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3 years ago

Solve each system by elimination

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

4 0

First equation 2(4X -5y = 4)
8X -10y = 8

Elimination 8x -10y =8
-8x + 9y =-8

-y =0
-1(-y =0)
y =0

8x -10(0) =8
8x =8
(8x =8)/8
x = 1

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A motorist drives from home to his office .The distance between his home and office is 32.27 km.After driving 15.65 km,he stoppe

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16.62 if rounded 17km

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3 years ago

write the x and y coordinate (in the second and third column, respectively) of dilation of quadrilateral ABCD with vertices A(1,

gayaneshka [121]

Answer:

The coordinates of the dillated vertices are $A'(x,y) = (2,2)$ , $B'(x,y) = (4,4)$ , $C'(x,y) = (8,2)$ and $D'(x,y) = (4,-2)$ .

Step-by-step explanation:

From Linear Algebra, we define dilation by the following equation:

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

Where:

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

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

$k$ - Scale factor, dimensionless.

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

If we know that $O(x,y) = (0, 0)$ , $k = 2$ , $A(x,y) = (1,1)$ , $B(x,y) = (2,2)$ , $C(x,y) = (4,1)$ and $D(x,y) = (2,-1)$ , then the dilated points are, respectively:

Point A

$A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]$ (2)

$A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)]$

$A'(x,y) = (2,2)$

Point B

$B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]$ (3)

$B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)]$

$B'(x,y) = (4,4)$

Point C

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

$C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)]$

$C'(x,y) = (8,2)$

Point D

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

$D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)]$

$D'(x,y) = (4,-2)$

The coordinates of the dillated vertices are $A'(x,y) = (2,2)$ , $B'(x,y) = (4,4)$ , $C'(x,y) = (8,2)$ and $D'(x,y) = (4,-2)$ .

4 0

3 years ago

The width of a rectangle is 15 ft. shorter than its length. Its perimeter is 262 ft. Let l equal the length of the rectangle.

masha68 [24]

Let the length be l.
For now, let's make the width be w.
Additionally, l = w + 15. Using this equation, width can also be written as l - 15.
The perimeter of a rectangle is length + length + width + width. This can also be written as l + l + (l-15) + (l-15) = l + l + l - 15 + l - 15 = 4l - 30.
Using this equation:
4l - 30 = 262
4l = 292
l = 73

4(w + 15) - 30 = 262
4w + 60 - 30 = 262
4w + 30 = 262
4w = 232
w = 58

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3 years ago

Which is the rationalized form of the expression. A, B , C, or D?

grin007 [14]

Answer:

Step-by-step explanation:

Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.

You get answer C.

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3 years ago

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dedylja [7]

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