(50 POINTS - WILL GIVE BRAINLIEST TO MOST HELPFUL ANSWER) I need help quickly-

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

x + 20 = y

Part B:

Pam spends 30 minutes practicing math every day.

Part C:

It is not possible for Pam to have spent 60 minutes practicing dance because this means she must have practiced math for 40 minutes (60 - 20 = 40). This would total out to 100 minutes of total practice, not 80 minutes. Therefore, this is impossible.

Step-by-step explanation:

Part A:

"She spends 80 minutes every day practicing dance and math."

x + y = 80

"She dances for 20 minutes longer than she works on math."

x + 20 = y

Part B:

Solve for x:

x + 20 = y

Isolate variable x:

x = y - 20

Plug in this new value for the first equation:

y - 20 + y = 80

Combine like terms:

2y - 20 = 80

Isolate variable y:

2y = 100

y = 50

Plug in the new value of y into any equation:

x + 50 = 80

Isolate variable x:

x = 30

Part C:

x + 20 = y

x + 20 = 60

x = 40

x + y = 80

40 + 60 = 80

100 = 80

Impossible.

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.

Solution given:

let math be x and dance be y.

She spends 80 minutes every day practicing dance and math.means:

x+y=80[I]

and

she dances for 20 minutes longer than she works on math.means:

y=x+20[2]

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).

Solution given:

solving equation [I]

x+y=80

x=80-y is a linear equation for x(math)

and

y=x+20 is a linear equation for y (dance)

Part B: How much time does Pam spend practicing math every day? Show your work. (3 points)

Substituting value of y in equation [I]

x+(x+20)=80

open bracket

x+x+20=80

subtract both side by 20

2x+20-20=80-20

2x=60

dividing both side by 2

2x/2=60/2

2x/2=60/2x=30min

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.

No it is not possible:

y=60

x+20=y[I]

substituting value of y

x=60-20

x=40

now

total =x+y=40+60=100

which is not equal to 80°

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.