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Schach [20]
3 years ago
14

Simplify. Remember to write the powers as a positive number.

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0
1. 1/a^8 (Sorry I can't find out what the others are)      
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Which expression is equivalent to the given expression after using the distributive property?
Jobisdone [24]

Answer:

Last one I think

Step-by-step explanation:

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What is the slope of the line that passes through the points (4, 8) and (-3, 1)?
blondinia [14]

Answer:

1

Step-by-step explanation:

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3 years ago
Analyze the diagram below and complete the instructions that follow. Find the area of QRS.
11Alexandr11 [23.1K]

<u>Answer-</u>

<em>The area of QRS is </em><em>238.7</em><em> sq units.</em>

<u>Solution-</u>

According to properties of supplementary angles,

m\angle R+124=180\\\\m\angle Q+132=180

So,

\Rightarrow m\angle R=180-124=56,\ m\angle Q=180-132=48

As the sum of measurement of all the angles in a triangle is 180, so

\Rightarrow m\angle S+m\angle R+m\angle Q=180

\Rightarrow m\angle S=180-m\angle R-m\angle Q

\Rightarrow m\angle S=180-56-48=76

Then the area of the triangle will be,

\text{Area}=\dfrac{1}{2}qr\sin S

=\dfrac{1}{2}\times 21\times 23.43\times \sin 76

=238.7\text{sq.units}

8 0
3 years ago
What multiplies to 30 but adds to -7
FinnZ [79.3K]

10 * 3

hope I helped :)

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3 years ago
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(a) Let R = {(a,b): a² + 3b &lt;= 12, a, b € z+} be a relation defined on z+)
grin007 [14]

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

4 0
2 years ago
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