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Margarita [4]
3 years ago
11

The image of F(-5,-9) after translating along <4, 6 > and then translating along < 3, 5> is? F’(?,?)

Mathematics
1 answer:
dusya [7]3 years ago
5 0
<h3>Answer:  (2, 2)</h3>

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

Explanation:

The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"

In general, "translated along <m,n>" is the same as writing (x,y) \to (x+m, y+n). If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.

-------------

With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.

We can say

(x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\

Showing that (-5,-9) moves to (-1,-3)

This is after the first translation, but there's a second translation.

We'll apply the same idea, but different numbers this time

(x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\

So (-1,-3) moves to (2,2)

Overall we have

  • (-5,-9) move to (-1,-3) after the first translation
  • (-1,-3) move to (2,2) after the second translation

Therefore, the original point ends up at (2,2) which is the final answer

--------------

Extra info:

A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.

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a rectangular plot of land 8m long and 6m wide.there is a flower bed in the form of a circle of radius 3m.find 1.area of land. 2
mixer [17]

Answer:

1)Area of the Land  is 48 square meters

2) Area of flower bed   is  28.26 square meter

3)Area of land excluding flower bed   is 19.74 square meters

4)cost of planting grass in land  excluding flower bed   is Rs 118.44

Step-by-step explanation:

Given:

Length of the Rectangular plot = 8m

Width of the rectangular plot =  6m

Radius of the circular flower bed = 3m

1)Area of the Land  

Area of the Rectangular plot  = Area of the Land  

Area of the Land   = length x width

Area of the Land   =  8*6

Area of the Land  = 48 square meters-----------------------------(1)

2. Area of flower bed

Area of flower bed =  4 x area of one quadrant

Area of flower bed =  area of the circle

Area of flower bed  = \pi r^2

where r is the radius

Now , substituting the values

Area of flower bed = \pi (3)(3)

Area of flower bed = 28.26 square meters-----------------------------(2)

3)Area of land excluding flower bed

Area of land excluding flower bed =  Area of the rectangular land - area of flower beds

Area of land excluding flower bed =  48 - 28.26

Area of land excluding flower bed = 19.74 square meters

4)cost of planting grass in land

Cost of planting grass per square meter = 6

Excluding the flower bed we have  19.74 square meters. to plant grass  for this 19. 74 square meters, the cost will be

=19. 74 \times 6

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3 years ago
PLEASE HELP Find the product. (n³)² • (n⁵)⁴​
Papessa [141]

Answer:

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Step-by-step explanation:

Raising something to a power to a power simply simply multiplies the two exponents

(n^3)^2 = n^6

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Zina [86]
Solve the following system using substitution:
{y + 2.3 = 0.45 x
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In the second equation, look to solve for y:
{y + 2.3 = 0.45 x
{-2 y = -3.6

-3.6 = -18/5:
-2 y = -18/5

Divide both sides by -2:
{y + 2.3 = 0.45 x
{y = 9/5

Substitute y = 9/5 into the first equation:
{4.1 = 0.45 x
{y = 9/5

In the first equation, look to solve for x:
{4.1 = 0.45 x
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4.1 = 41/10 and 0.45 x = (9 x)/20:
41/10 = (9 x)/20

41/10 = (9 x)/20 is equivalent to (9 x)/20 = 41/10:
{(9 x)/20 = 41/10
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Answer:  {x = 82/9
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