The cost of 5 dresses and 2 belts is $48. The cost of 3 dresses and 2 belts is $32. Find the cost of a dress and a belt. Let x denote the cost of a dress and y denote the cost of a belt. A: x = $8, y = $4
B: x = $5, y = $4
C: x = $7, y = $10
D: x = $4, y = $5

Step-by-step explanation:

• 5X + 2Y = 48

• 2Y = 48 - 5X

let's use this and replace it on the second equation

• 3X + 2Y = 32

• 3X + 48 - 5X = 32

• 3X - 5X = 32 - 48

• -2X = -16

• X = 8

now use the X value we found to find the Y

• 5X + 2Y = 48

• 5*8 + 2Y = 48

• 40 + 2Y = 48

• 2Y = 48-40

• Y = 8/2

• Y = 4

A: x = $8, y = $4

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}

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step-by-step explanation: