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wlad13 [49]
2 years ago
5

Math test pls help me

Mathematics
1 answer:
Natalija [7]2 years ago
3 0

Answer:

D. \frac{45}{x^{10}}

Step-by-step explanation:

(3 {x}^{ - 4} )^{2} (5 {x}^{ - 2} ) \\  \\  = (9 {x}^{ - 8} )(5 {x}^{ - 2} ) \\  \\  = 9 \times 5 \times  {x}^{ - 8 - 2}  \\  \\  = 45 {x}^{ - 10}  \\  \\  =  \frac{45}{ {x}^{10} }

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2 years ago
PLZ HEEEELP!!!!! 10 POINTS!!!!
katrin2010 [14]

Answer:

Step-by-step explanation:

Part a

We need two inequalities, one for time worked at each job and the other

for amounts of money earned.

time:  Let b and c represent the time (number of hours) worked at babysitting and landscaping respectively.  Then b + c ≤ 20 hrs/wk

earnings:  Let ($3/hr)(b) represents the amount of money earned babysitting for b hour.  Let  ($7/hr)(c) represent the money earned working at landscaping.  These amounts are <em>per week</em>.  The appropriate inequality is  ($3/hr)(b) +  ($7/hr)(c) ≥ $84 per week.  The other inequality is

b + c ≤ 20 hrs/wk.

Part b:

As before, b + c ≤ 20 hrs/wk.  What happens if Chet spends all his 20 hours babysitting?  To answer this, set c = 0 (no landscaping hours).  Then b ≤ 20 hours.  At $3/hr, he could earn only $60 and have no time left for landscaping.  Not good.

Let's experiment:  suppose he works 15 hours babysitting and 5 hours landscaping.  His earnings would be $45 + $35, or $80.  Still not enough; he wants to earn $84 total.    Let's redistribute his time and try again:  suppose he works 14 hours babysitting and 6 hours landscaping; his earnings would be $42 + $42, or $84.  So {b = 14 hours and c + 6 hours} is a solution.  As we continue to reduce the number of hours Chet works babysitting and correspondingly increase those he works landscaping, his earnings will go up, beyond $84.

Here's a table that summarizes this:

babysitting          landscaping    total amount

  hours                   hours               earned

      15                          5                      $60 (not acceptable)

       14                         6                       $84 (borderline acceptable)

       12                          8                       $36 + $42 = $78 (great)

        6                          14                       $116 (greater still)

         2                          18                     $132

          1                           19                      $134

          0                          20                      $140

Summary:  Chet can work anywhere from 0 to 14 hours babysitting and expect to earn $84 or more.

4 0
3 years ago
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