Answers
The first graph represents the function y=|x| and the second graph represents the function y=|x|-9.
As you can see they have the same shape.
The x-intercepts of the first and second graphs can be obtained substituting y=0, then:1st graph -
[tex]0=|x|,\\x=0.[/tex]
2nd graph -
[tex]0=|x|-9,\\ |x|=9,\\x=\pm 9.[/tex]
The y-intercept can be obtained substituting x=0, then1st graph -
[tex]y=|0|,\\y=0.[/tex]
2nd graph -
[tex]y=|0|-9,\\y=-9.[/tex]
From the previous statements you can conclude that the graphs have the same shape and the y-intercept of y=|x| is 0, the y-intercept of the second graph is -9.
Answer: correct choice is C.
Related Questions
Point A is located at (4, 8) and point B is located at (14, 10) . What point partitions the directed line segment AB⎯⎯⎯⎯⎯ into a 1:3 ratio? (612, 812) (9, 9) (1112, 912) (6, 6)
Answers
The 1:3 ratio means that the distance from A to the point is 1/4 of the distance from A to B.
The difference of y-coordinates is 10-8 = 2. 1/4 of that is 2·1/4 = 1/2, so the point of interest will have y-coordinate 8 + 1/2 = 8 1/2. This apparently corresponds to the first selection:
... (6 1/2, 8 1/2)
y=f(x)=-3x find f(x) when x is 3
Answers
f(3) = -9 for the function [tex]\( y = f(x) = -3x \) when \( x \) is 3.[/tex]
To find f(x) when ( x ) is 3 for the given function [tex]\( y = f(x) = -3x \),[/tex] you substitute 3 for ( x ) in the function: [tex]\[ f(3) = -3 \times 3 \][/tex]
Now, calculate the value: [tex]\[ f(3) = -9 \][/tex]
Therefore, when ( x ) is 3, f(x) is -9 for the function [tex]\( y = f(x) = -3x \).[/tex]
In more detail, this means that if you plug ( x = 3 ) into the function, it will result in ( y = -9 ). The function ( y = -3x ) represents a linear relationship where the coefficient of ( x ) is -3. This indicates that for each unit increase in ( x ), ( y ) decreases by 3 units. In the specific case of ( x = 3 ), substituting this value into the function gives [tex]\( y = -3 \times 3 = -9 \).[/tex]
This kind of analysis is fundamental in understanding the behavior of linear functions. It provides insight into how the function's output (y) changes in response to changes in the input ( x ). In this case, when ( x ) increases by 1, ( y ) decreases by 3, leading to the slope of -3 in the function ( y = -3x ).
Since it's Wednesday, Buy for Less gives a 5% discount for purchases. The items in Rhonda's cart total $53.75. She needs to know the cost of the items with the discount. So, she multiplies 5% times $53.75 and subtracts the amount from $53.75. Which expression would give Rhonda the same result in one step? A) .90(53.75) B) .95(53.75) C) 1.05(53.75) D) 53.75 - .05(53.75)
Answers
First we need to know how much the discount was so 5% is actually 0.05 then we need to multiply it by 53.75 which would equal 2.6875 then subtract it by 53.75 which would equal -51.0625.
B) .95(53.75)
This is a trick question because D) could also be correct if they said you could subtract it but it's not saying use the distributive property.
The answer would be B) .95(53.75)
there is a photo attached
drop down 1:
161/289 -- incorrect
-161/289 -- CORRECT
64/289
-64/289
drop down 2:
-30/217 -- incorrect
-30/161 -- INCORRECT
-240/217 -- incorrect
-240/161
Answers
Your question answers itself.
You have shown the correct answer for the first drop-down: -161/289
You have shown the 3 incorrect answers out of the 4 choices for the second drop-down. The correct choice is the remaining one: -240/161.
_____
Even if all you know is that tan = sin/cos, you would suspect that answer choice based on the numerator of the cosine: 161. That value is likely the one in the denominator of the tangent value.
_____
cos(2θ) = 2cos(θ)² . . . . trig identity
... = 2(-8/17)² -1 = 128/289 -1 = -161/289
sin(2θ) = √(1-cos(2θ)²) . . . . trig identity
... = √(289² -161²)/289 = √57600/289 = 240/289
tan(2θ) = sin(2θ)/cos(2θ) . . . . trig identity
... = (240/289)/(-161/289) = -240/161
What is the Equivalent ratio of 6:_= 9:12
Answers
[tex]\frac{6}{8}[/tex]
let x be the unknown value in the ratio, hence
[tex]\frac{6}{x}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
9x = 72 ( divide both sides by 9 )
x = 8
thus [tex]\frac{6}{8}[/tex] = [tex]\frac{9}{12}[/tex]
Help me please very confused
Answers
Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.
The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.
The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.
So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).
The appropriate choice and fill-in would be ...
... B. Reflection across the x-axis, translation 4 units left and 1 unit up, dilation with center (0, 0) and scale factor 3.
_____
You can check to see that these transformations also map the other points appropriately. They do.
The princess traces one plant’s roots to discover that it has exactly 5 roots. One of the roots she can trace to 2−3√5. At least two of the roots are the same and labeled −4.
What conclusions can the princess draw about the other two roots?
There may be more than one correct answer. Select all correct answers.
-One of the other roots is 2+ 3√5
-One of the other roots could be another −4.
-One of the other roots could be another 2− 3√5
-One of the other roots is 3+ 2√5
-One of the other roots is 3− 2√5
Answers
complex roots occur in conjugate pairs
given 2 - 3√5 is a root then 2 + 3√5 is also a root
one of the other roots is 2 + 3√5
there are 2 roots of - 4
one of the other roots could be another - 4
Final answer:
The princess can conclude that one of the other roots is 2+ 3√5, one of the other roots could be another −4, and one of the other roots could be another 2− 3√5.
Explanation:
The princess can draw the following conclusions about the other two roots:
One of the other roots is 2+ 3√5.One of the other roots could be another −4.One of the other roots could be another 2− 3√5.These conclusions are based on the fact that the princess has already traced one root to be 2−3√5 and at least two roots are labeled −4.
solve the system by graphing or using a table.
2x+4y=12
x+y=2
Answers
Answer: x = -2 and y = 4
Step-by-step explanation:
We have given a system of equations
2x + 4y =12 ...........(1)
and
x + y = 2 .............(2)
Now to plot them in graph we need to find the points of the above linear equations .
From equation 1 ,we get
[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]
So get the points (0,3) and (6,0).
From equation 2 ,we get
[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]
So we get the points (0,2) and (2,0).
So after plotting these points we get two lines intersecting at (-2,4).
Therefore our solution is x=-2 and y= 4.
Answer:
(-2, 4)
Step-by-step explanation:
What is the slope of your line perpendicular to y=5x-12
Answers
The slope of your line is the x-coefficient: 5.
The slope of a perpendicular line is the negative reciprocal of that: -1/5.
if 3x + 5y = 2 and 2x - 6y = 20 what is 5x - y
Answers
Hey!
We have:
... 3x + 5y = 2
... 2x - 6y = 20
In order to get 5x - y , we will need to add both the equations.
3x+5y=2
2x-6y=20
____________________________________________________
...5x - y = 22
Hence, the required answer is 22.
Hope it helps!
Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].
Given equations are mentioned below:
[tex]3x + 5y = 2\\2x - 6y = 20[/tex]
We need to determine the values of the expression [tex]5x - y[/tex].
For calculating the value of the above expression, first we need the value of the variables x and y.
How to calculate the values of the variables?The solution of linear equation in two variables can be calculated by different methods such as substitution, elimination and graphical methods.Here, in this question we used substitution method to calculate the desired value. Calculations:[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]
Now, substitute the value of the x in another expression and solve it further.
[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]
Now, calculate the value of x.
[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]
Now, calculating the value of [tex]5x - y[/tex].
[tex]5\times4 - (-2)=22[/tex]
Hence, the value of the expression [tex]5x - y[/tex] is 22.
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The bird population on an island is declining at a rate of 2.2% per year. The population was 3500 in the year 2009.
Which answer is the best prediction of the population in the year 2014?
A 2730
B 3062
C 3132
D 3423
Answers
The population is multiplied by 100% -2.2% = 97.8% each year. After 5 years, the population will have been multiplied by this value 5 times, so will be ...
... 3500×0.978⁵ ≈ 3132
The appropriate choice is ...
... C. 3132
Q # 8 please I need your help
Answers
A. -2/3 because you would go down two and then to the right three. I hope that helps.
Solution :
Given ,line that passes through the pair of points (1,7) and (10,1)
The slope of the line passing through the points [tex](x_{1},y_{1} ) \:and \:(x_{2},y_{2})[/tex] is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here, [tex](x_{1},y_{1} ) =(1,7)\:and \:(x_{2},y_{2})=(10,1).[/tex]
[tex]\Rightarrow m=\frac{1-7}{10-1} \\\Rightarrow m=\frac{-6}{9}=\frac{-2}{3}[/tex]
Hence , slope of the line passing through the pir of points (1,7) and (10,1) is [tex] \frac{-2}{3}[/tex] ( first option)
Jillian had
5
6
of a whole and took
3
6
away from it. How much does she have left?
Answers
2/6 is remaining from Jillian's whole.
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Since the denominators of both fractions are common , that is 6
To subtract, subtract the numerators leaving the denominator
[tex]\frac{5}{6}[/tex] - [tex]\frac{3}{6}[/tex] = [tex]\frac{5-3}{6}[/tex] = [tex]\frac{2}{6}[/tex]
This fraction may be simplified by dividing the numerator/ denominator by 2
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] ← in simplest form
ANSWER = BRAINLIEST
Why does a = 8sin40?
Answers
look at the shaded right-angled triangle on the left
8 is the hypotenuse n a is opposite to the 40-degree angle
by definition, sin = opposite side / hypotenuse
so sin40=a/8
rearranging a=8sin40
Two right-angled triangles share a common side with length a.
For the inverted triangle on the left, a is the opposite side to the 40-deg angle.
Its longest side, hypotenuse, is 8cm.
Use the sine function, sin40 = opposite/hypotenuse = a/8
Multiply 8 on both sides, a = 8sin40
Use the three steps to solve the problem.
One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.
Answers
Let x be the bigger number and y be the smaller number.
One number is 11 more than twice another number. Thus,
x = 2y + 11
The sum of the numbers is twice their difference, thus,
x + y = 2(x-y), which simplifies to:
x + y = 2x - 2y
3y = x (Now plug this back to the first equation:
3y = 2y + 11, and solve:
y = 11
Plug in y = 11 to the first equation:
x = 2(11) + 11 = 22 + 11 = 33
Thus the numbers are: x = 33, y = 11.
Consider the following investment. (Round your answers to the nearest cent.)
$3,000 at 6% compounded annually for 15 years
(a) FIND the future value of the given amount.
(b) INTERPRET the future value of the given amount.
After 15 years, the investment is worth $?
Answers
(a) 6% of the value of the investment is added each year. This means the value of the investment is multiplied by 1.06 each year. After 15 multiplications, the value is ...
... $3000×1.06¹⁵ ≈ $7189.67
(b) The interpretation of this result is ...
... After 15 years, the investment is worth $7189.67.
The future value of a $3000 investment at an annual interest rate of 6%, compounded annually for 15 years, is approximately $8093.97. This means that the original sum will grow to this amount after the set period.
Explanation:To find the future value of an investment, we use the formula for compound interest which is A = P(1 + r/n)^(nt). Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount you borrowed or deposited). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per unit t. t is the time the money is invested for in years.Given are P = $3000, r = 6%/100 = 0.06 (annually), n = 1 (since it's compounded annually), and t = 15 years. Plugging these into the formula, we get A = $3000(1 + 0.06/1)^(1*15) = $3000(1.06)^15 = $8093.97.
Interpreting this, it means that investing $3000 at 6% compounded annually would grow to approximately $8093.97 after 15 years.
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please help!!!
The value of " X " is...
2x + y − z = 3
−x + y + 2z = 0
3x + 2y + z = 9
12
2
3
-4
Answers
x = 3
2x + y - z = 3 → (1)
- x + y + 2z = 0 → (2)
3x + 2y + z = 9 → (3)
we require to eliminate the y and z terms from the equations
(1) + (3) : 5x + 3y = 12 → (4)
multiply (1) by 2
4x +2y - 2z = 6 → (5)
(2) + (5) : 3x + 3y = 6 → (6)
(4) - (6) : 2x = 6 ⇒ x = 3
3 and 5 form what type of angle pair? A. corresponding angles B. alternate interior angles C. consecutive interior angles D. alternate exterior angles
Answers
Answer:
C. consecutive interior angles
Step-by-step explanation:
The subject angles are between lines a and b, so are interior (not exterior). They are on different corners of the intersection, so are not corresponding. They are on the same side of line c, so are not alternate. The share a side, but not a vertex, so they are consecutive. The appropriate choice is ...
... C. consecutive interior angles
Answer: C. consecutive interior angles
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used. 10, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29 Number Frequency Relative Frequency 20 ______ ______% 21 ______ ______% 23______ ______% 24 ______ ______% 25 ______ ______% 26______ ______% 27 ______ ______% 28 ______ ______% 29 ______ ______%
Answers
Solution: We have to find the Frequency and Relative frequency of the given data:
Frequency is the number of times a number occurs.
Relative Frequency is the number of times a number occurs divided by the total number of items.
Therefore, the frequency and relative frequency are calculated as below:
Number Frequency Relative Frequency
20 1 [tex]\frac{1}{31} \times 100 =3.2\%[/tex]
21 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
22 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
23 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
24 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
25 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
26 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
27 5 [tex]\frac{5}{31} \times 100 =16.1\%[/tex]
28 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
29 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
Total 31
what is 352 divided by 53 please reply to this within a hour im timed....
Answers
352 divided by 53 is 6.64150943
Hi TaeArmy23,
352 / 53
= 6.6415
= 6.6
Hope This Helps!
y = 12x2 - 9x + 4 how many real solution 10x + y = -x2 + 2 how many real solution(s) 4y - 7 = 5x2 - x + 2 + 3y how many real solution(s) y = (-x + 4)2 how many real solution(s)
Answers
Answer:
(a) 0
(b) 2
(c) 0
(d) 1
Step-by-step explanation:
All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.
For y = ax² +bx +c
the value of the discriminant is
... b² -4ac
When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.
(a) The discriminant is ...
... (-9)² -4(12)(4), a negative number. There are no real solutions.
(b) This needs to be rearranged to ...
... y = -x² -10x +2
Then the discriminant is ...
... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.
(c) This needs to be rearranged to ...
... y = 5x² -x +9 . . . . add 7-3y
Then the discriminant is ...
... (-1)² -4(5)(9), a negative number. There are no real solutions.
(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.
how many times larger is 9 X 10 to the 6 exponent than 3 x 10 to the 4th exponent
Answers
300
divide 9 × [tex]10^{6}[/tex] by 3 × [tex]10^{4}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]10^{6}[/tex] / [tex]10^{4}[/tex]
= 3 × [tex]10^{6-4}[/tex] = 3 × [tex]10^{2}[/tex] = 300
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
Answers
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Lee converted 500 U.S. dollars to 625 Singapore dollars. If x represents U.S. dollars and s represents Singapore dollars, which of these equations represents the relationship between the two currencies?
Answers
Given
Lee converted 500 U.S. dollars to 625 Singapore dollars.
x represents U.S. dollars and s represents Singapore dollars.
Find out equations represents the relationship between the two currencies.
To proof
As given in the question
x represents U.S. dollars and s represents Singapore dollars.
converted 500 U.S. dollars to 625 Singapore dollars
500 x = 625 s
[tex]x = \frac{625}{500} s[/tex]
x = 1.25 s
This shows that the U.S dollars is equal to 1.25 times of singapore dollars.
Hence proved
Find the area of the sector of a circle with diameter 34 feet and an angle of π/5 radians. (Round your answer to four decimal places.)
Answers
The area of the sector of a circle with diameter 34 feet and an angle of π/5 radians is approximately 9.0095 square feet.
Explanation:To find the area of the sector of a circle, we need to use the formula A = πr2θ/360, where A is the area, r is the radius, and θ is the angle in radians. The given diameter is 34 feet, so the radius is 17 feet. The angle is π/5 radians. Plugging these values into the formula, we get A = π(17)2(π/5)/360. Simplifying, we find A = 9.0095 square feet. Rounded to four decimal places, the area of the sector is 9.0095 square feet.
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To find the area of the sector of a circle, you use the formula A = 0.5 * r² * θ where r is the radius (half of the diameter) and θ is the angle in radians. After plugging in the provided values, you calculate the area to four decimal points.
Explanation:The subject is related to finding the area of the sector of a circle. The formula to calculate the area of the sector is A = 0.5 * r² * θ, where r is the radius and θ is the angle in radians. In the given problem, the diameter of the circle is given as 34 feet, so the radius will be 17 feet, and the angle is given as π/5 radians.
Step 1: First, note down the radius from the given diameter, which would be 17 feet, as radius = diameter/2.
Step 2: Plug the value of the radius and the angle into the formula for the area of a sector. The calculation will look like this: A = 0.5 * (17)² * (π/5).
Step 3: Calculate the area by multiplying the values. The final answer will be rounded to four decimal places.
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97 POINTS WILL MARK BRAINLESS
I need help with these i'm so confused could you show me on how you got the answers Thank you so much
Answers
Answer:
2.
x = 15∠1 = 45°1.
x = 5∠A = 85°Step-by-step explanation:
2.Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...
... 135° + (2x+15)° = 180°
... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms
... 2x = 30 . . . . . . . . . . . . subtract 150
... x = 15 . . . . . . . . . . . . . . divide by 2
Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.
1.a) The sum of angles in a triangle is always 180°. This means ...
... (15x +10)° + (15x -10)° + (3x +15)° = 180°
... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms
... 33x = 165 . . . . . . . . . . subtract 15
... x = 5 . . . . . . . . . . . . . . . divide by 33
b) ∠A = (15x+10)° = (15·5 +10)°
... ∠A = 85°
(1)
(a)
the sum of the angles in a triangle = 180°, hence
3x + 15 + 15x - 10 + 15x + 10 = 180
33x + 15 = 180 ( subtract 15 from both sides )
33x = 165 ( divide both sides by 33 )
x = 5
(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°
(2)
2x + 15 + 135 = 180 ( straight angle )
2x + 150 = 180 ( subtract 150 from both sides )
2x = 30 ( divide both sides by 2 )
x = 15 ⇒ 2x + 15 = 45
∠1 = 45° ( alternate angles are congruent )
Please help! 15 Points! How do i do this? (View the picture down below)
Make 6 moves of [tex]\frac{2}{5}[/tex] to find the product.
Plot the product of the expression 6 ⋅ ( [tex]\frac{2}{5}[/tex] ) on the number line.
Answers
Ok, so what this question is really asking you is: [tex]2/5=0.4[/tex]
What is [tex]6*0.4[/tex] and that equals [tex]6*0.4=2.4[/tex]
Now because the the number is 2.4 plot that point
A segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither? Also need a picture of the image and preimage, thanks!
Answers
Answer:
parallel
Step-by-step explanation:
Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.
In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.
What’s is the product of the two solutions of the quadratic equation ax^2+bx+c=0
Answers
The product of the two roots is c/a.
_____
Consider the equation
... a(x -p)(x -q) = 0
which has solutions x=p and x=q.
When multiplied out, it becomes ...
... a(x² -(p+q)x +pq) = ax² -a(p+q)x +apq = 0
When apq = c, the product pq is c/a.
name a plane two different ways