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dalvyx [7]
3 years ago
15

A. Describe the universal set and subset shown in the figure below Universal set Subset​

Mathematics
1 answer:
muminat3 years ago
8 0

Set theory is the mathematical study of sets, which are well defined object collections

The description of the universal set and subset are as follows;

Universal set: \bigcup = {x ∈ N | 0 < x < 8} = { 1, 2, 3, 4, 5, 6, 7}

Subset: Set A = {x ∈ N | 0 < x < 8, x is odd} = {2, 4, 6 }

The reason the above values are correct are as follows;

The universal set, \bigcup is the set containing without repetition the elements of all sets that is related to it

From the diagram in the question, we have;

Universal set:

The universal set has all elements in the rectangular enclosed area, which are natural numbers, <em>N</em>, larger than 0, but less than 8

Therefore, we have;

  • Universal set: \bigcup = {<u>1, 2, 3, 4, 5, 6, 7</u>}, which is the set of natural numbers between 1 and 7

∪ = {x ∈ N | 0 < x < 8}

Subset:

A set <em>A</em> which is a subset of a set <em>B</em> is such that all the set <em>B</em> has all the elements of the set <em>A</em>

A subset is given by the set of elements enclosed in the circular area, which is a located within in the rectangular figure representing the universal set and , which is the set of all even natural numbers, <em>N</em>, larger than 0, but less than 8

Therefore, we have;

  • Subset: Set A = {<u>2, 4, 6</u> }, which is the set of even numbers between 1 and 7

A = {x ∈ N | 0 < x < 8, x is odd}

Learn more about about set theory here:

brainly.com/question/16823768

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<h3>Answer: choice A) </h3><h3>tan(Y) = 6/7 and tan(Z) = 7/6</h3>

Recall that the tangent of an angle is equal to the ratio of the opposite over adjacent sides

tan(angle) = opposite/adjacent

For reference angle Y, the opposite side is XZ = 6 and the adjacent side is XY = 7, so,

tan(Y) = XZ/XY = 6/7

For tan(Z), things will swap. The opposite side is now XY = 7 and the adjacent side is now XZ = 6

tan(Z) = XY/XZ = 7/6

We do not use the hypotenuse sqrt(85) at all in this problem because the tangent ratio does not involve the hypotenuse.

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Step-by-step explanation:

This is an obtuse isosceles triangle because it has two congruent sides, making it an isosceles triangle, and there is an obtuse angle, which is any angle greater than 90°.

The interior angles of a triangle add up to 180, so let's make an equation.

132+2x=180

Then solve for x

subtract 132 from both sides

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Divide by 2 on both sides

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Which of the following expression is equivalent to
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Step-by-step explanation:

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Answer the following
Amanda [17]

The set A satisfying the given inequality is A = (-\infty, -10].

<h3>What are some properties of an inequality relation? </h3>

Following are some facts which are true for an inequality relation:

  • Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.
  • The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.

\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)

Since y ∈ B, -2 ≤ y ≤ 7. So,

\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\;  y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, \infty) i.e.

10 ≤ -x ≤ \infty.

Multiplying -1 throughout gives

-10 ≥ x ≥ -\infty.

x, thus, lies in the range A = (-\mathbf{\infty}, -10}.

Learn more about the inequality here.

brainly.com/question/17801003

Disclaimer: The question was incomplete. Please find the full content below.

<h3>Question </h3>

Find the set A such that for x ∈ A

\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

#SPJ4

4 0
2 years ago
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