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Sliva [168]
3 years ago
6

Answer the following true or false. Justify your answer.

Mathematics
1 answer:
Anna007 [38]3 years ago
7 0

Answer:

a) False b) False c) True d) True e) True

Step-by-step explanation:

a) If A is a subset of B, and x∈B, then x∈A. False

Suppose A is Z (Set of Integers), and B is R (Set of Real Numbers). Then A is a subset of B. x ∈ B, let's say x equals π. If x ∈ B (B = Real Numbers) and x=π then x ∉ A (Z).

We could call A, any other subset of Real numbers (Q, I,..) and we both would come up to the same conclusion when it comes to Real numbers the Set.

So this conclusion is False. Not always an element of a subset is an element of a set.

b) False

For this one, I've drawn some lines, and it is useful to work with them.

Given the set {(x,y) ∈ R²| 0<x<0} then all negative and positive numbers but zero belong to this set.

c) If A and B are square matrices, then AB is also square. True

Taking into account the rules for multiplying matrices. The number of columns of A must be the same number of lines of B to there can be a matrix product.

Whenever we multiply square matrices, we'll always get square matrices. Then this conclusion is true.

d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S. True

Suppose A= Z (Integer Numbers) and B=Q (Rational Numbers) and S= R (Real Numbers)

A∩B = Z∩Q=∅ and A∪B =Z∪Q = subset

Since the ∅ empty set ⊂ in every set and ZUQ is another Subset of R this is a True conclusion.

e) True. For a matrix A, we define A²= AA

For any Power of Matrices, all we have to do is multiply any given matrix by itself for a given number of times.

M²=M*M

M³=M*M*M

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Question 3 (5 points)
Vedmedyk [2.9K]

A quadrilateral that has all congruent sides and all right angles is known as a square.

Given is a quadrilateral with all right angles and congruent sides.

<h3>What is a Quadrilateral?</h3>

A four-sided polygon having four sides and four corners is referred to as a quadrilateral in geometry .

<h3>What are Congruent sides?</h3>

Congruent sides refers to a figure's sides being equal to one another.

We know that,

A square is a quadrilateral with angles that are each 90 degrees.

Additionally, a square has four equal sides, making it a quadrilateral having all  sides congruent.

As a result, a square is a quadrilateral with congruent sides and all right angles.

Learn more about quadrilateral here:

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4 0
1 year ago
Although the numbers are not included on either axis, it is possible to determine from shape and location that the equation y =
e-lub [12.9K]

It looks like your question is incomplete. I believe you also have options to pick which graph is correct. However, I can still give you the information you are looking for.

The slope of the line is -1.2

The Y-intersect is (0, 4)

I have also attached an image of what the graph would look like.

Hope this helps.

3 0
2 years ago
Solve the equation 2/3x=-1/2x+5 what is the first step to isolate the variable term on one side of the equation
Komok [63]

Answer:

x= 30/7

Step-by-step explanation:

See image below:)

4 0
2 years ago
Read 2 more answers
2(3x+8)=6x+16<br> how many solutions does this equation have
Kisachek [45]

Answer:

infinite

Step-by-step explanation:

infinite

but solving for it we can get

3x + 8 = 3x + 8 (divided both sides by 2)

3x = 3x (subtracted 8)

x = x

1 = 1

therefore, for all values of x, the equation will be true so there are

infinite solutions

4 0
3 years ago
What equation in slope-intercept form represents the line that passes through
gregori [183]

Answer:

So, equation in slope-intercept form that represents the line that passes through  the points (1,3) and (2,5) is y=2x+1

Step-by-step explanation:

We need to write equation in slope intercept form that represents the line that passes through  the points (1,3) and (2,5)

The standard equation of slope-intercept form is: y= mx+b

where m is the slope of the lines and b is the y-intercept.

To make the equation we need to find slope (m) and y-intercept (b)

Find Slope

The formula to find slope m is: m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

We have x_{1}=1, x_{2}=2, y_{1}=3\ and \ y_{2}=5

Putting values in the formula to find slope

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{5-3}{2-1}\\m=\frac{2}{1}\\m=2

So, value of slope m is m=2

Find y-intercept

Using formula of slope-intercept formula we can find b

y=mx+b

Using point (1,3) (where x=1 ,y=3) and slope m=2

3=2(1)+b\\3=2+b\\b=3-2\\b=1

So, value of y-intercept b is: b=1

Required equation in Slope Intercept Form

We have slope m = 2 and y-intercept b=1

y=mx+b\\y=2x+1

So, equation in slope-intercept form that represents the line that passes through  the points (1,3) and (2,5) is y=2x+1

3 0
3 years ago
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