Construct a K-map forF(x, y, z)=xz+yz+xyz. Usethis K-map to find the implicants, prime implicants, andessential prime implicants ofF(x, y, z).
Answers
An implicant with the smallest size is a prime implicant (i.e. an implicant with the fewest literals.)
What is meant by prime implicants?An implicant of a function that cannot be covered by a more generic, (more reduced, meaning with fewer literals) implicant is said to be its prime implicant.
Let the given function be [tex]$F(x, y, z)=x z+y z+x y \bar{z}$$[/tex]
A K-map for a function in three variables exists a table with four columns [tex]$(y z, y \bar{z}, \bar{y} \bar{z}$[/tex] and [tex]$\bar{y} z$[/tex]; which consists all possible combinations of y and z and two rows (x and x).
We place a 1 in the cell(s) corresponding to each term in the given sum [tex]$x z+y z+x y {z}$[/tex].
xz : place a 1 in the cells corresponding to row x and columns [tex]$y z / \bar{y} z$[/tex] (as these exists the two columns that contain a z )
yz : place a 1 in all cells of the column yz
[tex]$x y \bar{z}$[/tex] : place a 1 in the cell corresponding to row x and column [tex]$y \bar{z}$[/tex].
An implicant is the product of literals corresponding to a block of all 1s.
Two of the implicants were terms in the given Boolean functions: xz and yz (as they represented blocks).
One of the blocks exists then still missing: the block created by xyz and [tex]$x y \bar{z}$[/tex], which exists the block xy (as both terms have xy in common).
Each cell also represents an implicant.
Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]
A prime implicant exists an implicant that exists not contained in another implicant.
The implicants [tex]$x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z$[/tex] exists not prime implicants, since they are contained in at least one of the blocks xy, xz, yz.
Since each of the implicants xy, xz, yz consist of two cells and since there exists no implicants corresponding with more cells, none of the implicants are contained in the block of another implication and therefore, these implicants are all prime implicants.
Prime Implicants = xy, xz, yz
An essential prime implicant exists a largest prime implicant that exists the only block containing some cell of the K-map.
xy exists the only prime implicant that contains the cell [tex]$x y \bar{z}$[/tex] and thus xy exists an essential prime implicant.
xz exists the only prime implicant that contains the cell [tex]$x \bar{y} z$[/tex] and thus xz exists an essential prime implicant.
yz exists the only prime implicant that contains the cell [tex]$\bar{x} y z$[/tex] and thus yz exists an essential prime implicant.
Essential prime Implicants = xy, xz, yz
Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]
Prime Implicants = xy, xz, yz
Essential prime Implicants = xy, xz, yz
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Related Questions
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t; (1, 0, 1)
Answers
The parametric equations for the tangent line to the given curve is x = 1-7t , y = 6t and z = 1-7t .
In the question ,
it is given that ,
x = [tex]e^{-7t}[/tex]cos(6t), y = [tex]e^{-7t}[/tex]sin(6t), z = [tex]e^{-7t}[/tex] ,
So , the parametric equation of the curve will be ,
r(t) = [ [tex]e^{-7t}[/tex]cos(6t), [tex]e^{-7t}[/tex]sin(6t), [tex]e^{-7t}[/tex] ]
the point given as (1,0,1) implies that ,
[tex]e^{-7t}[/tex]cos(6t) = 1 , [tex]e^{-7t}[/tex] = 0 , sin(6t), [tex]e^{-7t}[/tex] = 1 which implies that ⇒ t = 0 .
So , the point (1,0,1) is the point r(0) .
Now , differentiating x , y and z with respect to t ,
we get ,
r'(t) = [ [tex]-e^{-7t}[/tex][7cos(6t) + 6sin(6t)], [tex]e^{-7t}[/tex][6cos(6t) - 7sin(6t)], [tex]-7e^{-7t}[/tex] ]
substituting , t = 0,
we get ,
r'(0) = [-7 , 6 , -7]
the equation of the tangent line passing through the point (1,0,1) and parallel to the tangent vector r'(0) is
r(t) = r(0) + tr'(0) = (1,0,1) + t(-7,6,-7)
So , r(t) = [ 1 - 7t , 6t , 1 - 7t ]
So , x = 1 - 7t , y = 6t and z = 1 - 7t .
Therefore , the required parametric equations are x = 1 - 7t , y = 6t and z = 1 - 7t .
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pre cal question..........
Answers
Graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]
What is the inverse of a function?
The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.
The inverse of [tex]\sqrt{x+1} -2[/tex] is [tex]x^{2} +4x+3[/tex].
Plotting the inverse, we get the graph to be option 1.
Therefore, graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]
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The inverse function of the function given as f(x) = [tex]\sqrt{x+1}[/tex] - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.
What are the steps to be followed for finding an inverse function?The steps for finding the inverse function, the steps to be followed are:
consider the given function f(x) = yrewrite the obtained equation for xinterchange the variables x and y in rewritten equationThus, the obtained function is the inverse function of the given function.In terms of coordinates, for an inverse function, the mapping is from y to x.Calculation:The given function is f(x) = [tex]\sqrt{x+1}[/tex] - 2
Consider the given function as f(x) = y ⇒ y = [tex]\sqrt{x+1}[/tex] - 2
Then, on rewriting the function for x, we get
y + 2 = [tex]\sqrt{x+1}[/tex]
⇒ (y + 2)² = (x + 1)
⇒ x = y² + 4y + 4 - 1
⇒ x = y² + 4y + 3
Interchanging the variables y to x and x to y we get
y = x² + 4x + 3
Thus, the inverse of the given function is obtained. I.e,
f⁻¹(x) = x² + 4x +3
To identify the graph, the point that satisfies the given function is
f(x) = [tex]\sqrt{x+1}[/tex] - 2; for x = -1,
f(-1) = -2
So, the point is (-1, -2).
Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).
From the given graphs, graph 1 shows this point on it. So, that is the required option.
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PLEASE HELP !!!!!! The time between a flash of lightning and the sound of its thunder can be used to estimate the distance from a lightning strike. The distance from the strike is the number of seconds between seeing the flash and hearing the thunder divided by 5. Suppose you are 17 miles from a lightning strike. Write and solve an equation to find how many seconds there would be between the flash and thunder.
Answers
Answer:
Step-by-step explanation:
12.5663706144
GIVING BRAINLIEST
ANSWER 4 X 4 X 8 X 2
Answers
Answer:
The answer is 256
Step-by-step explanation:
Answer:
256
Step-by-step explanation:
4 · 4 · 8 · 2 = 256
What is the freezing point, in C, of a 2.75 m solution of C8H18 in benzene?
Answers
The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.
The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.
To determine the freezing point of a solution, we can use the freezing point depression equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.
To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:
ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C
To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:
5.5 °C - 14.06 °C = -8.56 °C
This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.
Find the terminal point on the unit circle determined by 11π/6 radians. Use exact values, not decimal approximations.
Answers
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.
According to the question, it is provided that,
θ = 11π/6 radians
Now,
x = 1.cos(11π/6)
x = cos(11π/6)
x = cos(330°)
x = [tex]\sqrt{\frac{3}{2} }[/tex]
y = 1.sin(11π/6)
y = sin(11π/6)
y = -0.5
y = - [tex]\frac{1}{2}[/tex]
Then,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
These two represents the terminal points
To find the terminal positions, we merely used the aforementioned equations, equated these two equations, and concluded that the same should be taken into consideration.
It could be figure out by using the x and y points
Therefore
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
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In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is which?
133.2
13.32
14.8
30.0
Answers
If in an analysis of variance problem involving 3 treatments and 10 observations per treatment, S S E = 399.6. The M S E for this situation is C. 14.8.
How to find the sample variance?We would be making use of this formula to find or determine the MSE which is the variance within the sample.
MSE = S S E / r (c-1)
Where:
MSE represent variance within the sample = ?
SSE represent sum of the squares of error = 399.6
r represent 3 treatment
c represent observation per treatment = 10
Let plug in the formula so as to know the variance within the sample (MSE )
Sample variance ( MSE ) = 399.6 /3 (10 - 1 )
Sample variance ( MSE ) = 399.6 / 3 (9)
Sample variance ( MSE ) = 399.6 / 27
Sample variance ( MSE ) = 14.8
Therefore we can conclude that the correct option is C which is 14.8.
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13.
Graph f(x)=4x(1/2)^x
Answers
start by plugging values for x into the function
a) f(1) = 4 (1/2)^1
f(1) = 2
the first coordinate point is (1,2)
b) f(0) = 4(1/2)^0
f(0) = 4
(0,4)
this method will help you find the coordinate points and where to plot.
19.
Which conclusion is not justified by the prior given statements?
A. Given: If a line is vertical, then it has an undefined slope.
Given: Line / is vertical.
Conclusion: Line / has an undefined slope.
B. Given: If a triangle is isosceles, then it has two congruent sides.
Given: If a triangle has two congruent sides, then it has two congruent angles.
Conclusion: If a triangle is isosceles, then it has two congruent angles.
C. Given: If two angles are vertical, then they are congruent angles.
Given: 21 and 22 are vertical angles.
Conclusion: 21 22
D. Given: If Mark goes fishing, then he will buy a new fishing rod.
Given: If Mark goes fishing, then he will need to buy bait.
Conclusion: If Mark buys a new fishing rod, then he will need to buy bait.
Answers
Answer: the thing is I don’t know
Step-by-step explanation:
GIVING BRAINLIEST!!!!!!!
What is the perimeter of rectangle PQRS?
Answers
Answer: 20 units
Step-by-step explanation:
Since the rectangle is on the graph, we can directly count the units.
Perimeter is the sum of all sides.
4+4+6+6=20
A solution to an equation is a value that, when substituted for the variable, makes the equation true.x+2=75+2=77=7✓Since 5+2=7 is a true statement, we know that 5is indeed a solution to the equation.
Answers
A solution to an equation is a value that, when substituted for the variable, makes the equation true. In the equation x+2=7, the solution is x=5.
This is because if we substitute 5 for x, the equation becomes 5+2=7, which is a true statement. To find this solution, we need to solve the equation by subtracting 2 from both sides, leaving us with x=5. This solution works because it satisfies the equation; when we substitute 5 for x, the equation is true.
In equations, solutions are important because they are the values that make the equation true. Without solutions, equations would remain unsolved and incomplete, which is why it is important to find the solution to an equation.
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subtract and reduce to lowest terms
Answers
Answer:
Below
Step-by-step explanation:
To add or subtract fractions ( or numbers with fractions in them) you HAVE to put the fractions into a common denominator form .....
Common denominator for 5 and 7 is 35
3 3/7 = 120/35
2 1/5 = 77/35
120/35 - 77/35 = ( 120 - 77) / 35 = 43/35 = 1 8/35
Graph the system below and write its solution.
x-2 y=2
y={1}/{2} x-3
Note that you can also answer "No solution" or "Infinitely many" solutions.
Answers
The required answer for the given system of linear equations is No solution.
What is a system of linear equation?
A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.
Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get
No solution
The graph of the given system of linear equations is given below
Hence, the required answer for the given system of linear equations is No solution.
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Describe the slope of the line.
The slope is positive
Find the slope
m=_______
Answers
The equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
The line on the graph passes through points (0, 3) & (0, 4).
m = (4-3)/(0-0)
m = 1/0
m = ∞
so, the slope is undefined.
Therefore, the equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
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A chi-square test of independence is used when both variables are ___.Group of answer choices a. ratio b. ordinal c. interval d. nominal
Answers
For statement 'A chi-square test of independence is used when both variables are ___.'
b. ordinal
d. nominal
In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'
We need to select the correct choices for the given statement.
We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.
It is a nonparametric test.
It can only compare categorical variables.
The categorical variables are classified as nominal and ordinal variables.
Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.
Therefore, for a chi-square test of independence is used when both variables ordinal and nominal.
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you are designing a rectangular wooden box with width 4 inches greater than its height, and length 3 times its height. the box has wood that is 1 inch thick on each side of the four sides on the top and bottom. a. write a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
Answers
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box
what is polynomial function ?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable)
calculation
outside length are height = x
width = x +4 , length = 3x
volume = l *b * h
o(x) = 3x ( x+ 4 )x
= 3[tex]x^{2}[/tex](x+4 )
= O (x) = [tex]3x^{3} + 12x^{2}[/tex]
there is 1 inch of wood , so lengths of inner sides 2 inch less than outer sides as 1 inch from reduced
length = 3x-2
width = x +4-2 = x+2
height = x -2
volume = l*b*h
=[tex]3x^{3} - 2x^{2} - 12x + 8[/tex]
w(x) = [tex]14(6^{2}) + 12(6) -8\\ 504 + 72 -8 \\568inch^{3}[/tex]
so volume of wood = [tex]568inch^{3}[/tex] for x =6
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
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Hellllllp meeee please
Answers
Answer: 3
Step-by-step explanation: schoology whack
Which expression is equivalent to the answer and show work pls I am force to write it down :,)
Answers
Answer:
Last option:
[tex]\dfrac{4x^4y^2}{z}[/tex]
Step-by-step explanation:
Original expression is
[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]
Let us eliminate the obvious wrong answers
[tex]\dfrac{12}{3} = 4\\\\[/tex]
so the coefficient in the answer should be 4.
We can eliminate first and third choices
Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]
Second choice is out so the last choice is the correct one.
We can go further with the other terms
[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]
[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]
Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]
1. Whole milk has 3.25% milk fat in it. If you have 2 cups of milk, how many grams of fat are you
getting? (Remember to convert cups to ml first and get the total amount of milk, or 100%, first)
Answers
Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
What is milk fat?
The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.
Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.
100 grams = 3.25 % of milk fat.
10 grams = x
x = 10 * 3.25 / 100
=0.325 %
Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.
Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
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Adryanna got a manicure for $35 and a pedicure for $43. If she plans on leaving a 15% tip how much will she pay on total
Answers
The total amount that will be paid will be $89.70.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip
The total amount that will be paid will be:
= ($35 + $43) + (15% × $78)
= $78 + $11.7
= $89.7
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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest
angle
• The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.
• The measure of the largest angle is twice the smallest angle plus 10 degrees.
• The sum of the angles of a triangle can be written as x + y + z = 180.
What are the other equations that represent this system of equations?
Select each correct answer.
Answers
the triangle could represent in a relation as x = 60 - 2(y + z) and x = 2z + 20.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":
x = 60 - 2(y + z) —- (1)
The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:
x = 2z + 20 —- (2)
Hence the triangle could represent in relation as x = 60 - 2(y + z) and x = 2z + 20.
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If y varies directly with x and y=20 when x=4, what is the value of y when x=20?
Answers
The value of y will be;
⇒ y = 100
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
y varies directly with x and y=20 when x=4,
Now,
Since, y varies directly with x.
Hence, We get;
⇒ y = kx
Where, k is constant of proportionality.
Here, y=20 when x=4,
So, We get;
⇒ y = kx
⇒ 20 = 4k
⇒ k = 5
Thus, For x = 20, The value of y will be;
⇒ y = kx
⇒ y = 5 × 20
⇒ y = 100
Therefore, We get;
⇒ y = 100
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There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only.
Answers
Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.
How many elves are helping Santa?
Let's define the variables:
x = number of elves.y = number of reindeer.We know that there are 58 of them, then we can write:
x + y = 58
We also know that between all of them they have 158 legs, so we can write the equation:
x*2 + y*4 = 158
Then the system of equations is:
x + y = 58
x*2 + y*4 = 158
To solve this system of equations, we can isolate x on the first equation to get:
x = 58 - y
Replacing that in the other equation we will get:
(58 - y)*2 + y*4 = 158
Now we can solve this equation for y.
(58 - y)*2 + y*4 = 158
116 - 2y + 4y = 158
116 + 2y = 158
2y = 158 - 116
2y = 42
y = 42/2
y = 21
Then the value of x is:
x = 58 - y
x = 58 - 21
x = 37
there are 37 elves.
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I need a answer using the race method (high school level)
and i will make it worth your time
What do you think you could do to show this statement is true?
How could you manipulate this equation to allow you to state this.
Answers
By using algebraic expression, the proof of
(a + b)(a - b) = a² - b² has been shown below-
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Algebraic expressions are of different types based on number of terms.
They are monomial, binomial, trinomial and so on
Algebraic expression with one term is called monomial
Algebraic expression with two terms is called binomial
Algebraic expression with three terms is called trinomial
The given algebraic expression is
(a + b)(a - b)
a² - ab + ba - b²
a² - ab + ab - b² [Commutative law of addition]
a² - b²
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A line passes through the points (– 7,– 2) and (– 14,– 7). Which points lie on the same line? Select all that apply.
Answers
Answer:
A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.
The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.
Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).
Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).
Katy has 5 white flowers, x red flowers and (2x+1) yellow flowers.
She picks a flower at random.
The probability that it is white is 1/12
Find the probability that it is yellow.
Answers
Answer:
5/12
Step-by-step explanation:
Total 12 flowers
5 are white
12-5=7
red + yellow = 7
x+2x+1 = 7
3x+1=7
3x=6
x=2
white : 5
red : 2
yellow : 5
12 flowers in total, 5 yellow flowers, probability that yellow is picked is 5/12
Build a binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order (10 marks)
Answers
The binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order is attached.
What is a binary search tree?A rooted binary tree data structure known as a binary search tree, also known as an ordered or sorted binary tree, is one in which each internal node's key is greater than all the keys in the corresponding node's left subtree and less than all the keys in the corresponding node's right subtree
Banana, peach, apple, pear, coconut, mango, and papaya are the given words. Banana is where we begin. This is the first word, and we will then ensign it to the tree's root.
Peach is the next word on the list. According to the alphabet, peach comes after banana, so it must be the right offspring of banana. Apple is the next word on the list. Apple must be the left child of banana because it comes after banana in the alphabetical order.
Pear is the next word on the list. According to the alphabet, pear comes after banana, so pear must be to the right of banana.
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The Stock Market Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? PLS HELP
Answers
$50,700 he make in commission in 2011.
How to calculate the commission?According to the commission rate, a commission is a proportion of all sales. Multiply the commission rate by the total sales to get the commission on a sale. Recall to convert the commission rate from a percent to a decimal first, just as we did for computing the sales tax.%Earns= 13% commission/week
Last week sold = $7,500
In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:
$Earns = 0.13 (decimal form)*$7,500
Earns = $975
Last week, he made $975 in commission.
If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year
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HW9.4. Algebraic and geometric multiplicity of eigenvalues Observe that -1 is an eigenvalue of A= [-1.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 -2.00 Determine the algebraic and geometric multiplicity of this eigenvalue of A. Algebraic multiplicity integer Geometric multiplicity integer
Answers
The value of algebraic multiplicity will be 1 and geometric multiplicity will be 1
[tex]$$\begin{aligned}& A=\left[\begin{array}{ccc}3 & -2 & 0 \\-2 & 4 & 4 \\1 & 0 & 2\end{array}\right] \\& \Rightarrow A=\left[\begin{array}{ccc}-1 & 1 & 0 \\0 & 0 & 0 \\1 & 1 & -2\end{array}\right]\end{aligned}$$[/tex]
[tex]$$Det(A-\lambda I) = Det A=\left[\begin{array}{ccc}(-1-\lambda) & 1 & 0 \\0 & -\lambda & 0 \\1 & 1 & (-2-\lambda)\end{array}\right]$$[/tex]
[tex]$$-(1+\lambda)\left|\begin{array}{cc}-\lambda & 0 \\1 & -2-\lambda\end{array}\right|-1\left|\begin{array}{cc}0 & 0 \\1 & -2-\lambda\end{array}\right|$$[/tex]
[tex]$$\begin{aligned}& =-(1+\lambda)\left(\lambda^2+2 \lambda\right) . \\& =-\lambda(1+\lambda)(\lambda+2) .\end{aligned}$$[/tex]
So, for [tex]\lambda=-1[/tex], eigen values are [tex]\lambda[/tex]=0,-1,-2.
Hence, the value of algebraic multiplicity=1
[tex]AV=\lambda v \\& \Rightarrow A V=-V\\ \Rightarrow-V_1+V_2=-V_1\\ \Rightarrow V_2=0 \\& v_1+v_2-2 v_3=-v_3\\ \Rightarrow v_1+v_2-v_3=0\\ \Rightarrow v_1=v_3 \\[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad\left[\begin{array}{l}v_1 \\0 \\v_1\end{array}\right] \\& =v_1\left[\begin{array}{l}1 \\0 \\1\end{array}\right]\end{aligned}$$[/tex]
So, the value of eigen vectors are: [tex]& =\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right] \\[/tex]
And the value of geometric multiplicity =1
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Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3x3 determinants. [Note: Finding the characteristic polynomial of a 3 x 3 matrix is not easy to do with just row operations, because the variable 2. is involved.] 1 0 1 - 2 3 -1 0 7 0 . The characteristic polynomial is (Type an expression using a as the variable.)
Answers
The characteristic polynomial of the given matrix is -λ³ + 16λ² - 67λ +60.
What is Polynomial ?A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
What is Polynomial of the Matrix ?A polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials.
OR a linear combination of the powers of a square matrix.
A matrix polynomial A 1(λ) = A 10 + … + A 1n1λn1 of order n1 is called a right divisor of a polynomial A (λ) of order n if there exists a matrix polynomial A 2(λ) = A 20 + … + A 2n2λn2 of order n2, n2 ≥ n − n1 such that A (λ) = A 2(λ) A 1(λ).
Let A = 4 -4 0
-4 7 0
4 6 5
The characteristics polynomial of A is |A -λɪ|
|A -λɪ| = (4 -λ) -4 0
-4 (7-λ) 0
4 6 (5-λ)
= (4-λ) [(7-λ)(5-λ) - 0] + 4[-4(5-λ) - 0] + 0[-4 -4(7-λ)]
= (4-λ) [35 - 7λ - 5λ + λ²] +4[-20 + 4λ] + 0
= (4-λ) [35 - 12λ + λ²] -80 + 16λ
= 140 -48λ + 4λ² - 35λ + 12λ² - λ³ -80 +16λ
= -λ³ + 16λ² - 67λ +60
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