State whether the given measurements determine zero, one, or two triangles. A=35°, a=6, b=13

Answers

Answer 1

Answer: If we were to use the sine law we would get

sin(B) / b = sin(A) / a ----> sin(B) = b*sin(A)/a = 13*sin(35)/6 = 1.24275 to 5 d.p..,

so since this is greater than 1 there can be 0 triangles with these dimensions,

as the range of the sine function is [-1,1].

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2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Answers

The true statement about the juan and lisa is Juan made a higher rate of pay than Lisa.

Juan made a lower rate of pay because he made less money.

This statement is false. Juan and Lisa made a similar rate of pay per hour ($14.80 and $14.00 respectively).

Lisa made a better rate of pay because she made more money.

This statement is false. The total earnings do not determine the rate of pay; the hourly rate does.

Lisa said she made a better rate of pay because her rate was $14 an hour.

This statement is false. Lisa's actual rate was $14.00 per hour, not $14.00 as stated.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

This statement is true. Juan's hourly rate was $14.80, which is higher than Lisa's rate of $14.00 per hour.

To calculate the rate of pay, we divide the money earned by the hours worked.

Juan's rate of pay is $37.00 / 2.5 hours = $14.80 per hour.

Lisa's rate of pay is $42.00 / 3 hours = $14.00 per hour.

Therefore, Juan made a higher rate of pay than Lisa.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

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The following question may be like this:

Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

Lisa said she made a better rate of pay because her rate was $14 an hour.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Answer:

2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Lisa said she made a better rate of pay because her rate was $14 an hour.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

How does

h(x)=-(x-3)^2+4

compare to the graph

g(x)=x^2

Answers

Top equation opens down and the second opens up

You are walking down a road seeking treasure the real branches of into 3 paths a guard stands in each path you only know that only one of the girls is telling the truth and the other two are lying this is what they say guard one the treasure lies down this path guard to no treasure lies down this path seek elsewhere Garth 3 the first guard is lying

Answers

Answer:

Guard Two

Step-by-step explanation:

Guard two has the path to the treasure because he's telling people that there's no treasure. That makes him suspicious because he might want the treasure for himself

Final answer:

This is a logic puzzle wherein the guards' statements are evaluated based on the given criteria: only one guard is truthful. Upon analysis, we find that only the path guarded by Guard 2 aligns with this criteria, indicating that this is the path you should take to find the treasure.

Explanation:

This is a classic logic problem, often called the 'Liar and Truth-Teller' puzzle. Here's how we can tackle it:

Guard 1 says: 'The treasure lies down this path.'

Guard 2 says: 'No treasure lies down this path, seek elsewhere.'

Guard 3 says: 'The first guard is lying.'

Since we know that only one guard is telling the truth, let's consider if Guard 1 tells the truth. If so, Guard 2 and Guard 3 would be lying, which contradicts the statement of Guard 3 (who confirms Guard 1's statement as a lie).

If Guard 2 is telling the truth (which means there's no treasure on his path), then both Guard 1 and Guard 3 would be lying, which fits our criteria.

If Guard 3 told the truth, this would mean that Guard 1 is lying, but then Guard 2 would also be telling the truth--this contradicts our initial information (only one guard is truthful).

So, based on these evaluations, you should take the path guarded by Guard 2 because he's the only one telling the truth according to the given criteria.

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Construct a polynomial function with the following properties: fifth degree, −2 is a zero of multiplicity 2, 4 is the only other zero

Answers

5th degree means highest power is 5 total

zeroes/roots are
(x-r)
so -2 is a root
(x-(-2))
(x+2) is a root
multiplicity 2 means it happens 2 times ie
(x+2)^2
e
4 is the only other zero
(x-4)

so now we have
(x-4)(x+2)^2
but that is only 3rd degreed
I could add 2 more degrees that are complex roots and therefor won't be graphed on the plane since they are complex so
find a 2nd degree polynomial that has only complex roots
a complex 2nd degree polynomial
x^2+x+10

ok so this is the function
f(x)=(x-4)(x+2)^2(x^2+x+10)

Which property can be used to show that if 3a = 4b, then 4b = 3a?