Two angles are considered submissive when their sum equals 180 degrees. For example, the angles of 40 - 60 degrees complement one another. The difference between a supplementary angle and a supplementing angle is that a Triangle angle has two angles joined to produce a 90 degree angle. When two angles add up to 90 degrees, they are said to be complementary. Alternatively, the complementary angles result in a right angle (90 degrees).
Here,
Given :
Allow x to equal the complementary angle.
Given: x plus 32° the opposite angle
Recognized: Complementary angles sum to 90°
=>x + x + 32° = 90° (Adding the two angles) (Adding the two angles)
2x + 32° = 90° (adding the unknown factors) (adding the unknown variables)
=>2x = 90° - 32° (subtract 32 from both sides) (subtract 32 from both sides)
=> 2x = 58° (assess the right side) (evaluate the right side)
=>x = 29° (split both sides by 2) (divide both sides by 2) (One reply)
=> x + 32° = 61° (Add 32 to x) (Add 32 to x) (The other response)
There are two angles: 29° and 61° QED.
Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.
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The complete question is "The measure of one angle is 32° greater than the measure of its complement. What are the measures of the angles?"
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
Slope = 3/2 , y-intercept = 0
Answer:
y = [tex]\frac{3}{2}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = [tex]\frac{3}{2}[/tex] and y- intercept c = 0 , then
y = [tex]\frac{3}{2}[/tex] x + 0 , that is
y = [tex]\frac{3}{2}[/tex] x
Given the following Venn diagram, where A and B are each represented by an oval:IV LT IIIWhich regions make up ( AExam ImageB )c?a) III and IVb) I, II and IVc) I, II and IIId) II
A and B are each represented by an oval:IV LT III regions make up
the answer is (d) II.
What is Venn diagram ?
A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
The set (A union B) complement is defined as the set of all elements in the universal set that are not in A union B. In set notation, it can be expressed as (A union B)^c = U - (A union B), where U is the universal set and c represents the complement.
In a Venn diagram, the complement of a set is represented by the region outside of the set. In the given Venn diagram, the region outside of A and B is represented by region IV, so (A union B) complement = IV.
Therefore, A and B are each represented by an oval:IV LT III regions make up the answer is (d) II.
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The length of a ide of a triangle i in the extended ratio of 3:5:7. The perimeter of the triangle i 120cm. What are the length of the ide?
The height of the corresponding to the longest side is 25.03 cm
What is triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base. After that, enter the height and base measurements you have into the formula.Given data :
Let the sides of triangles are 3x,5x and 7x.
And perimeter of the triangle is 120cm.
So , 3x + 5x +7x =120
15x = 120
x = 8
so, the sides are triangle are 3(8) = 24cm, 5(8) = 40cm , 7(8) = 56cm
so , the longest side is 56 cm.
Area of triangle = [tex]\sqrt{s(s - a)(s -b)(s-c)}[/tex]
here , s = 64 and a = 24, b = 40c = 56
= [tex]\sqrt{64*(64-24)(64-40)(64-56)}[/tex]
= [tex]\sqrt{64*(40)(24)(8)}[/tex]
=[tex]\sqrt{491520}[/tex]
= 701.08
So, the area of triangle is 701.08 cm 2 and the height corresponding to longest side
h = 2 x 701.08 / 56 = 25.03 cm
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A pancake recipe calls for `8` eggs, but Alisha only has `3` eggs. Adjust the amount needed for each ingredient in the table so that the recipe still tastes the same with only `3` eggs.
Alisha needs to use a fraction of 3/8 of each of the ingredients on the recipe.
How we need to adjust the recipe?We know that a pancake recipe calls for 8 eggs and some other ingredients.
But Alisha only has 3 eggs, so she needs to adjust the recipe.
The fraction of each one of the other ingredients that she needs to use is equal to the fraction between the number of eggs that she has and the number of eggs that the recipe calls, it is:
N = 3/8
So she needs to use 3/8 of each of the ingredients that the recipe calls.
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How do I solve this problem?
Answer:
sup dudes pls what state is this and plus is this logarithms
To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car’s stopping distance (in feet) for each volunteer. The value of r for the scatterplot is 0. 935.
How would the correlation change if the stopping distances were recorded in meters, rather than feet?
A. The value of the correlation coefficient would not change.
B. Since the points would be more spread out, the value of the correlation coefficient would decrease.
C. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase.
D. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease
The value of the correlation coefficient would not change.
The following would be the correlation change if the stopping distances were recorded in meters, rather than feet.
Hence, option (A) is the correct choice.
Correlation is a statistical number derived based on historical data (profitability), and, contrary to popular belief, it is not constant and can change over time.
Correlation is a statistical term that reflects how much two or more variables vary in relation to one another.
The correlation coefficient is evaluated on a scale ranging from + 1 to - 1. The degree of correlation between two variables is denoted by + 1 or -1. When one variable rises as the other rises, the correlation is positive; when one falls as the other rises, the correlation is negative.
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Which value of x is a solution to this equation?
2x2+7x−30
Question 2 options:
2. 5
5
-2. 5
-3
If the equation be 2x² + 7x – 30 then the solution to this equation be 2.5.
What is meant by equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Let the given equation be 2x² + 7x – 30 = 0
Factorizing it as
(2x – 5) (x + 6) = 0
then we get
2x – 5 = 0 or x + 6 = 0
simplifying the equation we get
2x = 5 or x = –6
x = 5/2 or x = –6
x = 2.5 or x = –6
Therefore, the correct answer is option a) 2.5.
The complete question is:
Which value of x is a solution to this equation?
2x² + 7x – 30
a) 2. 5
b) 5
c) -2. 5
d) -3
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if f(x) = 14x2 − x3, what is the rate of change of f '(x) at (1, 13)?
The rate of change of f'(x) at (1, 13) is 25.
We have,
To find the rate of change of the derivative f'(x) at point (1, 13), we first need to find the derivative of the function f(x).
Given: f(x) = 14x² - x³
To find f'(x), we differentiate f(x) with respect to x:
f'(x) = d/dx (14x² - x³)
= 28x - 3x²
Now, to find the rate of change of f'(x) at x = 1,
we substitute x = 1 into the derivative expression f'(x):
f'(1) = 28(1) - 3(1)²
= 28 - 3
= 25
Therefore,
The rate of change of f'(x) at (1, 13) is 25.
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Karia gave each of her 8 friends an equal number of flyers to pass out at the upcoming student government vote. She also gave each of them person 2 bags to carry their flyers. Karia had 200 items to hand out to students including the bags. Write an equation to represent this situation
PLEASE HELP!!! 10 POINTS!!
Answer:
8x + 8 * 2 = 200
Step-by-step explanation:
Let's assume that each friend received x flyers to pass out.
The equation would be:
8x + 8 * 2 = 200
8x = 184
x = 23
So each friend received 23 flyers and 2 bags, and in total, they received 23 * 8 + 8 * 2 = 200 items.
which of the following is not a characteristic of the normal probability distribution? a. the total area under the curve is always equal to 1. b. the mean is equal to the median, which is also equal to the mode. c. the graph of the curve is the shape of a rectangle. d. the random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time.
The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."
The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.
The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.
Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.
In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.
Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.
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The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."
The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.
The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.
Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.
In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.
Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.
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Please calculate in the following in details
Jay is given 65% discount
What is percentage discount?Percentage discount is a discount that is given to a product or service that is given as an amount per hundred
Percentage discount can be gotten with the formula below:
Discount % = (Discount/Original Price) × 100.
From the question,
Jay pays 27300, instead of 42000
Using the percentage discount above
Percentage Discount = 27300/42000 x 100
Percentage Discount = 65%
Hence, jay got 65% discount from the school
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Catori is a landscape photographer. One weekend at her gallery she sells a total of 52 prints for a total of $2,975. How many of each size print did Catori sell?
Answer:
15 prints
Step-by-step explanation:
Let's call the number of small prints sold as "x".
The number of medium prints sold is then (52 - x) prints.
We know that the total revenue from all the prints sold is $2,975, so we can set up the following equation:
$2975 = (x * $50) + ((52 - x) * $75)
Expanding and solving for x:
$2975 = $50x + $3900 - $75x
$2975 = $3900 - $25x
$-925 = -$25x
x = 37
So, Catori sold 37 small prints and (52 - 37) = 15 medium prints
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Which of the following is not an assumption of the general linear model? a. Linearity b. Normally distributed residuals c. Dependence d. Additivity.
Normally distributed residuals is not an assumption of the general linear model and hence option b is correct
Linear regression models relate to some assumptions about the distribution of error terms. If they are violated violently, the model is not suitable for drawing conclusions. Therefore, it is important to consider the suitability of the model for information before further analysis can be performed based on this model.
The fit of the model is related to the remaining behavior complying with the basic assumptions for error values in the model. When a regression model is constructed from a series of data, it should be shown that the model responds to the standard statistical assumptions of the linear model because of conducting inference. Residual analysis is an effective tool to investigate hypotheses. This method is used to test the following statistical assumptions for a simple linear regression model:
-Regression function is linear in parameters,
-Error conditions have constant variance,
-Error conditions are normally distributed,
-Error conditions are independent.
Normally distributed residuals is not an assumption of the general linear model and hence option b is correct
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The Joseph family took out a $175,000, 25-year mortgage at an APR of 4%. The assessed value of their house is $9,000. The annual property tax rate is 97.22% of assessed value. What is the annual property tax?
The annual property tax for the Joseph family is $8749.8.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
The Joseph family took out a $175,000,
25-year mortgage at an APR of 4%.
The assessed value of their house is $9,000.
The annual property tax rate is 97.22% of assessed value.
The annual property tax = 9000 x 97.22/100
The annual property tax = $8749.8
Therefore, the annual property tax = $8749.8
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a, P(A B) ≥ P(A). True/Falseb, If P(A B) = P(A) + P(B), then A and B are mutually exclusive. True/Falsec, If A and B are mutually exclusive events, then P(A | B) = 0. True/Falsed, P(A|B) = P(B|A) for all events A and B. True/False
P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive.
therefore the given condition is not true and hence statement is not true for the given events
Two events are called mutually exclusive they are independent to each other.
Also, If A and B are any two events,
Then they are called mutually exclusive,
If P(A ∪ B ) = P(A) + P(B)
Or P ( A or B ) = P(A) + P(B)
Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27
Since,
0.27 ≠ 0.37 + 0.38
⇒ P ( A or B ) ≠ P(A) + P(B)
Hence, A and B are not mutually exclusive.
therefore the given condition is not true and hence statement is not true
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Area of a circle 12 mm diameter
Answer:
Area of a circle= 1/4*π d^2
A=1/4*π*12^2=
A=1/4*π*144=113.1
Step-by-step explanation:
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In which of the rectangles are the area and the perimeter the same number of units or square units?
In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.
What are the perimeter and area?
The area is the region covered by shape or figure whereas the perimeter is the distance covered by the outer boundary of the shape. The unit of area is given by a square unit or unit2 and the unit of the perimeter is the same as the unit.
(a)
Area of a rectangle = length × breadth
=(8×6)
=48 feet²
Perimeter of the rectangle = 2(length + breadth)
=2(6+8)
=28 feet
(b)
Area of a rectangle = length × breadth
= (4×4) yards²
= 16 yards²
Perimeter of the rectangle = 2(length + breadth)
=2(4+4)
=16 inches
(c)
Area of a rectangle = length × breadth
=(9×4) inches²
= 36 inches²
Perimeter of the rectangle = 2(length + breadth)
=2(9+4)
=26 inches
(d)
Area of a rectangle = length × breadth
=(7×4) meters²
=28 meters²
Perimeter of the rectangle = 2(length + breadth)
=2(7+4)
=22 meters
Hence, In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.
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“Find the total surface area of the rectangular prism”
step by step pls help
The total surface area of the rectangular prism is 103.12 square inches.
What is the total surface area of the rectangular prism?The surface area of the rectangular prism can be calculated using the formula which is given as: 2 * (lw + lh + wh), where:
w = width of the prism
h = its height
l = its length.
Given the following:
Length = 7.1 in
Width = 2.8 in
Height = 3.2 in
Therefore:
Total surface area = 2 * (7.1 * 2.8 + 7.1 * 3.2 + 2.8 * 3.2)
= 2 * (19.88 + 22.72 + 8.96)
= 2 * 51.56 in^2
= 103.12 square inches.
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Drew practices piano at least 45 minutes per day. He has already practiced 18.5 minutes today. Determine how much longer he will have to practice. Then interpret the solution
So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).
Answer:
Step-by-step explanation:
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.
How much was the tip in dollars?
Type your numeric answer only (no spaces/units/etc.). Round to the nearest hundredth.
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.
How much was the tip in dollars?
Answer:
7.77
Step-by-step explanation:
49.77 - 42 = 7.77
Whats the answer to x>2+2x+4?
Answer:=1±√5
Step-by-step explanation:
aight so bassically i looked this shi up and yeah thats what what i got bro
The illustration shows a wheelchair ramp from the side. The support at BC binds the ramp to the floor. Are Triangles ABC and ADE similar?
Triangle ABC is similar to triangle ADE by AA test of similarity
What is similarity in triangle?Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.
here, we have,
There are different types of similarity test by which we can prove the similarity of triangles.
We are given that BC is parallel to Line DE
As the lines are parallel the respective angle are corresponding angles
hence Angle D = Angle B
And Angle E = Angle C
And both triangle have angle A as common angle
By AA test of similarity we can say that the two triangles are similar
Hence by AA test similarity the two triangles are similar
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if x=1y=2, what is the ratio of x4 to y4 ? A.1/16 B.1/2 C.1/1 D. 256/1
The ratio of the given expression is equal to 1:16.
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.
We have x=1 and y=2, and we have to find the ratio of x4:y4,
x=1 and y=2 (given)
[tex]x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16[/tex]
the ratio of the given expression is equal to 1:16.
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1. A 600g packet of biscuits costs $2. 40. Calculate How much would a 200g packet cost?
2. A 200g packet of Orea’s costs $2, Calculate How much would a 100g packet cost?
$0.80 required for a 200g packet cost and $0.01 required for a 100g packet cost
To find the cost of a 200g packet,
you can use the unit price,
which is the cost per gram of the biscuits.
To get the unit price, divide the cost of the 600g packet by its weight: $2.40 / 600g = $0.004/g.
Then multiply the unit price by the weight of the 200g packet to get its cost:
$0.004/g * 200g = $0.80.
To find the cost of a 100g packet of Orea's,
Use the same process as above:
$2 / 200g = $0.01/g.
Then multiply the unit price by the weight of the 100g packet to get its cost:
$0.01/g * 100g = $0.01.
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Calculate the volume of this cylinder. Give your answer to 1 d.p. and remember to give the correct unit
Solution is in the attachment!!
Joshua is skating at a rate of 35 meters every five seconds. Which equation shows Joshua's skating rate in meters per second?
The speed of Joshua's skating rate is given by the equation A = 7 m/s
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The rate of Joshua's skating is given by S = 35 meters / 5 seconds
So , the rate S = 35/5
And , the unit rate of Joshua's skating rate is given by A = 35/5
On simplifying the equation , we get
The unit rate of Joshua's skating rate is given by A = 7 meters per second
The unit rate of Joshua's skating rate is given by A = 7 m/s
Hence , the skating rate of Joshua's skating is 7m/s
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A financial manger ha $14,000 to invet for her company. She plan to invet part of the money in
tax-free bond at 6% interet rate and the reminder in taxable bond at 9%. She want to earn $1005
per year in interet from the invetment. Find the amount he hould invet at each rate
Answer:
she should charge $10 for interest or even more is she wants to make $1005 per year from investing
find r in the qr factorization given a and q
Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.
The QR factorization is the factorization of a matrix A into an orthogonal matrix Q and an upper triangular matrix R. Given matrices A and Q, the matrix R can be calculated as:
R = Q^T * A
Where Q^T is the transpose of Q.
Note that this calculation assumes that Q is an orthogonal matrix, meaning that its transpose is equal to its inverse. If Q is not orthogonal, it will not have an inverse and the QR factorization cannot be calculated in this manner.
Therefore, Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.
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What is the correct way to report the length of the rectangle in centimeters? Select one: a)15.60 cm b)15.6 cm c)15.600 cm d)16 cM
The correct way to report the length of the rectangle in centimeters would be (b)"15.6 cm".
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°).
The general practice is to report measurements to the appropriate number of significant digits. In this case, "15.6 cm" accurately reflects the measurement to the nearest tenth of a centimeter and uses the proper unit symbol (cm). "15.600 cm" and "15.60 cm" include more significant digits than are necessary and "16 cM" uses an incorrect unit symbol.
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A teacher asks three students to complete the following statement about the nature of the roots
of a quadratic equation.
If q
2
– 4pr > 0, the roots of the quadratic equation px2 + qx + r = 0 will be...
Zain answers, "always positive".
Vipul answers, "positive, if p, q, and r are positive".
Suman answers, "negative, if p, q, and r are positive".
Who answered correctly
If q² – 4pr > 0, the roots of the quadratic equation px² + qx + r = 0 will be: "negative, if p, q, and r are positive". Therefore, Suman answered correctly.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
Generally speaking, the standard form of a quadratic function is given by ax² + bx + c = 0.
Assuming the roots of the quadratic function are a and b. Therefore, the sum of the roots of the quadratic function would be equal to -q/p;
a + b = -q/p
ab = r/p
This ultimately implies that, the nature of the roots would depend on the value of p, q and r, which make Zain's answer to be wrong.
Additionally, if p, q, and r are positive, a + b would be negative, and one or both roots must be negative, which make Vipul's to be wrong.
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