multiplication of matrices
with full workings and explanations

The dimensions of the rectangular prism are:

Length = 4 meters.

Width = 2 meters.

Height = 2 meters.

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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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.

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.

Answer:

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Step-by-step explanation:

Point (2,0) is the solution for the inequality y > -3x +2

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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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

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.

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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In order to prove the opposite sides are congruent, the two diagonals of parallelogram ABCD needed.

The given quadrilateral WXYZ 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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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  

An equation in slope-intercept form of the line perpendicular to y = 2x-4

is y =(-1/2)x+10.

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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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.

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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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.

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

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

In a normal distribution, a minimum percentage of 68% is anticipated, while an expected percentage of 60% is lower at 60%.

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.

Answer:

0.325

Step-by-step explanation:

The number of steps in order to return to the starting point will be negative 16.

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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(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.

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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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.

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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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.

The netball team scored 26 points in their fifth game.

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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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.

You can find corresponding sides several ways:

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

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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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°

The answer is 406 apples.

2436 apples divided by 6 boxes gives you the number of apples in each box.

Answer: The formula for explicit sequence is F(n)=6n

n=7

7) =6*7=42

Step-by-step explanation: Hope this was helpful

Using system of linear equations, the price of bread is $3 and cookies is $4

The 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;

We 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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Answer: The line that divides the plane into an area that is triangular and an area that is rectangular.