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4 years ago

Solve by factoring 4x^2-25=0

1 answer:

3 0

   4x² - 25 = 0
      4x² - 10x + 10x - 25 = 0
2x(2x) - 2x(5) + 5(2x) - 5(5) = 0
      2x(2x - 5) + 5(2x - 5) = 0
   (2x + 5)(2x - 5) = 0
   2x + 5 = 0 U 2x - 5 = 0
       - 5 - 5 + 5 + 5
       2x = -5    2x = 5
      2 2 2    2
   x = -2¹/₂    x = 2¹/₂

Solution Set: {-2¹/₂, 2¹/₂}

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HURRY PLEASE!!!!! Triangle RST is translated 2 units left and then reflected over the y-axis.

AVprozaik [17]

Answer:

The correct options are 1 and 2.

Step-by-step explanation:

The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).

If triangle translated 2 units left,

$(x,y)\rightarrow (x-2,y)$

and then reflected over the y-axis,

$(x-2,y)\rightarrow (-x+2,y)$

The relation between image and preimage is

$(x,y)\rightarrow (-x+2,y)$ ..... (1)

The vertices of image are

$S(-4,4)\rightarrow S'(6,4)$

$T(-1,4)\rightarrow T'(3,4)$

$R(-1,1)\rightarrow R'(3,1)$

Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).

1. A reflection over the y-axis and then a translation 2 units right is defined as

$(x,y)\rightarrow (-x+2,y)$

It is equivalent to relation 1, therefore option 1 is correct.

2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as

$(x,y)\rightarrow (-x+2,y)$

It is equivalent to relation 1, therefore option 2 is correct.

3. A reflection over the y-axis and then a translation 2 units left is defined as

$(x,y)\rightarrow (-x-2,y)$

It is not equivalent to relation 1, therefore option 3 is incorrect.

4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as

$(x,y)\rightarrow (-x-2,y)$

It is not equivalent to relation 1, therefore option 4 is incorrect.

5. A reflection over the x-axis and then a translation 2 units right is defined as

$(x,y)\rightarrow (x+2,-y)$

It is not equivalent to relation 1, therefore option 5 is incorrect.

6. A reflection over the x-axis and then a translation 2 units left is defined as

$(x,y)\rightarrow (x+2,-y)$

It is not equivalent to relation 1, therefore option 6 is incorrect.

Therefore the correct options are 1 and 2.

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Since Timmy is helping his grandpa on his chicken farm, and he has to pack 66 eggs into cartons, minimizing the packing cost, and he can use 12-egg cartons and 6-egg cartons, and two 12-egg cartons cost as much as three 6-egg cartons, to determine how many cartons of each should be used, the following calculation must be performed:

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