Answer:
308 feet ^3
Step-by-step explanation:
Volume of a cylinder: V=πr^2h
Substituting radius = 7 and height = 2:
V = π (7)^2 (2) = 307.88 ~= 308 feet ^3
Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. We also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. Therefore, angle 1 is-congruent-to angle 8 by the substitution property.
We also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the vertically opposite angles Therefore, angle 1 is-congruent-to angle 8 by the substitution property.
How to find angles when parallel lines are cut by a transversal?
When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line e and f are parallel lines cut by the the transversal g.
∠1 ≅ ∠4(vertically opposite angles)
Hence,
∠4 ≅ ∠8(corresponding angles)
Since, ∠1 ≅ ∠4
Then, by substitution,
∠1 ≅ ∠8 (transitive property)
∠5 ≅ ∠8 (vertically opposite angles)
Therefore, ∠1 ≅ ∠8 by the transitive property.
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How do I prove my SSS postulate?
The SSS postulate states that "if all the three sides of a triangle are equal to the sides of another triangle then the given triangles are congruent" is proved.
Assume that the lengths of all three sides of the triangles ABC and DEF are known.
The diagram is attached at the end of the solution.
Pick a side from triangle ABC. Find the side with the same length as triangle DEF. For example, we pick [tex]\overline{AB}[/tex] and find that [tex]\overline{D E}[/tex] is equivalent in length to [tex]\overline{AB}[/tex].
Next, write a proof statement about our conclusion and the reason for it. For the reason clause, we state that the two sides are given, since no other work was involved besides reading the lengths of the sides of the diagram. The three dots in the upside-down triangle means "because".
[tex]$$\overline{AB} \cong \overline{DE}$$[/tex]
Choose the other side from triangle ABC. Find the side with the same length as triangle DEF.
We choose the second side [tex]\overline {BC}[/tex] and find from the diagram that [tex]\overline{EF}[/tex] has the same length. The proof statement for this step is:
[tex]$$\overline{BC} \cong \overline{EF}$$[/tex].
Step 3: Pick the last side from triangle ABC. From triangle DEF, identify the side that is the same length. [tex]\overline{AC}[/tex] and [tex]\overline{DF}[/tex] have the same length. We add another proof statement.
[tex]$$\overline{AC} \cong \overline{DF}$$[/tex]
Step 4: We've discovered that the two triangles have three pairs of congruent sides. That means, by the SSS congruence theorem, triangles ABC and DEF are congruent.
Add a proof statement for this conclusion. The list of the proof statements looks like this.
[tex]$\overline{AB} \cong \overline{DE}[/tex] because [tex]\overline{AB}$[/tex] and [tex]$\overline{DE}$[/tex] are given.
[tex]$\overline{BC} \cong \overline{EF}[/tex] because [tex]$\overline{BC}$[/tex] and [tex]$\overline{EF}$[/tex] are given.
[tex]$\overline{AC} \cong \overline{DF}[/tex] because [tex]$\overline{AC}$[/tex] and [tex]$\overline{DF}$[/tex] are given.
[tex]$\triangle A B C \cong \triangle D E F$[/tex] by SSS congruence theorem.
We have proved that the SSS congruence theorem holds for triangles ABC and DEF.
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If 5 and (5+ square root 5) are two of the
roots of a third degree polynomial with integer coefficients, what is the other root?
Answer:
5 - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
a polynomial of degree 3 has 3 roots
radical roots occur in conjugate pairs.
given 5 + [tex]\sqrt{5}[/tex] is a root then 5 - [tex]\sqrt{5}[/tex] is also a root.
the 3 roots are therefore
x = 5 and x = 5 ± [tex]\sqrt{5}[/tex]
Please help me with 9-14 please
Answer:
9. 33% Increase
10. 14 games
11. $3.6
12. $10.80
13. 630
14. 6.3
The coordinates of triangle ABC are (1,4), (4, 1) and (1,1). Find the new points of A'B'C' with a dilation centered at the origin and a scale factor of 2.
A' (___)
B' (___)
C' (___)
Draw the image on the Coordinate plane.
ryan planted flowers in a rectangular garden. the width of the garden is (x-7) feet and the length of the garden is 3 feet longer than the width. write an expression for the area of the garden.
The rectangle's length and width can be replaced by variables. and can make use of the area. The area of the garden under consideration can be expressed as x^2-11x+28 square feet.
What mathematical expressions can be created using the above description?
Variables can be used to represent the unknowable amounts. Follow the description and mathematically convert each item one by one. For instance, if you are instructed to multiply an item by 4, you can do so by adding 4. You can multiply anything by two, for instance, if it is doubled, and so on to translate a description into a mathematical expression.
How can you describe the size of the garden in words?
Let the garden's length be y feet.
Since the garden's length is one foot longer than its breadth, which is specified as being (x-7) feet, y=3+ (x-7)
y=3+(x-7)
y=x-4 feet
Since the length and breadth of the rectangle under consideration are multiplied to determine the area of the rectangle, the following results are obtained:
A= length * width
A= (x-4)(x-7)
A= x^2-7x-4x+28
A= x^2-11x+28
Consequently, one phrase for the size of the garden under consideration is x^2-11x+28 square feet.
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What are the 3 benefits of SSS?
Two triangles with three congruent sides are referred to as side-side-side (SSS) triangles. The measures are identical, or congruent, which means they are precisely the same. All three sides of SSS triangles will be equal to their corresponding sides in the second triangle, however individual triangle sides are not always equal to one another.
Theorems of Triangle Congruence
One of four triangle congruence theorems, the SSS theorem is unique in that it excludes the need of an angle. The following three are listed:
Two sides and the angle separating them are congruent, or side angle side (SAS).
Angle Side Angle (ASA): Congruence of two angles and the side joining them.
The three angles are all congruent (AAA).
The 3 benefits of SSS theorem are as follow,
To measurement of the area of a triangle.The values for the height and base will be different.To determine if two triangles are congruent even if they are oriented differently.For such more question on SSS.
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Which equation provides the best estimate for 35.78 ÷ 12.31?
30 ÷ 15 = 2
36 ÷ 12 = 3
30 ÷ 10 = 3
40 ÷ 10 = 4
Please help me with this question
step by step explanation
The surface area of the cuboid is given as follows:
147.68 cm².
What is a cuboid?A cuboid is equivalent to a rectangular prism, having dimensions given as follows:
Length l.Width w.Height h.The volume of the cuboid is given by the multiplication of the base area and the height, as follows:
V = Ab x h.
In which:
Ab = l x w.
Considering the base area and the volume of the cuboid, the height is obtained as follows:
120 = 30 x h
h = 120/30
h = 4 cm.
A cuboid has a square base, hence the length = width are obtained as follows:
l² = 30
l = square root of 30
l = w = 5.48 cm
Hence the surface area of the cuboid is obtained as follows:
S = 2(lw + wh + lh)
S = 2(30 + 4 x 5.48 + 4 x 5.48)
S = 147.68 cm².
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You sell small and large candles at a craft fair. You collect $192 selling small candles for $4 a
piece and large candles for $6 a piece. You sold a total of 34 candles in all. Create and solve
a system of equations to find the number of small candles (x) and large candles (y) that were
sold.
How many large candles did you sell at a the craft fair?
The number of small candles (x) and large candles (y) that were
sold 16 large candles and 12 small candles were sold.
How many large candles did you sell at a the craft fair?number of small candles (x)
large candles (y)
4x+6y=144 ....equation 1.
x+y=28 ....equation 2.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph always emerges.To learn more about Linear equations refer to:
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The function f is such that f(x) = x^2 - 8x +5 Where x<=4 express the inverse function f-1 in the form f-1(x)
Answer:
[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, x=-11
Step-by-step explanation:
y = x^2 - 8x + 5, x<=4
x = y^2 - 8y + 5, y<=4 ==> switch the x and y variables to find the inverse
x = y^2 - 8y + 5 ==> solve for y
x + 16 = y^2 - 8y + 16 + 5 ==> add 16 to get a perfect polynomial square
x + 16 = (y - 8/2)^2 + 5 ==> simplify
x + 16 = (y - 4)^2 + 5
x + 16 - 5 = (y - 4)^2 + 5 - 5 ==> isolate y by subtracting 5 on both sides
x + 11 = (y - 4)^2 ==> simplify
[tex]\sqrt{x+11}[/tex] = [tex]\sqrt{(y - 4)^2}[/tex] ==> take the square root of both sides to remove the
square
[tex]\sqrt{x+11}[/tex] = y - 4
y = [tex]\sqrt{x+11}[/tex] + 4 ==> add 4 on both sides to isolate y
[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4 ==> substitute [tex]f^{-1}[/tex](x) for y
[tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, [tex]f^{-1}[/tex](x)<=4 ==> add in the domain restriction
4 = [tex]\sqrt{x+11}[/tex] + 4 ==> plugin the domain restriction for [tex]f^{-1}[/tex](x)
0 = [tex]\sqrt{x+11}[/tex] ==> subtract 4 on both sides
x + 11 = 0 ==> the square root of 0 is 0
x = -11 ==> subtract 11 on both sides
Hence, answer is: [tex]f^{-1}[/tex](x) = [tex]\sqrt{x+11}[/tex] + 4, x=-11
What is number line class 6?
A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered.
A number line is a pictorial representation of numbers on a straight line. It's a reference for comparing and ordering numbers.
A number line is usually represented horizontally and can be extended infinitely in any direction.The first mention of the number line as a tool for adding and subtracting is found in the Treatise on Algebra by John Wallis. In his work, Wallis describes addition and subtraction on it in terms of moving forward and backward, in the context of a person walking.A blank number line is a visual diagram with no numbers or markers and is essentially used as a tool for solving word problems.Steps to add/subtract on a number line:
Locate the first number on the number line. To add: move as many steps as the second number to the right.To subtract: move as many steps as the second number to the right.The number you land on is the answer.Learn more about Number line at:
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What is the opposite of (-16+4)?
Answer: (16 + -4)
Step-by-step explanation:
You have to swap the negative numbers with positives and positive numbers for negative.
calculate the residual for the iron shark, which has a height of 100 feet and a top speed of 52 miles per hour.
The iron shark has a top speed of 2.4 miles per hour faster than the regression line prediction.
ŷ = 0.2143 (100) + 28.17
ŷ = 49.6
Now, we have to subtract y from ŷ
That is,
52 - 49.6 = 2.4
Hence, 2.4 miles per hour
One or more independent (predictor) variables and one or more dependent (criterion) variables are related in regression analysis, a statistical method. A predicted value for the criterion is obtained from the analysis as a result of a linear combination of the predictors. Your independent variable and your dependent variable are related, as seen by the regression line.
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What are 2 congruent triangles?
Answer:
⭐Congruent is another word for "same"
Congruent triangles have the same corresponding side lengths and same corresponding angle measures.
Is there only 1 prime number?
Since, a prime number is whole number higher than one that cannot be divided exactly by any other whole number than itself and one. No, there are many prime numbers.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.
Prime number 2,5,7,13, ......
so there are multiple prime numbers.
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(04.05 MC)
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience Salary
0 $52,000
1 $53,150
2 $54,260
3 $55,285
4 $56,921
5 $57,126
Use the equation for the line of best fit to predict the salary for an employee with 6 years of experience? (Round your answer to the nearest dollar.)
$61,150
$58,587
$59,672
$57,990
The salary of an employee with 6 years of experience, based on the line of best fit, is B. $ 58,587
How to find the salary ?First, find the slope of the line of best fit as:
= ( Y2 - Y1) / ( X2 - X1 )
= ( 57, 126 - 52, 000 ) / ( 5 - 0 )
= 1, 025.2
The y - intercept can be found by substituting the values of y, x, and the slope into the linear function of y = mx + c. The point to be used is (5, 57, 126) :
57, 126 = 1, 025.2 ( 5 ) + c
c = 52, 000
The line of best fit is:
y = 1, 025.2x + 52, 000
If an employee with 6 years experience, their salary would be:
= 1, 025.2x + 52, 000
= 1, 025.2 (6 ) + 52, 000
= $ 58,587
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What is the discriminant of 3x2 5x =- 4?
For the given expression 3x² + 5x = - 4, the value of the discriminant is equal to -23.
As given in the question,
Given expression is written as :
3x² + 5x = - 4
⇒ 3x² + 5x + 4 = 0
General formula of the discriminant for the given quadratic function
ax² + bx + c = 0 is written as :
Discriminant is written as 'D'
D = b² - 4ac
Here b = 5 , a = 3 and c = 4
Substitute the value in the discriminant formula we have,
D = 5² - 4(3)(4)
⇒D = 25 - 48
⇒ D = -23
Therefore , the value of the discriminant for the given quadratic expression 3x² + 5x + 4 = 0 is equal to -23.
The above question is incomplete ,the complete question is :
What is the value of discriminant 3x² + 5x = -4 ?
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Consider the sinusoidal function y=−1/2sin(3πx−5)−2.
What is the midline of the function? Enter your answer as an equation.
What is the amplitude of the function?
What is the period of the function?
What is the phase shift of the function?
5 point per question.
The features of the sinusoidal function are given as follows:
Midline: y = -2.Amplitude: 1/2.Period: 2/3.Phase shift: 5 units.What are the parameters of the sine function?The general definition of the sine function in this problem is given as follows:
y = asin(b(x+c))+d.
The parameters of the general function are explained as follows:
a: amplitude.2π/b: period.c: phase shift.d: vertical shift, representing the midline.The equation in this problem is given as follows:
y=−1/2sin(3πx−5)−2.
From the vertical shift, the midline is given as follows:
y = -2.
The period is calculated as follows:
p = 2π/3π = 2/3.
The phase shift and the amplitude are given, respectively, by:
c = 5 units right(as c = -5).a = 1/2. (the negative just means that the function was reflected over the x-axis).More can be learned about sinusoidal functions at brainly.com/question/28574324
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What is the preimage of 3?
Let x represent the precursor to 3. Preimages of 3 are 13 and 15, respectively. the collection of all domain components that correspond to a certain subset of the codomain;
Mages and pre-images: what are they?
On geometry, new shapes can be produced by shifting, scaling, and other geometrical transformations of figures in a plane. Images are the new (modified) forms, whereas preimages are the old, unchanged ones.
What in geometry is a pre-image?
The pre-image of a figure in a transformation process is that figure's original look.
Let x represent a 3 picture. Preimages of 3 are 13 and 15, respectively.
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!Please help! will give 10 pts!
:)
Answer:
5 1/3 books
Step-by-step explanation:
1 1/3 = 4/3
So, she read
4/3 book = 1/2 day
8/3 book = 1 day
16/3 book = 2 days
16/3 = 5 1/3 books
So, he read 5 1/3 books in two days at this rate
At the football game, 4 hamburgers and 6 soft drinks cost $34, and 4 hamburgers and 2 soft drinks cost $22. Which system of linear equations below can be used to determine the price of a hamburger and the price of a soft drink?
Let x represent the cost of a hamburger and y represent the cost of a soft drink.
Answer:
Soft drink: $3
Burger: $4
Step-by-step explanation:
We have equations
4x + 6y = 34
4x + 2y = 22
Multiply the second equation by -1
4x + 6y = 34
-4x + -2y = -22
4y = 12
y = $3
Now put 3 back in to solve for burger
4x + 6(3) = 34
4x +18 =34
4x = 16
x = $4
asmita went to a blackjack table at the casino. at the table, the dealer has just shuffled a standard deck of 52 cards. asmita has had good luck at blackjack in the past, and she actually got three blackjacks with aces in a row the last time she played. because of this lucky run, asmita thinks that ace is the luckiest card. the dealer deals the first card to her. in a split second, she can see that it is a non-face card, but she is unsure if it is an ace. what is the probability of the card being an ace, given that it is a non-face card? answer choices are in a percentage format, rounded to the nearest whole number. 8% 10% 69% 77%
The probability of the card being an ace, given that it is a non-face card is option A: 8% .
What is the probability about?To find the probability of an event occurring, we can use the formula:
Probability = number of ways the event can occur / total number of outcomes.
In this case, we are trying to see the probability of drawing an ace from a standard deck of 52 cards, given that the card is a non-face card. There are 4 aces in a standard deck of 52 cards, so the number of ways the event (drawing an ace) can occur is 4. There are 52 total cards in the deck, and 48 of them are non-face cards. So, the total number of outcomes is 48.
Therefore, the probability of the card being an ace, given that it is a non-face card, is 4/48.
4/48 = 0.083
When converted to percentage, it is approximately 8.3%.
Therefore, This means that the probability of the card being an ace, given that it is a non-face card, is approximately 8%, which is seen as the closest to the answer choice "8%".
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How do you plot or graph a quadratic inequality in a number line?
A quadratic inequality of the form
y>a[tex]x^{2}[/tex]+bx+c
(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola
A quadratic inequality of the form
y>a[tex]x^{2}[/tex]+bx+c
(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola .
To graph a quadratic inequality, start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality.
If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.
Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary.
Example:
Graph the quadratic inequality.
y≤[tex]x^{2}[/tex]−x−12
The related equation is:
y=[tex]x^{2}[/tex]−x−12
First we notice that a , the coefficient of the [tex]x^{2}[/tex] term, is equal to 1 . Since a is positive, the parabola points upward.
The right side can be factored as:
y=(x+3)(x−4)
So the parabola has x -intercepts at −3 and 4 . The vertex must lie midway between these, so the x -coordinate of the vertex is 0.5 .
Plugging in this x -value, we get:
y=(0.5+3)(0.5−4)
y=(3.5)(−3.5)
y=−12.25
So, the vertex is at (0.5,−12.25) .
We now have enough information to graph the parabola. Remember to graph it with a solid line, since the inequality is "less than or equal to".
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Why is it important to clean your instrument?
Your instrument's pads, finish, springs, and other metal components can all be damaged if you let dirt, moisture, and other debris build up inside of it. It can also corrode strings and other metal components. These faults might cause expensive long-term consequences and are not easily fixed.
Clean the body, head stock, tuners, and fret board using a damp cloth dipped in vinegar, making careful to follow up with a dry towel. Keep in mind that too much moisture ruins wooden instruments. To keep your case odor-free, wait 30 minutes before storing it.
Due to the fact that these solutions often offer the best material compatibility profile and effective filth removal, neutral or detergent solutions with a pH close to neutral are frequently employed for instrument cleaning. Sometimes neutral pH solutions with proteases added to them help remove organic debris.
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How do you find the median of a class?
In a grouped data,
it is not possible to find the median for the given observation by looking at the cumulative frequencies.
The middle value of the given data will be in some class interval. So, it is necessary to find the value inside the class interval that divides the whole distribution into two halves.
In this scenario, we have to find the median class.
To find the median class, we have to find the cumulative frequencies of all the classes and n/2.
After that, locate the class whose cumulative frequency is greater than (nearest to) n/2. The class is called the median class.
After finding the median class, use the below formula to find the median value.
[tex]Median = l +(\frac{\frac{n}{2}- cf}{f} )*h[/tex]
Where
l is the lower limit of the median class
n is the number of observations
f is the frequency of median class
h is the class size
cf is the cumulative frequency of class preceding the median class.
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Express x^2 - 5x + 8 in the form of (x - a)^2 + b where a and b are too heavy fractions
Answer:
To express the quadratic expression x^2 - 5x + 8 in the form of (x - a)^2 + b, we need to complete the square. To do this, we can add and subtract the square of half the coefficient of the x term. In this case, that would be (1/2)(-5) = -5/2. Therefore, we add and subtract (1/2)(-5)^2 = (-5/2)^2 = 25/4 to get:
x^2 - 5x + 8 = (x^2 - 5x + (25/4)) + (8 - (25/4))
Next, we need to add and subtract 25/4 in such a way that we can factor the quadratic expression as the square of a binomial. To do this, we add 25/4 to the first term and subtract 25/4 from the second term to get:
x^2 - 5x + (25/4) + (8 - (25/4)) = (x^2 - 5x + 25/4) + (8 - 25/4)
Now we can factor the quadratic expression as the square of a binomial:
(x^2 - 5x + 25/4) + (8 - 25/4) = (x - 5/2)^2 + (8 - 25/4)
Therefore, we can express x^2 - 5x + 8 in the form of (x - a)^2 + b where a is -5/2 and b is 8 - 25/4.
Note that the values of a and b are not whole numbers because we added and subtracted a fraction when completing the square.
What are the different types of whole numbers?
The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions. It is denoted by the letter "W," and the set of numbers is "0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...." So, the first five whole numbers are 0 through 4, respectively.
what is whole numbers?An integer is either zero, a positive natural number, or a negative integer denoted by a minus sign. The inverse additive of the matching positive integers is represented by the negative numbers. The blackboard bold Z boldface Z is a common way to represent the set of integers in mathematical notation.
Whole numbers refer to the entire set of natural numbers, including "0." Here are some examples: 0, 11, 25, 36, 999, 1200, etc.
The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions.
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Y=10x/3+19 find the x-intercept
The x-intercept is 19.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Where x₁ - x coordinate; y₁ - y coordinate
m - slope
Given the equation as;
Y=10x/3+19
Then;
the slope m = 10/3
The intercept is 19.
Hence, the x intercept is 19.
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How many real roots can a quadratic equation of the form have x2 +5x 6 0?
The real roots of the quadratic equations are
x = -6 and x = 1
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
x² + 5x - 6 = 0 be equation (1)
On simplifying the equation , we get
x² - 1x + 6x - 6 = 0
Taking the common factors in the equation , we get
x ( x - 1 ) + 6 ( x - 1 ) = 0
On factorizing the equation , we get
( x + 6 ) ( x - 1 ) = 0
So , we have two real solutions to the equation ,
( x + 6 ) = 0 and ( x - 1 ) = 0
So ,
when ( x + 6 ) = 0
Subtracting 6 on both sides of the equation , we get
x = -6
And ,
when ( x - 1 ) = 0
Adding 1 on both sides of the equation , we get
x = 1
Therefore , the values of x are -6 and 1
Hence , the real roots of the quadratic equations are -6 and 1
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