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Sauron [17]
4 years ago
5

What is the scale factor for pre-image IJKH to image MNOL?

Mathematics
1 answer:
solniwko [45]4 years ago
5 0

Answer:

Step-by-step explanation:

Given are two rectangles MNOL and IJKH

MNOL is the image and IJKH is the preimage.

OBviously similarity is preserved between these.

Hence sides will be proportional

i.e. l1/l2 = w1/w2 = Scale factor k

This can also be written as

Scale factor square = k^2=\sqrt{ \frac{areaI}{area2} }

Scale factor = square root of ratio of rectangle areas

Find ratio as

\frac{375}{135} =\frac{25}{9}

k = Scale factor = square root of the above fraction

=\frac{5}{3}

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Answer:

  • The epicenter is ( - 2, 3)

Step-by-step explanation:

Let the epicenter be E(x, y).

Use the distance formula for each given distance:

  • AE² = (x + 2)² + (y - 5)² = 2²
  • BE² = (x - 2)² + (y - 3)² = 4²
  • CE² = (x + 2)² + (y + 4)² = 7²

Use the first and third equations, considering both have same term for x, and solve for y:

  • (y - 5)² - 4 = (y + 4)² - 49
  • y² - 10y + 25 - 4 = y² + 8y + 16 - 49
  • 18y = 54
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Substitute y into one of equations and solve for x:

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2 years ago
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fenix001 [56]

Answer:

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Step-by-step explanation:

5 0
3 years ago
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Use the long division method to find the result when x^3+7x^2+12x+6x 3 +7x 2 +12x+6 is divided by x+1x+1. If there is a remainde
Aliun [14]

Answer:

By long division (x³ + 7·x² + 12·x + 6) ÷ (x + 1) gives the expression;

x^2 + 5 \cdot x + 7 - \dfrac{1}{(x + 1)}

Step-by-step explanation:

The polynomial that is to be divided by long division is x³ + 7·x² + 12·x + 6

The polynomial that divides the given polynomial is x + 1

Therefore, we have;

\ \ \ \ \ \  \ \ \ \ \ \ x^2 + 5\cdot x + 7\\ (x + 1) \sqrt{x^3 + 7\cdot x^2 +12\cdot x + 6} \\\ {} \  {} \ {}  \  \ {} \  {} \ {}  \ {} \  {} \ {}   \ {}     \ \ x^3 + 2 \cdot x^2 \\\  \ \ \ {} \   \ {} \  {} \ {}   \  \ {} \ {} \  \   \ {} \  {} \ {}  \  \ {} \  {} \ {}  \ \ 5 \cdot x^2 + 12\cdot x + 6\\  \ {} \  {} \ {}    \ {} \  {} \ {}  \ \ {} \ {} 5 \cdot x^2 + 5\cdot x\\\ 7\cdot x+6\\7\cdot x+7\\-1

(x³ + 7·x² + 12·x + 6) ÷ (x + 1) = x² + 5·x + 7 Remainder -1

Expressing the result in the form q(x) + \dfrac{r(x)}{b(x)}, we have;

(x^3 + 7\cdot x^2 + 12 \cdot x + 6)\div (x + 1) =  x^2 + 5 \cdot x + 7 - \dfrac{1}{(x + 1)}

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Clara lends half her collection of formal attires to her sister, Susan. Clara then buys four more attires now, how many attires
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Answer:

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( as the number of formal attires originakly with Clara is not specified)

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