Triangle ABC is defined in the coordinate plane by the points A(1, 2), B(4, 3), and C(4, 0).
Under which transformations will the image of triangle ABC be similar to the preimage?
select all that apply
Answers
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
According to the figure AB=1. AC=4
A'B' = 3, A'C' = 12
FAB'=3AB [A'C' = BAC
So, the scale factor is 3
Dilation is a method for producing comparable numbers. By increasing distances by the scale factor, each point is extended outwards from the center point D. (If the scale factor is more than one, go outwards.)
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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
A. [tex]$T(x, y) \rightarrow(-x, -y)$[/tex]
This is a reflection to the origin that does not preserve angles or aspect proportions. Therefore, triangle ABC under this transformation does not resemble that image.
Example: [tex]$T(x, y) \rightarrow(x, x-y+1)$[/tex]
This is a shear transformation that does not preserve angles or aspect ratio. Therefore, triangle ABC under this transformation does not resemble that image.
C. [tex]$T(x, y) \rightarrow(x+3, y)$[/tex]
This is a translation that preserves angles and aspect ratio. So the triangle ABC under this transformation resembles that image.
D. [tex]$T(x, y) \rightarrow(0.2x, 4y)$[/tex]
This stretches by a factor of 0.2 in the x direction and 4 in the y direction, preserving angle and horizontal proportions. So the triangle ABC under this transformation resembles that image.
E. [tex]$T(x, y) \rightarrow(2x, 2y)$[/tex]
This is a stretch by a factor of 2 in both the x and y directions, preserving the proportions of the angles and sides. So the triangle ABC under this transformation resembles that image.
F. [tex]$T(x, y) \rightarrow(3x, 4y)$[/tex]
This stretches by a factor of 3 in the x direction and 4 times in the y direction, preserving the proportions of angles and sides. So the triangle ABC under this transformation resembles that image.
Therefore, the similarity-preserving transformations between triangle ABC and its image are C, D, E, and F.
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Related Questions
Let A, B, and C be three events in a random experiment
with sample space S. Write expressions for each of the following sets in terms of the set operations "union," "intersection",
"complement," and "difference":
• (a) only A occurs: A − B − C
• (b) A and B occur but C does not occur: (A ∪ B) − C
• (c) exactly one of the events occurs: (A − B − C) ∪ (B − A −C) ∪ (C − A − B)
• (d) at least one of the events occurs: A ∪ B ∪ C
• (e) at most one of the events occurs: S − (A ∩ B) − (A ∩ C) −(A ∩ B)
• (f) exactly two of the events occur: (A ∩ B − C) ∪ (A ∩ C −B) ∪ (B ∩ C − A)
• (g) at least two of the events occur: (A∩B)∪(A∩C)∪(B∩C)
• (h) at most two of the events occur: S − (A ∩ B ∩ C)
• (i) all three events occur: A ∩ B ∩ C
• (j) none of the events occur: S − A − B − C
Answers
(a) only A occurs: A − B − C
(b) A and B occur but C does not occur: (A ∪ B) − C
(c) exactly one of the events occurs: (A − B − C) ∪ (B − A −C) ∪ (C − A − B)
(d) at least one of the events occurs: A ∪ B ∪ C
(e) at most one of the events occurs: S − (A ∩ B) − (A ∩ C) − (B ∩ C)
(f) exactly two of the events occur: (A ∩ B − C) ∪ (A ∩ C − B) ∪ (B ∩ C − A)
(g) at least two of the events occur: (A∩B)∪(A∩C)∪(B∩C)
(h) at most two of the events occur: S − (A ∩ B ∩ C)
(i) all three events occur: A ∩ B ∩ C
(j) none of the events occur: S − A − B − C
(a) If only event A occurs, then the event A is said to be the difference of the universal set (S) and the events B and C (S − B − C).
(b) If events A and B occur but event C does not occur, then the union of events A and B (A ∪ B) is the difference of the universal set (S) and the event C (S − C).
(c) If exactly one of the events occurs, then it can be represented as the union of the differences of the universal set (S) and the other two events for each of the three events (A − B − C) ∪ (B − A −C) ∪ (C − A − B).
(d) If at least one of the events occurs, then it can be represented as the union of all three events (A ∪ B ∪ C).
(e) If at most one of the events occurs, then it can be represented as the difference of the universal set (S) and the intersection of any two events (S − (A ∩ B) − (A ∩ C) − (B ∩ C)).
(f) If exactly two of the events occur, then it can be represented as the union of the intersections of two events and the difference of the third event (A ∩ B − C) ∪ (A ∩ C − B) ∪ (B ∩ C − A).
(g) If at least two of the events occur, then it can be represented as the union of the intersections of any two events (A∩B)∪(A∩C)∪(B∩C).
(h) If at most two of the events occur, then it can be represented as the difference of the universal set (S) and the intersection of all three events (S − (A ∩ B ∩ C)).
(i) If all three events occur, then it can be represented as the intersection of all three events (A ∩ B ∩ C).
(j) If none of the events occur, then it can be represented as the difference of the universal set (S) and all three events (S − A − B − C).
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Felix's dinner costs $16.49. Felix pays a $20 bill. ABOUT how much change did he receive? Show your work.
Answers
Answer: $3.50
Step-by-step explanation:
20.00 - 16.49 = 3.51
3.51 rounded to the nearest 10 is 3.50
Answer: 3.50
Please help me with this question.
Answers
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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EASY POINTS!
A small business takes out an $18,800 loan from a bank. How much will the small business need to repay one year later if the interest is 4.4%?
$32,720
$19,627.20
$42,727
$827.20
Answers
Answer:
$827.20
Step-by-step explanation:
0.044 x 18800 = 827.20
Please help me with this question.
Answers
The values that make vector b a linear combination of vectors A1, A2 and A3 are given as follows:
[tex]\alpha_1 = -1.9, \alpha_2 = 1.1, \alpha_3 = 1.5[/tex]
What is a linear combintion?A vector is a linear combination of other vectors when it can be obtained via a system of equations from the other vectors.
Considering the matrices, the system of equations to obtain the values of the variables that make vector b a linear combination of vectors A1, A2 and A3 are given as follows:
x - y = -3.2x + 3y + z = 1.x + 4y - z = 1.Adding the second and the third equation, we have that:
3x + 7y = 2.
Since x = y - 3, the value of y is obtained as follows:
3(y - 3) + 7y = 2
3y - 9 + 7y = 2
10y = 11
y = 1.1.
Then the value of x is of:
3x = 2 - 7(1.1)
x = [2 - 7(1.1)]/3
x = -1.9.
The value of z is obtained as follows:
z = 1 - 2x - 3y
z = 1 - 2(-1.9) - 3(1.1)
z = 1.5.
In the desired notation, these values are given as follows:
[tex]\alpha_1 = -1.9, \alpha_2 = 1.1, \alpha_3 = 1.5[/tex]
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Describe the x-values at which the function is differentiable. (Enter you answer using interval notation.)
f(x) = (x+2)^2/3
Answers
(-∞,∞)
Select the correct answer. In the notation "s(x) = ...," what does "s(x)" represent? A. There is not enough information to answer this question. B. The value of s(x) depends on the value of x, since s is a function of x. C. The value of x depends on the value of s(x), since x is a function of s. D. The value found when s is multiplied by the value x.
Answers
The value of s(x) depends on the value of x since s is a function of x.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here,
We know that for any function f(x) ; x represents the independent variable i.e. the variable whose value is defined and y=f(x) denotes the dependent variable i.e. the variable whose value is defined corresponding to the independent variable.
i.e. it depends on the variable x.
Similarly here s(x) is the dependent variable since it is defined corresponding to the variable x.
Hence, The value of s(x) depends on the value of x, since s is a function of x.
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Find the point-slope form of the equation of the line satisfying the conditions below and use this to write the slope-intercept form of the equation:
Slope = 3/4, passing through (0, 4)
Select one:
a.
y = 3/4x - 4
b.
y = 3/4x + 4
c.
y = -3/4x - 4
d.
-4/3x - 16/3
Answers
Answer:
b
Step-by-step explanation:
Point (0,4) slope (3/4) form would be
y-4 = 3/4 ( x-0) re-arrange to y = mx + b form
y = 3/4x + 4
PLEASE LIST A,B,C,D,E,F
Answers
Answer:
G H I J K L M N O P Q R S T U V W X Y Z
Step-by-step explanation:
Part of a roller coaster path/height can be modeled when the roller coaster ride starts at t=0 and 45 feet above the ground. The roller coaster enters an underground tunnel after 30 seconds, and then emerges from underground at 50 seconds.
a.) draw a sketch of the roller coaster.
b.) using the graph, what are the zeros of the polynomial?
c.) using the zeros and y-intercept to write the general function of the roller coaster. (Remember can’t assume a=1)
Answers
a) The graph of the quadratic function that models this situation is given by the image presented at the end of the answer.
b) The zeros are given as follows: x = 30 and x = 50.
c) The function is defined as follows: y = 0.03x² - 2.4x + 45.
How to define the quadratic function?The quadratic function with roots x* and x** is given by the equation presented as follows:
y = a(x - x*)(x - x**)
The roots = zeros are the values of x for which the graph of the function crosses the x-axis, hence:
x* = 30, x* = 50.
Then the function is:
y = a(x - 30)(x - 50)
y = a(x² - 80x + 1500).
When x = 0, y = 45, hence the leading coefficient a is obtained as follows:
1500a = 45
a = 45/1500
a = 0.03.
Hence the definition of the function is given as follows:
y = 0.03(x² - 80x + 1500).
y = 0.03x² - 2.4x + 45.
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Jillian is using integer tiles to add 7+(-2). She uses the steps below.
ᎧᎧᎧᎧᎧ
Step 1
Step 2
Step 3
Step 4
7+(-2)=2
+
Answers
This process that Jillian used is called the Countermatching algorithm which is a method of adding and subtracting integers.
The Countermatching algorithm
Step 1: Jillian puts a 7 tile on the table. Step 2: She then puts a negative two tile next to the 7 tile. Step 3: Jillian then counts the total amount of tiles on the table, which is 5.Step 4: She then concludes that 7+(-2)=2. In this algorithm, each number is represented by a corresponding amount of tiles.The two integers are placed side by side and then the total amount of tiles is counted.This number is the sum of the two integers. In this example, there were five tiles in total, so the sum was two.Jillian arranges two sets of integer tiles, one with a value of 7 and one with a value of -2. She then combines the two sets of integer tiles, putting the 7 together with the -2. Jillian then counts the total number of tiles, which is 5. She then reads the result of the addition, which is 2. This process of solving an addition problem using integer tiles is called a model method. This method helps students visualize the operations they are performing, allowing them to better understand the mathematics.It is especially useful for students who may have difficulty conceptualizing math operations and helps them to more easily find the solution to the problem. In addition, the model method can also be used to solve subtraction, multiplication, and division problems.To learn more about the Countermatching algorithm refer to:
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HELP SOS MATHHH MATHH
Answers
Answer:
(2s,0)
Step-by-step explanation:
since there are no numbers at point M to help find point L answer should be (2s,0)
Answer:
(2s,0)
Step-by-step explanation:
because it's isosecle triangle so do a line from M to x axis, it should be the mid point of L. so L =2s
L is on x-axis, so y=0
A camera has a listed price of $704.95 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer:
$773.55
Step-by-step explanation:
To find the total cost of the camera with the sales tax included, you need to calculate the amount of sales tax and add it to the listed price of the camera.
The sales tax rate is given as 9.75%. To convert this to a decimal, divide the percentage by 100: 9.75/100 = 0.0975
To find the amount of sales tax, multiply the listed price of the camera by the sales tax rate as a decimal: $704.95 x 0.0975 = $68.60
To find the total cost of the camera, add the amount of sales tax to the listed price: $704.95 + $68.60 = $773.55
So the total cost of the camera with the sales tax included is $773.55
Please Help!!! Cannot figure out how to answer this.
Answers
Answer:
10
Step-by-step explanation:
Given the limits of the functions f(x) and g(x) as x approaches -2, you want the limit of their product at that point.
LimitsThe limit of a product is the product of the limits:
[tex]\displaystyle \lim_{x\to -2}(f(x)\cdot g(x))=(\lim_{x\to -2}f(x))\cdot(\lim_{x\to-2}g(x))=5\cdot2=\boxed{10}[/tex]
(a+8)/5 + (a-8)/7 = 4
Answers
The value of a is 31/3 in the equation (a+8)/5 + (a-8)/7 = 4.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is (a+8)/5 + (a-8)/7 = 4
Multiply with the LCM
7(a+8)+5(a-8)=140
Apply distributive property
7a+56+5a-40=140
Add the like terms
12a+16=140
12a=124
Divide both sides by 12
a=124/12
a=31/3
Hence, the value of a is 31/3 in the equation (a+8)/5 + (a-8)/7 = 4.
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HELP PLEASE I WILL GIVE BRAINLIEST
If algebra tiles have the dimensions shown here, what would you call this tile collection?
In other words, what is the total area of all of the pieces?
Write the expression algebraically, using `x,\ x^{2},\ y,\ y^{2}` and `xy`.
Answers
Answer:
Below
Step-by-step explanation:
Add all of the areas area = L x W
x * 1 + xy +y*1 + y*y + x * x =
x + xy + y + y^2 + x^2 =
x^2 + y^2 + xy + x + y
Write the following set as an interval using interval notation {x|-9∠x≤2}
Answers
Answer:
(-9, 2]
Step-by-step explanation:
"( )" means that the number does not include (> or <)
"[ ]" means that the number includes ( ≥ or ≤)
Which expressions are equivalent to
3
(
−
2
�
−
4
)
+
3
�
3(−2a−4)+3a3, left parenthesis, minus, 2, a, minus, 4, right parenthesis, plus, 3, a
Answers
The answer is (A) because -6a -12 +3a is the expression that equals 3 (-2a-4) +3a.
What are Expressions?A group of numbers or variables coupled with the operations +, -,/, or form an expression.
Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.
So, we have the expression:
3 ( -2a-4) +3a
There is just one variable in this expression: a.
The bracket will be opened using the distributive property.
The Distributive property states that multiplying a number by the sum of two other numbers will have the same outcome as multiplying the number by each addend separately.
3 * (-2a) + (3 * ( -4)) +3a
When addressing the brackets:
-6a -12 +3a
Putting like phrases together:
Similar phrases are grouped together using the Associative feature.
The associative property states that even if the order of the numbers is changed, the total of two or more remains the same:
-6a +3a -12
+3a -12
Therefore, the answer is (A) because -6a -12 +3a is the expression that equals 3 (-2a-4) +3a.
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Complete question:
Which expressions are equivalent to 3(-2a-4)+3a3(−2a−4)+3a3, left parenthesis, minus, 2, a, minus, 4, right parenthesis, plus, 3, a ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -6a-12+3a−6a−12+3aminus, 6, a, minus, 12, plus, 3, a (Choice B) B 3a+123a+123, a, plus, 12 (Choice C) C None of the above
I added a screenshot.
Answers
433/917=0.472
Answer:
gyyvggghhbbdsdgbnkkk
1. Select all the expressions equivalent to 54. (53)4. 0511 ☐ 516 0 548 0 54.5¹ 0 54.57 054.512 2.
Answers
An expression is equivalent to 54 if it represents the same numerical value as 54.
The following options are equivalent to 54:
53 + 1
54
54.5 - 0.5
54.57 - 0.07
54.512 - 0.512
The options that are not equivalent to 54 are:
(53)4
0511
516
054.512
Note that a number followed by a trailing zero is not equivalent to the same number without trailing zero as trailing zeroes don't change the value of the number.
In one day, the stock price for Warbucks Coffee rose from $5 to $6 per share. By what percent did this stock price rise?
Answers
By 17.77 percent this stock price rises.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, In one day, the stock price for Warbeck's Coffee rose from $5 to $6 per share.
From the general formula of percentage:
Percentage = difference value/ total value * 100
In our case,
Difference value = 6-5
Difference value = 1
total value = 6
thus,
Percentage change = 1/6 * 100
percentage change = 17.77%
Therefore, By 17.77 percent this stock price rises.
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In Exercises 25 and 26, find a parametric equation of the line M through p and q . [Hint: M is parallel to the vector q−p . See the figure below.] 25. p=[ 2 −5 ],q=[ −3 1 ] 26. p=[ −6 3 ],q=[ 0 −4 ] The line through p and q
Answers
The assumed line's and direction's parametric equation is x = 5 + t; y = -1; z = 3 -2t
How can the parametric equation be found?
The absence of points and lines renders the question insufficient.
I will therefore utilize the following presumptive parameters:
As the line traverses: (5, -1, 3)
The direction is ~v = <1, 0, -2>
The parametric equation of the line is represented as:
r<x,y,z> = Line + t<direction>
This gives
r<x,y,z> = (5, -1, 3) + t<1, 0, -2>
Express the equation in terms of x, y and z
x = 5 + t * 1
y = -1 + 0 * t
z = 3 -2 * t
Solve the equations
x = 5 + t
y = -1
z = 3 -2t
Consequently, the assumed line's and direction's parametric equation is x = 5 + t; y = -1; z = 3 -2t
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If a car travels at a constant speed of v miles per hour for t hours, it will travel vt miles.
Evaluate vt for v=61 and t=5. What does your result mean in this situation?
Answers
Answer:
Below
Step-by-step explanation:
Traveling VT miles is the same as multiplying V and T
They give us both V and T so we will multiply those two numbers
(61)(5) = 305
This result means that
The car was driving 61 miles per hour
The car was driving this speed on average for 5 hours
The car traveled 305 miles in 5 hours
Complete parts (a) through (c) below.
a. A warehouse is 65 yards long, 28 yards wide, and 8 yards high. What is the area of the warehouse floor? If the
warehouse is filled to half its height with tightly packed boxes, what is the volume of the boxes?
b. A room has a rectangular floor that measures 24 feet by 18 feet and a flat 9-foot ceiling. What is the area of the
floor and how much air does the room hold?
c. A grain silo has a circular base with an area of 165 square feet and is 22 feet tall. What is the total volume?
a. The area of the warehouse floor is
(Type an integer or a decimal.)
Answers
The area of the rectangle shaped floor is 1820 square yard and other values are given below.
What is a rectangle?
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.
A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.
Perimeter, P = 2 (Length + Width)
Area of Rectangle=Length*Breadth
Now,
For a
As Given A warehouse is 65 yards long, 28 yards wide, and 8 yards high.
then area=65*28=1820 square yards and
If the warehouse is filled to half its height with tightly packed boxes,
the volume=L*B*H=65*28*8/2=7280 cubic yard
For b
As given A room has a rectangular floor that measures 24 feet by 18 feet and a flat 9-foot ceiling.
Area=24*18=432 square feet
volume=24*18*9=3888 cubic feet
For c
A grain silo has a circular base with an area of 165 square feet and is 22 feet tall.
area of circle=πr^2=3.14*r²=165
r²=52.5 feet
Volume=π*r²*h=3.14*52.5*22=3630 cubic feet
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Very confused please help!
Answers
The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour is 6 = 0.15 gallons per hour and 2 R(t) dt using the average Riemann sum with four equal length partitions is 383.04 gallons.
How to calculate the total estimate?(a) R'(7), you can use the mean rate of change formula.
R'(7) ≈ [R(10) - R(4)] / [10 - 4]
With the data from the table it looks like this:
R(10) = 11.3 gallons per hour
R(4) = 10.4 gallons per hour
For this,
R'(7) ≈ (11.3 - 10.4) / 6 = 0.15 gallons per hour
The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour squared.
(b) To approximate 2 R(t) dt using the average Riemann sum with four equal length partitions, we can use
Δt = (24 - 0) / 4 = 6
2 R(t) dt ≈ 2Δt [R(1.5Δt) + R(4.5Δt) + R(7.5Δt) + R(10.5Δt)]
With the data from the table it looks like this:
R(1.5Δt) = R(4.5) = 10.4 gallons/hour
R(4.5Δt) = R(10.5) = 11.3 gallons per hour
R(7.5Δt) = R(16.5) = 10.2 gallons/hour
R(10.5Δt) = R(22.5) = 9.6 gallons per hour
For this,
2 R(t) dt ≈ 2(6) [10.4 + 11.3 + 10.2 + 9.6] = 383.04 gallons
The approximate unit of integral is the gallon.
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Find the area of the shape.
Either enter an exact answer in terms of iT or use 3.14 for
and enter your answer
as a decimal.
units?
Answers
The area of the shape is 12.56 square units
How to determine the rea of the shapeFrom the question, we have the following parameters that can be used in our computation:
Radius = 2
The area of a circle is calculated as
Area = pi * r^2
Substitute the known values in the above equation, so, we have the following representation
Area = 3.14 * 2^2
Evaluate
Area = 12,56
Hence, the area is 12.56 square units
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Complete question
A circle has a radius of 2 units
Find the area of the shape.
Either enter an exact answer in terms of iT or use 3.14 for
and enter your answer
as a decimal.
units?
find the value of a b c d
Answers
Answer:
a= 110°, b= 70°, c= 110°*, d=70°
Step-by-step explanation:
A is congruent to 110. 180-110= 70. C is possibly drawn incorrectly if the other angle is truly 100°.
Help. Please explain it
- Find the range of the function f(a) = 5+ 1/2a when the domain is (0,4,6)
Answers
Step-by-step explanation: The range of the function is the set of all its output values. To find the range of f(a) = 5 + 1/2a when the domain is (0, 4, 6), we can substitute these values into the function and see what the output is:
f(0) = 5 + 1/2 * 0 = 5
f(4) = 5 + 1/2 * 4 = 7
f(6) = 5 + 1/2 * 6 = 8
So the range of f(a) is the set of values {5, 7, 8}.
What is the value of the determinant of a 3x3 matrix A, where A = [[1,2,3], [4,5,6], [7,8,9]] ?
Answers
The determinant of the 3*3 matrix A where A = [[1,2,3], [4,5,6], [7,8,9]] is zero (0).
What is the determinant of a matrix?A matrix's determinant refers to the scalar value calculated for a given square matrix. The determinant is a concept in linear algebra, and its components are square matrixes. It may be viewed as the matrix transformation's scaling factor.
To find the determinant of the given matrix A = [[1,2,3], [4,5,6], [7,8,9]];
Choose the row or column with the most 0 elements. If there are no 0 elements choose any row or column. Multiply every element in row 1 by its cofactor and add. The cofactor is "the minor" with the sign changed if the indices match the a − position on the sign chart.From the attached steps in the image below, the next following step would be to add the determinants;
= 1 ×(−3)−2×(−6)+3×(−3)
= -3 + 12 - 9
= 12 - 12
= 0
Therefore, we can conclude that the determinant of the 3*3 matrix A where A = [[1,2,3], [4,5,6], [7,8,9]] is zero (0).
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quadratic factoring 9x^2-8x-20
Answers
The value of the quadratic equation is A = ( 9x + 10 ) ( x - 2 )
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
A = 9x² - 8x - 20 be equation (1)
On simplifying the equation , we get
A = 9x² - 18x + 10x - 20
On factorizing the equation , we get
A = 9x ( x - 2 ) + 10 ( x - 2 )
Taking the common factors in the equation , we get
A = ( 9x + 10 ) ( x - 2 )
So , when A = 0
( 9x + 10 ) = 0
x = -10/9
And , when ( x - 2 ) = 0
x = 2
Hence , the quadratic equation is A = ( 9x + 10 ) ( x - 2 )
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