Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math. Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she dances every day (y). (5 points) Part B: How much time does Pam spend practicing math every day? Show your work. (3 points) Part C: Is it possible for Pam to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)

Part A)

x+y=80

y=x+20

B)

30 minutes

C)

no

If Pam was to spend 60 minutes practicing dance, then she would only get 20 minutes of math. 60-20=40. She would be practicing dance 40 minutes more than math, not just 20.

see below

Step-by-step explanation:

x- time spent on math and y- time spent on dancing

Total time 80 minutes a day

Part A:

The equations:

x+y= 80

y-x= 20

Part B:

Using the pair of equations above, when adding them up we get:

2y= 100 ⇒ y= 50 min dancing

and

x= 80- 50 =30 min math

Part C:  

if y= 60 and x= 60 -20= 40

then total time spent would be 100 min, which is more than 80 minutes

So answer is no, it is not possible

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).