Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas. Which equation represents the relationship between the number of cheese pizzas and the number of vegetable pizzas? Which equation represents the total number of pizza slices?

Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas.

Which equation represents the relationship between the number of cheese pizzas and the number of vegetable pizzas?

✔ c = 4v

Which equation represents the total number of pizza slices?

✔ 8c + 6v = 152

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}