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zimovet [89]
4 years ago
15

If DE = 4x + 10, EF = 2x-1, and DF = 9x-15, find DF

Mathematics
2 answers:
Komok [63]4 years ago
6 0
DE = 4x + 10

EF = 2x -1

DF = DE + EF = 4x + 10 + 2x - 1 = 6x + 9

Given,

DF = 9x - 15

6x + 9 = 9x - 15

3x = 24

x = 8

Hence, DF = 9x - 15 = 9*8 - 15 = 72 - 15 = 57
Dmitrij [34]4 years ago
5 0
Hello,
<span>We have that:
(4x+10)+(2x-1)=9x-15

</span>We solve the equation:
4x+10+2x-1=9x-15;
6x+9=9x-15;
6x-9x=-15-9;
-3x=-24;
3x=24;

<span>from which
</span>x=24:3=8

<span>Then:
DF=9x-15=(9</span>×8)-15=72-15=57

bye :-)
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Answers:

  1. C) x = plus/minus 11
  2. B) No real solutions
  3. C) Two solutions
  4. A) One solution
  5. The value <u>  18  </u> goes in the first blank. The value <u>  17  </u> goes in the second blank.

========================================================

Explanations:

  1. Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
  2. There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
  3. The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
  4. We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
  5. Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
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Price-club sells a 12-ounce package of spaghetti noodles for $3.44 and Shop Mart sells a 2-pound box of spaghetti noodles for $8
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The unit price per ounce at Price club is $0.29 and the unit price per ounce at Shop Mart is $0.26

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Price of 12 ounce package at Price Club = $3.44

Unit rate per ounce = \frac{Price\ of\ package}{Weight\ of\ package}

Unit rate per ounce = \frac{3.44}{12} = \$0.29

Price of 2 pound box at Shop Mart= $8.35

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2 pound = 16*2 = 32 ounces

Unit rate per ounce = \frac{Price\ of\ package}{Weight\ of\ package}

Unit rate per ounce = \frac{8.35}{32} = \$0.26

The unit price per ounce at Price club is $0.29 and the unit price per ounce at Shop Mart is $0.26

Keywords: unit rate, division

Learn more about division at:

  • brainly.com/question/4401748
  • brainly.com/question/4459688

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