Answers
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}4&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}2\\ \:-1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}4&5\end{pmatrix}\begin{pmatrix}2\\ -1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}4\cdot \:2+5\left(-1\right)\end{pmatrix}[/tex]
[tex]C = (3 )[/tex]
Therefore , the value of matrix C is [tex]C = (3 )[/tex]
b)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}2&6\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}-3\\ \:-4\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}2&6\end{pmatrix}\begin{pmatrix}-3\\ -4\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}2\left(-3\right)+6\left(-4\right)\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}0&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}0&5\end{pmatrix}\begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}0\cdot \:3+5\cdot \:4&0\cdot \:6+5\cdot \:1\end{pmatrix}[/tex]
[tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Hence ,
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
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Related Questions
the teacher decides to let your class get in groups of four to complete the homework. if you are like most people, your effort on this group task will be
Answers
The effort required to complete this group task will be less than the effort required to complete the task as individual homework.
In social psychology, social influence is a topic of study. Social compliance, persuasion methods, brainwashing, and social obedience are a few examples of issues studied in this field.
Several phenomena show how having others around affects performance, one of which is social loafing.
When someone works less hard on a task when doing it in a group, this unique phenomena happens.
Your class is divided into groups of four and given the assignment by the teacher. This group assignment will require less effort from you than completing it as individual homework would have required. This exemplifies the social loafing principle.
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PLEASE HELP
Fill in the blanks below with the correct units.
Answers
Answer:
a) Liters.
b) Kilograms.
c) Kilometers.
Step-by-step explanation:
I'm not completely sure about C). But after some researching and calculating these answers seem the most correct. But I'm pretty sure A) and B) are right.
In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
Answers
The netball team scored 26 points in their fifth game.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
Let x be the no. of points the netball team scores in the fifth game.
∴ (31 + 31 + 31 + 31 + x)/5 = 30.
(124 + x)/5 = 30.
124 + x = 150.
x = 26.
So, They scored 26 points in their fifth game.
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Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10). What one additional step
does Cecel need in order to return to the starting point?
Answers
The number of steps in order to return to the starting point will be negative 16.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10).
Let 'x' be the number of steps in order to return to the starting point. Then the equation is given as,
x + 10 + (−5) + 19 + 6 + (−19) + 5 + (−10) = 0
Simplify the equation, then the equation is given as,
x + 10 − 5 + 19 + 6 − 19 + 5 − 10 = 0
x + 40 − 24 = 0
x + 16 = 0
x = − 16
The number of steps in order to return to the starting point will be negative 16.
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Darren ha a piece of wood that i 7 in by 8 in. Explain how he could divide thi large rectangle into two maller rectangle
Answers
On solving the provided question, we got that - he could divide the large rectangle into two smaller rectangle by cutting into 7 inches by 4 inches each.
What is rectangle?The opposite sides of a rectangle are equal and parallel, making it a form of quadrilateral. Four of its sides are equal to 90 degrees, making it a four-sided polygon. Two-dimensional shapes include rectangles.
We know that Darren has a wood piece that measures 7 inches by 8 inches. We are expected to explain how he managed to separate these two enormous rectangles into smaller ones.
Let's imagine that a huge rectangle has a width of 8 inches and a length of 7 inches.
Darren needs to cut two rectangles that are each 4 inches wide and 7 inches long to divide a giant rectangle into two smaller rectangles.
In order to make two smaller rectangles that are each 7 inches long and 4 inches broad, Darren can cut a larger rectangle.
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i have no clue how to do this please help me out :))
Answers
Answer:
∆QRS / ∆XZY = 1/2
Step-by-step explanation:
You want the similarity ratio of ∆QRS to ∆XZY. Side lengths are marked in the diagram.
The similarity ratio will be the ratio of two corresponding side lengths.
Corresponding sidesYou can find corresponding sides several ways:
Use the similarity statement to identify corresponding vertices. A side will be defined by 2 of them. Use vertex identifiers that are in the same positions in both triangle names: QR : XZ (first two vertices listed), for example.Use the markings in the figure to identify corresponding sides. Corresponding sides will have the same angle marks at either end. For example, the side marked 1 in ∆QRS has 1-arc and 3-arc angle markings at its ends. The side marked 2 in ∆XZY also has 1-arc and 3-arc angle markings at either end. It will be the corresponding side.Use side lengths. When both triangles have their side lengths sorted into increasing order, the corresponding numbers are corresponding sides. The side lengths in ∆QRS are {1, 2, 2}. In ∆XZY, they are {2, 4, 4}.The ratios of corresponding sides are 1:2, 2:4, and 2:4. The 2:4 ratios reduce to 1:2, which is the answer you're looking for. Written as a fraction, the ratio is ...
1/2 . . . . ratio of ∆QRS to ∆XZY
For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean and compare the result to the expected percentage of a normal distribution.
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
A. 40%; This percentage is lower than expected in a normal distribution.
B. 50%; This percentage is lower than expected in a normal distribution.
C. 60%; This percentage is lower than expected in a normal distribution.
D. 70%; This percentage is close to the expected percentage in a normal distribution
Answers
In a normal distribution, a minimum percentage of 68% is anticipated, while an expected percentage of 60% is lower at 60%.
What is standard Deviation ?The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is.
According to the given information
8, 12, 27, 32, 45, 57, 61, 73, 82, 94 data points are provided.
Their average mean is 49.1.
The computed standard deviation is 29.31988.
The lower and upper limits are provided by the following when one standard deviation from the mean is taken into account.
= [ 49.1 - 29.31988, 49.1 + 29.31988 }
= [ 19.78012 , 78.41988 ]
We can observe that only six points—27, 32, 45, 57, 61 and 73—or 60% of the total—remain within one standard deviation of the mean.
In a normal distribution, a minimum percentage of 68% is anticipated, while an expected percentage of 60% is lower at 60%.
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Answer: C 60%; This percentage is lower than expected in a normal distribution.
What is 6/2(19x6+17)
Answers
Hope this helps :)
PLEASE HELP ASAP!!!!!!!!
Answers
Answer:
The lie is #3.
Step-by-step explanation:
1 divided by 7^-3 is not equal to 7^-3. 7^-3/1 is equal to 7^-3 though.
Is 3 : 9 and 6 : 36 equivalent ratios?
Answers
Answer: False
Step-by-step explanation: they are not the same because if you times 3:9 ratio times 2 then it makes it 6 and 18 and does not make 6 : 36
Your welcome - your friend green
If 5 bunnies can eat all the crops in a garden in 8 hours, how long would it take for 8 bunnies to eat the same amount of crops? Please help!
Answers
Answer:
5 hours
Step-by-step explanation:
40=8x
x=5
The number of hours taken for 8 bunnies to eat the same amount of crops will be 5 hours.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If 5 bunnies can eat all the crops in a garden in 8 hours. The relation between work and time will be inverse. Then the product of the number of bunnies and the number of hours remains constant.
Let 'x' be the number of hours. Then the equation is given as,
8 × x = 5 × 8
Simplify the equation, then we have
8 × x = 5 × 8
8x = 40
x = 40 / 8
x = 5 hours
The number of hours taken for 8 bunnies to eat the same amount of crops will be 5 hours.
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guys pls help!! i really need help on these two questions
Answers
In order to prove the opposite sides are congruent, the two diagonals of parallelogram ABCD needed.
The given quadrilateral WXYZ is a parallelogram.
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel.
The quadrilateral ABCD have congruent opposite sides only when the diagonals are bisect.
Given that the diagonals of quadrilateral WXYZ intersect at point R.
Since the R is the midpoint.
The opposite sides are equal and opposite angles are equal.
Hence we can say that the given quadrilateral WXYZ is a parallelogram.
Similarly, in order to prove the opposite sides of the parallelogram ABCD is congruent, both diagonal required.
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THE SOULITIONS TO the inequality y>-3x+2 are shaded in the graph. Which point is a solution?
A. (0,2)
B. (2,0)
C. (1,-2)
D.(-2,1)
Answers
Point (2,0) is the solution for the inequality y > -3x +2
What is the solution of inequality?Here we have,
y > -3x +2
The shaded area above the dotted line is the solution.
We are aware that
If a point is a solution to an inequality, then its coordinates must satisfy the inequality.
We will investigate all cases to find a solution to the problem.
A) Point (0,2)
Here,
x = 0
y = 2
Verify the inequality by changing the values of x and y.
2 > -3 x 0 + 2
2 > 2
It is not correct.
Therefore the point is not to solve the inequality.
B) Point (2,0)
Here
x = 2
y = 0
Verify the inequality by changing the values of x and y.
0 > -3 x 2 + 2
0 > -4
This is correct
Therefore the point is to solve the inequality.
Therefore point B is the solution.
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What are the coordinates of the point on the directed line segment from (1, 5) to
(6, 10) that partitions the segment into a ratio of 3 to 2?
Answers
(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.
Define mid point theorem,According to the midpoint theorem, the line segment drawn from the intersection of two triangle sides is parallel to and equal to half of the third side. To determine precise information about the lengths of triangle sides, one uses the Midpoint Theorem. According to the Midpoint Theorem, the segment connecting two triangle sides at their midpoints is parallel to the third side and is half its length.
Given
Points (1,5) (6.10)
Ratio 3 :2
Using mid point theorem,
( (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) )
3(6) + 2 (1)/ 3+2, 3(10) + 2(5)/ 2+3
18 + 2/5 , 20 + 10/5
20/5 , 30/5
4, 6
(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.
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A small coffee shop sells a variety of different pastries and treats. The banana bread is sold
by the loaf, and each loaf is sold for the same price. The cookies are sold by the dozen, and
each dozen is sold for the same price.
On Friday, the bakery collected $260 from selling 40 loaves of bread and 35 dozen cookies.
On Saturday, the bakery collected $360 from selling 64 loaves of bread and 42 dozen
cookies.
At what price does the bakery sell each item for?
Answers
Using system of linear equations, the price of bread is $3 and cookies is $4
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = bread y = cookiesWe can write a system of linear equation with this;
40x + 35y = 260 ....eq(i)
64x + 42y = 360 ...eq(ii)
Solving equation (i) and (ii)
The value of x is 3 and y is 4
This shows that the price of bread is $3 and cookies is $4
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Graph the equation on the coordinate plane
Y=1/2x-3
Answers
Answer:
Step-by-step explanation:
Start at origin 0,0 make a point
go up 1 and over 2 make a point
connect with straight line
During a class trip to an apple orchard, a group of
students picked 2436 apples. They packed them into
6 boxes to take to the local food bank. If each box
held the same number of apples, how many apples
were in each box?
2) 46
3) 460
4) 406
5) 14,616
Answers
4)406
We just divide the total number of apple which were 2436 divided by the number of boxes which was 6, that’s how we get the answer as 406.
The answer is 406 apples.
2436 apples divided by 6 boxes gives you the number of apples in each box.
Dear Everyone, Please solve thid problem
1+1+1-1=
Answers
Answer:
2
Step-by-step explanation:
Pretty sure u know how to do this but
You have 1 dot and you add another dot which gives you 2 dots. And then you add another dot which gives you 3 dots. And then your mean friend takes away one of yours dots, which gives you 2 dots left.
Point A has coordinates
(-4, -2). Point B has
coordinates (6, 3). Find the coordinates of
point P on directed line segment AB that
partitions AB so that AP: AB is 3:5.
Answers
P = (1 - t)A + tB
where A and B are the coordinates of the two points, and t is a value between 0 and 1 that determines where the point P lies on the line segment AB.
In this case, we are told that the ratio of AP to AB is 3:5. We can set t equal to 3/5, which means that point P is 3/5 of the way from A to B along the line segment AB:
P = (1 - 3/5)A + (3/5)B
= (2/5)A + (3/5)B
Substituting the coordinates of A and B, we get:
P = (2/5)(-4, -2) + (3/5)(6, 3)
= (-8/5, -6/5) + (18/5, 9/5)
= (10/5, 3/5)
= (2, 3/5)
Therefore, the coordinates of point P are (2, 3/5).
The formula for explicit sequence
Answers
Answer: The formula for explicit sequence is F(n)=6n
n=7
7) =6*7=42
Step-by-step explanation: Hope this was helpful
If baeball cot $12 and are marked down by the ame percentage a baeball bat, how much will a baeball cot?
Answers
The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.
What is meant by the term percentage?One technique to express a number as a fraction of 100 is through the use of percentage. It is typically used to denote a percentage or share of a larger whole, and it is frequently written with the sign "%." For instance, a student who obtains an 80 is referred to as having gotten a "80%" or "80%".
Percentages can be used to compare distinct numbers, to assess change over time, or to establish the proportion of a group or population that fits into a specific category. For example, a survey may state that 60% of respondents said "yes" to a certain question, or that the price of a product has grown by 10% in the last year.
How to solve.
If the price of a baseball is marked down by the same percentage as a baseball bat, then the price of a baseball will not change.
The percentage markdown only affects the price of the baseball bat, not the price of the baseball. Therefore, the price of a baseball will remain the same at $12.
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just type 2 for the answer
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Hello please solve this with steps
Answers
The dimensions of the rectangular prism are:
Length = 4 meters.
Width = 2 meters.
Height = 2 meters.
What are the dimensions of the storage space?A rectangular prism of width W, height H, and length L has a volume given by the formula:V = W*H*L
Here we know that: the height and the width are both 2 meters less than the depth, then:W = L - 2H = L - 2 and the volume is 16 cubic meters
Replacing that in the volume equation we will get:16 = L*(L - 2)*(L - 2)It is ratter easy to notice that if we take L = 4, we will get:16 = 4*(4 - 2)*(4 - 2) 16 = 4*(2)*(2)16 = 4*416 = 16 So L = 4 is a solution, then:
W = L - 2W
= 4 - 2 = 2
And also the height is:H = 4 - 2 = 2
These are the dimensions.
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There are 28 right-handed students in a class of 3 1. What is the probability that a student
chosen at random will be left-handed?
31/28
28/31
3/28
3/31
Answers
Answer:
3/31
Step-by-step explanation:
31 - 28 = 3 left handed students
31 total students
probability that a student chosen at random will be left-handed is 3/31
Alavaro selects a colored marble at random from a bag, records the color, and replaces the marble in the bag. After 20 trials, the experimental probability of selecting a pink
marble is selecting a yellow marble is, and selecting an orange marble is. On the 21st trial, Alavaro selects a blue marble. What is the experimental probability of
selecting a pink marble after 21 trials?
Answers
Answer:
0.325
Step-by-step explanation:
I just need to know how to get to 55 pls
Answers
Answer/Step-by-step explanation:
Okay, so this question really is a nightmare, because this image is just not possible. Like, literally, Z is or is not the center, you do or do not have enough info. Its a bad question. This is not your fault. If you don't care why its a bad question scroll down to "How could someone get 55°"
If Z is the center, BZ and CZ are radii and equal. Angle CBZ is 60° because
AngleABC + Angle CBZ = 180°
120° + CBZ = 180°
CBZ = 60°
That means AngleC is also 60°. And then, since 180° in a triangle, AngleCZB also must be 60°.
This makes AngleCZD 120°.
But if Z is the center and ArcCD is 115°, then AngleCZD should be 115°.
Contradiction! Angle CZD can't be both 120° and 115° something is wrong here. See image.
How could someone get 55°? Well, it is also not correct but... If ArcCD is 115° then AngleCZD is 115° (if Z is the center) So AngleCZB is 180°-115°, which is 65°.
AngleCBZ is 60°
60° + 65° + C = 180°
125 + C = 180
C = 55°
50 points!! (Factoring Algebraic Expressions MC)
Rewrite 1/14 x^3y +8/14xy^2 using common factor
1/7xy(2x^2 + 8y)
1/7x^2y(2x+8y)
1/14xy(x^2+ 8y)
1/14 x^3y^2(y+8)
Answers
Answer:
7
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out of
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7
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y
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2
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2
y
−
3
x
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−
7
x
y
(
−
2
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.
−
7
x
y
(
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Step-by-step explanation:
Which is the best definition of a boundary line for a linear inequality?
The line that divides the plane into an area that is triangular and an area that is rectangular.
The line that divides the plane into an area with solutions and an area that does not have solutions.
The line that divides the plane into four quadrants.
The line that divides the plane into eight quadrants.
Answers
Answer: The line that divides the plane into an area that is triangular and an area that is rectangular.
Write an equation in slope-intercept form of the line that is perpendicular to the one given and passes through the given point. (4,8); y=-2x - 4
Answers
An equation in slope-intercept form of the line perpendicular to y = 2x-4
is y =(-1/2)x+10.
What are lines and their slopes?We are aware that there are many types of equations for lines, with the
general type being Ax+ By + C = 0, and the slope-intercept form equation
being y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept is the point (0,b) where the line intersects the y-axis when
x = 0, and the slope is the rate of change of the y-axis relative to the x-axis.
We are aware that the slopes of perpendicular lines are oppositely negative.
The slope of the given line, y = 2x-4, is 2.
Consequently, the given line will pass through point with a slope of (-1/2). (4,8).
∴8= (-1/2)(4)+b
8= -2+b
b = 10.
∴ y =(-1/2)x+10 is our required line.
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How do I do y=mx+b in these type of questions
1. y<-3/4x+2
2. y≤5
3. x+y>6
Answers
With linear inequalities in two variables, you still have y=mx+b and it still tells you the same thing.
The inequality portion adds two additional layers on top of the y=mx+b line.
If the inequality is > or <, then you draw the line as a dashed line.
If the inequality is ≥ or ≤, then you draw the line as a solid line.
The difference is that points on the > or < line do NOT make the inquality true, while points on the ≥ or ≤ line do.
The other piece is that all the points on one side of the line will also make the inequality true.
If you have "y>mx+b" or "y≥mx+b", then you shade above the line.
If you have "y<mx+b" or "y≤mx+b", then you shade below the line.
So there are three parts:
1. Where is the line?
2. Is the line solid or dashed?
3. Do you shade above or below the line?
The three graphs are attached.