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3 years ago

What is the answer to this equation

Mathematics

1 answer:

julia-pushkina [17]3 years ago

6 0

Answer:

$x = - \frac{494}{3}$ $= - 164\frac{2}{3}$

Step-by-step explanation:

$75 + \frac{3}{8} x = 13\frac{1}{4}\\\\75 + \frac{3}{8} x = \frac{53}{4}\\\\\frac{3}{8}x = \frac{53}{ 4} - 75\\\\\frac{3}{8}x = \frac{53-300}{4}\\\\\frac{3}{8}x = - \frac{247}{4}\\\\x = -\frac{247 \times 8}{4 \times 3} \\\\x = -\frac{494}{3}$

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Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation $(x+0,y-2)$ will map vertices of the square into points

$(2,1)\rightarrow (2,-1);$
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2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

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These points are exactly the vertices of the initial square.

Consider option B.

1st transformation $(x+2,y-0)$ will map vertices of the square into points

$(2,1)\rightarrow (4,1);$
$(1,2)\rightarrow (3,2);$
$(2,3)\rightarrow (4,3);$
$(3,2)\rightarrow (5,2).$

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

$(4,1)\rightarrow (2,1);$
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These points are exactly the vertices of the initial square.

Consider option C.

1st transformation $(x+3,y+3)$ will map vertices of the square into points

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$(1,2)\rightarrow (4,5);$
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2nd transformation = reflection over y = -x + 7 will map vertices into points

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These points are exactly the vertices of the initial square.

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1st transformation $(x-3,y-3)$ will map vertices of the square into points

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$(3,2)\rightarrow (0,-1).$

2nd transformation = reflection over y = -x + 2 will map vertices into points

$(-1,-2)\rightarrow (4,3);$
$(-2,-1)\rightarrow (3,4);$
$(-1,0)\rightarrow (2,3);$
$(0,-1)\rightarrow (3,2)$

These points are not the vertices of the initial square.

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