document.write( "Question 1133112: Algebra 2: Please help me understand to solve these problems. Thank you!\r
\n" ); document.write( "\n" ); document.write( "1. Factor completely: 3x2 - 75\r
\n" ); document.write( "\n" ); document.write( "2. A car travels for 2½ hours and covers a
\n" ); document.write( "distance of 125 miles. What was the
\n" ); document.write( "car’s average speed?\r
\n" ); document.write( "\n" ); document.write( "3. If f(x) = 2x - 3, g(x) = x2, and
\n" ); document.write( "h(x) = !3x, find (g f h )(2).\r
\n" ); document.write( "\n" ); document.write( "4. Factor: 15x2 + 7x - 36\r
\n" ); document.write( "\n" ); document.write( "5. Find the zeros of the polynomial
\n" ); document.write( "function f(x) = 15x2 + 7x - 36.\r
\n" ); document.write( "\n" ); document.write( "6. If g(x) = 5x + 6, find g -1(x) solved for y.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #750287 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "1. Factor completely: \r
\n" ); document.write( "\n" ); document.write( " $\"3x%5E2+-+75+\"$
\n" ); document.write( " $\"3x%5E2+-+3%2A25+\"$
\n" ); document.write( " $\"3%28x%5E2+-+25+%29\"$
\n" ); document.write( " $\"3%28x%5E2+-+5%5E2+%29\"$
\n" ); document.write( " $\"3%28x+-+5+%29%28x%2B5%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. A car travels for $\"2\"$ $\"1%2F2\"$ = $\"2.5\"$ hours and covers a distance of $\"125\"$ miles. What was the car’s average speed? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"distance=+speed%2Atime\"$ \r
\n" ); document.write( "\n" ); document.write( "given:\r
\n" ); document.write( "\n" ); document.write( " $\"distance=125mil\"$
\n" ); document.write( " $\"time+=2.5h\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"125mil=+speed%2A2.5h\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"speed=125mil%2F2.5h\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"speed=50%28mil%2Fh%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "3. If $\"f%28x%29+=+2x+-+3\"$ , $\"+g%28x%29+=+x%5E2\"$ , and $\"h%28x%29+=+3x\"$ , find $\"%28g+f+h+%29%282%29\"$ .=> I guess you have product here\r
\n" ); document.write( "\n" ); document.write( " $\"+%28g+f+h+%29%28x%29=g%28x%29%2Af%28x%29+%2Ah%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+%28g+f+h+%29%28x%29=x%5E2%2A%282x+-+3%29+%2A3x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%28x%29=3x%5E3%2A%282x+-+3%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%28x%29=6x%5E4+-+9x%5E3\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x=2\"$ , we have \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%282%29=6%2A2%5E4+-+9%2A2%5E3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%282%29=6%2A16+-+9%2A8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%282%29=96+-+72\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28g+f+h+%29%282%29=24\"$ \r
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\n" ); document.write( "\n" ); document.write( "4. Factor: \r
\n" ); document.write( "\n" ); document.write( " $\"15x%5E2+%2B+7x+-+36\"$ ..........write $\"7x\"$ as $\"27x-20x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"15x%5E2+%2B27x-20x-36\"$ .....group\r
\n" ); document.write( "\n" ); document.write( " $\"%2815x%5E2+-20x%29%2B%2827x-36%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5x%283x+-4%29%2B9%283x-4%29%7D%7D%0D%0A%0D%0A%7B%7B%7B%283+x+-+4%29+%285+x+%2B+9%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "5. Find the zeros of the polynomial function $\"f%28x%29+=+15x%5E2+%2B+7x+-+36\"$ .\r
\n" ); document.write( "\n" ); document.write( "=> $\"f%28x%29+=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0+=+15x%5E2+%2B+7x+-+36\"$ ....use already factored form above\r
\n" ); document.write( "\n" ); document.write( " $\"+0=%283+x+-+4%29+%285+x+%2B+9%29\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "if $\"0=%283+x+-+4%29+\"$ => $\"3x=4\"$ => $\"+x=4%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"0=+%285+x+%2B+9%29\"$ => $\"5x=-9\"$ => $\"+x=-9%2F5\"$ \r
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\n" ); document.write( "\n" ); document.write( "6. If $\"g%28x%29+=+5x+%2B+6\"$ , find $\"g%5E+-1%28x%29+\"$ solved for $\"+y\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+5x+%2B+6\"$ ..........since $\"g%28x%29+=y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+5x+%2B+6\"$ ..........swap $\"x\"$ and $\"y\"$ variables\r
\n" ); document.write( "\n" ); document.write( " $\"x=+5y+%2B+6\"$ .........solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-6=+5y+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=%28x-6%29%2F5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%28x-6%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"g%5E+-1%28x%29=%281%2F5%29%28x-6%29\"$ \r
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