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avanturin [10]
2 years ago
10

In the rectangular coordinate system above the area of pqr is what fraction of the area of lmn

Mathematics
1 answer:
enot [183]2 years ago
3 0

In the rectangular coordinate system above the area of PQR is what fraction of the area of LMN

From the attached figure we find the area of PQR and area of LMN

WE know the formula for area of triangle = \frac{1}{2} * base * height

In the triangle PQR,

Base PR= 4

Height = distance between x- axis and point Q = 4

Area of the triangle PQR = \frac{1}{2} * 4 * 4 = 8

Similarly we find the area of LMN

In the triangle LMN,

Base LN= 12

Height = distance between x- axis and point M = 12

Area of the triangle LMN = \frac{1}{2} * 12 * 12 = 72

Hence , \frac{area PQR}{Area LMN} = \frac{8}{72} = \frac{1}{9}

Area of PQR = \frac{1}{9} of the area of LMN

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3a^2+4a^2+7a^2

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Factor out a^2

a^2(3+4+7)

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an engineer has a 54 inch wire that she has to cut into two pieces so that one piece is 8 inches shorter than the other find the
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Hey there!!

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Just number 7 would be fine but if you could also number 8 would help a lot​
BlackZzzverrR [31]

Answer:

7. r = -5

8. x = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

r + 2 - 8r = -3 - 8r

<u>Step 2: Solve for </u><em><u>r</u></em>

  1. Combine like terms:                    -7r + 2 = -3 - 8r
  2. Add 8r to both sides:                   r + 2 = -3
  3. Subtract 2 on both sides:            r = -5

<u>Step 3: Check</u>

<em>Plug in r into the original equation to verify it's a solution.</em>

  1. Substitute in <em>r</em>:                    -5 + 2 - 8(-5) = -3 - 8(-5)
  2. Multiply:                              -5 + 2 + 40 = -3 + 40
  3. Add:                                    -3 + 40 = -3 + 40
  4. Add:                                    37 = 37

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

<u>Step 4: Define equation</u>

-4x = x + 5

<u>Step 5: Solve for </u><em><u>x</u></em>

  1. Subtract <em>x</em> on both sides:                    -5x = 5
  2. Divide -5 on both sides:                      x = -1

<u>Step 6: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    -4(-1) = -1 + 5
  2. Multiply:                               4 = -1 + 5
  3. Add:                                     4 = 4

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

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