To subtract 178-135 mentally carmine adds 5 to each number karen adds 2 to each number will both methods work to find the correct answer? why or why not?

  Yes

Step-by-step explanation:

Both methods will work. You can add or subtract any number you wish from both numbers and the result will be the same.

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Comment on the approach

By adding 5, Carmine makes the subtrahend have a units digit of 0, making the units digit of the answer easier to find.

By adding 2 to both numbers, Karen makes the minuend have a units digit of 0, so the units digit of the answer will be the 10's complement of 7. Depending on Karen's knowledge of arithmetic facts, this may be more work for her than Carmine's method is for Carmine.

Since all digits of the subtrahend are less than or equal to all digits of the minuend, no adjustment is needed and the subtraction can proceed directly.

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}

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.