MATHEMATICS HIGH SCHOOL

Let p: A triangle is acute. Let q: A triangle is equilateral. If q is true, which statements must be true? Check all that apply. a.p ∨ q
b.p ∧ q
c. p → q
c.q → p
d. q ↔ p

Answers

Answer 1
Answer: "q is true" is a given statement. So q = T where T stands for T (while F is for false)

If the triangle is equilateral, then all three angles are 60 degrees. So the triangle is also acute. This makes statement p true as well. 

So p and q are both true logical statements. 

That makes p v q true. It's only false if BOTH are false but that's not the case here.

That makes p ∧ q true as well. BOTH statements are true, so the entire thing is true.

p --> q is true as well. This is only false if p were true leading to q being false. Again not the case.

In the other direction, q --> p is also true for similar reasons as the last explanation above.

q <--> p is true because p and q have the same truth value T

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In summary, every choice is true. 
Answer 2
Answer:

A statement is true if both p and q will be true.

As, given ,p: A triangle is acute

q: A triangle is equilateral.

p ∧ q→ p is true as well as q is true.

That is if triangle is acute it means it is equilateral is not possible, and  if triangle is equilateral it means it is acute angled triangle.So,this contradicts p∧q.

So, Option (c) q → p,  supports the two statement , that is if if triangle is equilateral it means it is acute angled triangle.

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Answers

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6
(
f
+
4
)
+
2
(
f
+
4
)

Answers

6(f+4) + 2(f+4)

Use the distributive property:

6f+24 + 2f + 8

Now combine like terms:

8f +32

The answer is 8f + 32

Answer:

8 f + 32

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30

B.
2

C.
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Answers

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A 135 degree central angle intersects a circle with a radius of 8in what is the length of the intersected arc?

Answers

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Step-by-step explanation:

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Answers

Answer:

First you can substitute y with the value of it. So -3x=(4x+17)+4. Once you've found x plug in that value in -3x and solve for y.
plug the first equation into the second
-3x = 4x+17 + 4
-7x = 21
x = -3

plug this value into the he first equation
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hello I am trying to figure out how much rent I would have to pay if I abated the rent 30%. My rent is $610.

Answers

If you were to get 30% backed off, lucky you !
You would then pay only the remaining 70%.

70% means 0.70

0.70 x $610 = $427
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