PLEASE HELP ASAP WILL MARK BRAINLIEST, SIMPLE MATH PROBLEM

Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How

mylen [45]

Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

$D=C+4...(1)$

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be $D+3$ and $C+3$ respectively.

We can represent this information in an equation as:

$D+3+C+3=13...(2)$

From equation (1), we will get:

$C=D-4$

Upon substituting this value in equation (2), we will get:

$D+3+D-4+3=13$

Combine like terms:

$2D+2=13$

$2D+2-2=13-2$

$2D=11$

$\frac{2D}{2}=\frac{11}{2}$

$D=5.5$

Therefore, Robert's dog is 5.5 years old right now.

3 0

3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so: