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dusya [7]
3 years ago
6

Exercise

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0
X - nominator
y - denominator

\frac{3x}{y+12}=\frac{3}{4}\\
\frac{x+7}{3y}=\frac{1}{2}\\\\
3(y+12)=12x\\
2(x+7)=3y\\\\
3y+36=12x\\
2x+14=3y\\\\
2x+14+36=12x\\
10x=50\\
x=5\\\\
3y=2\cdot5+14\\
3y=10+14\\
3y=24\\
y=8\\\\
\frac{x}{y}=\boxed{\frac{5}{8}}
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Which of the following are solutions to the equation below?
scoundrel [369]

Answer:

The correct options for the solution values are:

  • x=2\sqrt{2}-5
  • x=-2\sqrt{2}-5

Step-by-step explanation:

Given the expression

x^2+10x+25=8

Subtract 25 from both sides

x^2+10x+25-25=8-25

Simplify

x^2+10x=-17

Add 25 or 5² to both sides

x^2+10x+5^2=8

as

x^2+10x+5^2=\left(x+5\right)^2

so the expression becomes

\left(x+5\right)^2=8

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solve

x+5=\sqrt{8}

Subtract 5 from both sides

x+5-5=2\sqrt{2}-5

x=2\sqrt{2}-5

solve

x+5=-\sqrt{8}

Subtract 5 from both sides

x+5-5=-2\sqrt{2}-5

x=-2\sqrt{2}-5

Therefore, the solution to the equation

x=2\sqrt{2}-5,\:x=-2\sqrt{2}-5

Hence, the correct options for the solution values are:

  • x=2\sqrt{2}-5
  • x=-2\sqrt{2}-5

6 0
3 years ago
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