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crimeas [40]
2 years ago
6

Please help me simplify the expression and please show work!!! <3

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
8 0

Step-by-step explanation:

\frac{x + 4}{3 {x}^{2}   - 12x - 96}  =  \frac{x + 4}{3( {x}^{2} - 4x - 32) }  =  \frac{x + 4}{3(x - 8)(x + 4)}

=  \frac{1}{3(x - 8)}  =  \frac{1}{3x - 24}

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A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens an
Mkey [24]

Answer:

  • <u>120 pens and 200 pencils.</u>

<u></u>

Explanation:

You can set a system of two equations.

<u>1. Variables</u>

<u />

  • x: number of pens
  • y: number of pencils

<u>2. Cost</u>

  • <em>each pen costs</em> $1, then x pens costs: x
  • <em>each pencil costs</em> $0.5, then y pencil costs: 0.5y

  • Then, the total cost is: x + 0.5y

  • The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

<u>3. </u><em><u>There were 80 more pencils than pens</u></em>

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

<u>4. Solve the system</u>

i) Substitute the equation (2) into the equation (1):

  • x + 0.5(80 + x) = 220

ii) Solve

  • x + 40 + 0.5x = 220
  • 1.5x = 180
  • x = 180/1.5
  • x = 120 pens

iii) Substitute x = 120 into the equation (2)

  • y = 80 + 120
  • y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

6 0
2 years ago
What are the missing angles? What is the relationship between the measures of supplementary angles?
goldenfox [79]

Answer:

6=100°

8=80°

7=100°

9=80°

Step-by-step explanation:

If 6 is 100°

in a straight line theres 180 degrees

180-100=80°

8 is 80°

opposite 6 to 7 there are parallel corresponding angles meaning the angle opposite it will be the same. 8 with 9.

same with

5 0
3 years ago
LXISSUU<br> Simplify<br> -8-1+4.2<br> Enter your answer in the box
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Answer:

-4.8

Step-by-step explanation:

4 0
3 years ago
A property was assessed at 25% of value with a tax rate of $12 per hundred. if the taxes totaled $11,400, what was the value? 1
shusha [124]

11400 ÷12 = 950 hundreds

95000 x 100/25 = $380,000 <== value of the property

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Molly has (4x+10)dollars and rod has (20-5x)dollars.
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what's the question?

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