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2 years ago

14

2/3 + -1/16= What is the fraction?

1 answer:

Marrrta [24]2 years ago

5 0

Find a common denominator for the two fractions to be able to combine them.
Let's use 48.

Multiply both parts of 2/3 by 16, then multiply both parts of -1/16 by 3.
32/48 + -3/48

This is the same as subtracting the second fraction from the first, so let's write it like that.
(32-3)/48
29/48

Since 29 is a prime number, the fraction cannot be reduced, so that is the final answer.

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3 years ago

Quadrilateral P'Q'R'S' is a dilation of the quadrilateral PQRS, with the origin as the center of dilation.

liraira [26]

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The rule used to create this dilation is 0.5

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2 years ago

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2 years ago

On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.

$P(x,y)$ - Original point.

$k$ - Scale factor.

$P'(x,y)$ - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

( $P(x,y) = (10, 40)$ , $Q(x,y) = (70, 120)$ , $O(x,y) = (0,0)$ , $k = 5$ )

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$

$P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]$

$P'(x,y) = (50,200)$

$Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]$

$Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]$

$Q'(x,y) = (350, 600)$

Then, the length of the resulting segment is determined by following Pythagorean identity:

$l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}$

$l_{P'Q'} = 500$

The length of the resulting segment is 500.

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2 years ago