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choli [55]
3 years ago
12

What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round u

p if the value of the hundredth is 5 or greater.
Triangle H G F has a base of 6.5 centimeters and a height of 3.0 centimeters.

cm2
Mathematics
1 answer:
denpristay [2]3 years ago
7 0

Answer:

9.8

Step-by-step explanation:

The formula for the area of a triangle is a=bh/2, where a is area, b, is the base, and h is the height. If we substitute the values in the question in the equation, we get:

a=(6.5*3)/2

a=19.5/2

a=9.75

a≈9.8

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(a) Let R = {(a,b): a² + 3b <= 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
Q2. Do as directed(You can solve on a piece of paper and send picture in assignment) (4)
zepelin [54]

Step-by-step explanation:

true equation when x is replaced by 2, and is a false ... is written in terms of P, R, and T.” In some cases, before using a formula it may be ... (2) a number line graph, or (3) interval notation.

8 0
2 years ago
Find an equation of the tangent line to the curve <br> xey + yex = 5
Harman [31]
I got:

<span>y′=(−y<span>e^−x</span>−e^y)/xe^y+e^x</span>
then plugged in x and y and got slope of (-5-e^5)
and ended with equation of y=(-5-e^5)x+5

I'm not sure with my solution though i hope this might help you.

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
8 0
3 years ago
B) Imagine that you earned $8.425 in one year. If the government enforce
Eddi Din [679]

Answer:

take the tax %, divide by 100, and multiply by 8,425.

Step-by-step explanation:

Take the tax %, divide by 100, and multiply by 8,425.

8 0
3 years ago
D is the same as 359 more than the product of 344 and d<br>write the sentence as an equation ​
nignag [31]

Answer:

d = 359 + 344d

Step-by-step explanation:

d = 359 + 344d

7 0
3 years ago
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