A

1003032107

Level: 
A
The average distance of the Moon from Earth is \( 3.84\cdot10^8\,\mathrm{m} \), and the average distance of Earth from the Sun is \( 1.5\cdot10^{11}\mathrm{m} \). How many times further is it from Earth to the Sun than from Earth to the Moon?
about \( 390 \) times
about \( 39 \) times
\( 3\,900 \) times
about \( 4 \) times

1003136406

Level: 
A
Choose the resulting form of the given equation after multiplying both sides by \( x^2+5x+6 \). \[ -1+\frac{x-2}{x+2}=\frac{1+x}{x^2+5x+6}-\frac x{x+3} \]
\( -x^2-5x-6+(x-2)(x+3)=1+x-x(x+2) \)
\( -1\left(x^2+5x+6\right)+(x-2)(x-3)=1+x-x(x-2) \)
\( -1\left(x^2+5x+6\right)+(x-2)(x+3)=1+x+x(x+2) \)
\( -x^2-5x-6+(x-2)(x+2)=1+x-x(x+3) \)

1003136405

Level: 
A
Choose the resulting form of the given equation after multiplying both sides by \( x^2-25 \). \[ 1+\frac x{5-x}=\frac{3+x}{x+5}+\frac x{x^2-25} \]
\( x^2-25-x(x+5)=(3+x)(x-5)+x \)
\( x^2-25+x(x+5)=(3+x)(x-5)+x \)
\( x^2-25-x(x-5)=(3+x)(x-5)+x \)
\( x^2-25+x(x-5)=(3+x)(x+5)+x \)

1003136403

Level: 
A
Choose the operation, which most effectively eliminates fractions from the equation. \[ \frac{2x}{x^2-25}+\frac{3+x}{5-x}=\frac{x+1}{x+5} \]
multiplying both sides by \( x^2-25 \)
multiplying both sides by \( (5-x)\left(x^2-25\right) \)
multiplying both sides by \( x^2+25 \)
multiplying both sides by \( (5-x)(x+5)\left(x^2-25\right) \)

1003136402

Level: 
A
Choose the operation, which most effectively eliminates fractions from the equation. \[ \frac2{x^2-9}+\frac3{3-x}=\frac{x+1}{2x} \]
multiplying both sides by \( 2x\left(x^2-9\right) \)
multiplying both sides by \( 2x\left(x^2-9\right)(3-x) \)
multiplying both sides by \( 2x^2-9 \)
multiplying both sides by \( 18x^2 \)

1003136401

Level: 
A
Choose the operation, which most effectively eliminates fractions from the equation. \[ 3+\frac2{x+4}=\frac1{3x+12} \]
multiplying both sides by \( 3x+12 \)
multiplying both sides by \( (x+4)(3x+12) \)
subtracting \( \frac2{x+4} \) from both sides
multiplying both sides by \( 12x \)

1103124503

Level: 
A
The picture shows graphs of functions: \[ \begin{aligned} f(x)&=\frac2x\text{, }x\in\left[\frac12;4\right], \\ g(x)&=\frac{-3}x\text{, }x\in\left[\frac12;4\right], \\ h(x)&=\frac4x\text{, }x\in\left[\frac12;4\right]. \end{aligned} \] Choose the correct statement.
The function \( f \) is graphed in blue and the function \( h \) is graphed in green.
The function \( g \) is graphed in red and the function \( f \) is graphed in green.
The function \( f \) is graphed in green and the function \( h \) is graphed in blue.
The function \( g \) is graphed in green and the function \( f \) is graphed in blue.