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gogolik [260]
3 years ago
8

Please solve and show work! Thanks!

Mathematics
2 answers:
notsponge [240]3 years ago
6 0

Answer:

1) x < 1, x > 9

2) 2 < x ≤ 6, -4 ≤ x < 0

Step-by-step explanation:

1) lx - 5l > 4

x - 5 = 4

x = 9

-(x - 5) = 4

x = -4 + 5 = 1

x < 1, x > 9

3) 1 < lx-1l ≤ 5

1 < x-1 ≤ 5

2 < x ≤ 6

1 < -(x-1) ≤ 5

-5 ≤ x-1 < -1

-4 ≤ x < 0

OleMash [197]3 years ago
3 0

Answer:

1  x<1  or x>9

2 -4 ≤ x < 0  or 2 < x ≤ 6  

Step-by-step explanation:

1) lx - 5l > 4

When we have absolute values, we end up with 2 inequalities, one positive and one negative.  Remember when we have the negative inequality we have to flip the inequality symbol

x - 5 > 4      or         x - 5 <- 4

We use or since the absolute value is on the greater than side

Add 5 to each side

x - 5+5 > 4+5    or          x - 5+5 <- 4+5

x>9                  or                       x < 1

3) 1 < lx-1l ≤ 5

We will again have 2 equations , one positive and one negative (remembering to flip the inequalities on the negative)

1 < x-1 ≤ 5    or   -1 > x-1 ≥ -5

Add 1 to all sides

1+1 < x-1+1 ≤ 5+1    or  -1+1 > x-1+1 ≥ -5+1

2 < x ≤ 6          or          0 > x  ≥ -4

Rewriting

-4 ≤ x < 0  or 2 < x ≤ 6    

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Answer:

-(x-8)(x+6)

Step-by-step explanation:

-x^2+2x+48

-(x^2-2x-48)

-(x-8)(x+6)

The trick is to find two numbers that when they multiply, you get the third term, which in this case, is -48. And when you add those two numbers, you get the second term, which is -2 in this case. The two numbers in this case are -8 and 6.

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3 years ago
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Miss Lopez had 618 and 5400s in her checking account she deposits 50 and 2500 into her account how much will she have left in he
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4 years ago
2) Evaluate 9 X 364 – 9 X 125 – 9 X 39 without the use of your calculator
Brums [2.3K]

Answer:

<em>9*364 - 9*125 - 9*39 = 1,800</em>

Step-by-step explanation:

<em>Mental Calculation</em>

If we detect known patterns in the calculations, we could easily give their results without the use of calculators.

We are given the expression to evaluate:

9*364 - 9*125 - 9*39

The first thing to note is the 9 is a common factor of all terms, thus we take it out:

9*(364 - 125 - 39)

The negative numbers can be easily added

     125

+     39

------------

     164

Now our expression is much easier:

9*(364 - 164)

The subtraction of 364-164 is 200, thus the result of the operations is:

9*200. We only need to recall 9*2=18 and add two zeros to get 1,800, thus:

9*364 - 9*125 - 9*39 = 1,800

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3 years ago
PLS HURRY AND HELP ME Larry buys peanut butter and bananas at the grocery store. He spends $3.89 on peanut butter and $9.38 in a
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Answer:

x = $5.49 cost of the bananas

Step-by-step explanation:

x = cost of the bananas

$3.89 = cost of the peanut butter

$ 9.38 is the cost of both

Bananas + peanut butter = $9.38

    x         +   $3.89           =   $9.38

   <u>             - $ 3.89            =  -$3.89      </u>    Subtract $3.89 from both sides

      x                                 =  $5.49  

5 0
3 years ago
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