Answer:
1. 83.6
2. 24
3. 95/2
4. 3
5. 30
6. 84.5
Step-by-step explanation:
Answer:
First, plug-in x and y as 3sinθ-2 and 3cosθ+4 into the equation, respectively:

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

We can factor out 3^2 = 9 from both equations:

We know from a trigonometric identity that
, meaning we can reduce the equation to:


And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sinθ-2 and y=3cosθ+4.
Hope this helped you.
The answer is D) Yes; because x and y must be integers, and integers are rational.
Answer:
<em>In 5 years the product of their ages will be 208</em>
Step-by-step explanation:
The age of two children is 11 and 8 years.
Let's call x the number of years ahead.
We need to find when the product of their future ages is 208. The 11 years old child will be 11+x years old and the other child will be 8+x years, thus:
(11+x)(8+x)=208
Operating:

Simplifying:

Factoring:
(x-5)(x+24)=0
Solving:
x=5, x=-24
The negative solution is not valid, thus x=5
In 5 years the product of their ages will be 208
Answer:
7/12
Step-by-step explanation:
Simplification is something we can do if both the numerator and denominator are divisible by the same number.
In 14/24, both numbers are divisible by 2.
So, we divide both the numerator and denominator by 2. We get 7/12.
Therefore 14/24 = 7/12.