Maths-
General
Easy
Question
What is the Quotient of
.
Hint:
The expansion of the identity,
.
We are asked to find the quotient of the given expression.
The correct answer is: the quotient of the expression is 2(x + 2)/(x + 4)
Step 1 of 2:
The given expression is:
.
Take the reciprocal of the second expression and multiply it with the first expression. It serves the same effect as division;
![fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 x plus 6 over denominator x squared plus 3 x minus 4 end fraction](data:image/png;base64,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)
Step 2 of 2:
Simplify the expression and cancel out the common factors;
![fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 x plus 6 over denominator x squared plus 3 x minus 4 end fraction equals fraction numerator x squared plus 2 x minus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator x squared plus 4 x minus x minus 4 end fraction](data:image/png;base64,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)
![equals fraction numerator x left parenthesis x plus 2 right parenthesis minus 1 left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator x left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis end fraction](data:image/png;base64,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)
![equals fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPIAAAAnCAYAAAA1mxU4AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAA/RJREFUeNrtnLFrFEEUxgeRQySNBElhEQhBxEIEqxBCEERELESwOCxEhCASxF6sbA4LsbARSwtBREQkCIcECUcQRMRCJI3/Qwo5grC+yY5yLLt7b9zdmbdvvx98kGTvyDf75s3Ozs4+Y5rnNmlg5DJwHrX61wriEpBTpO0W+Bw5r9r8awVxidCQ0wJ8HCfdJ30tOH6GtCXQ/zLpFWmXtOf8X/Pw3ya4bZUQl7OkDdIv0pi0Q3pMmlUYl/0TPRLi5TlpjZSUfGbLnXhJ/j+S+qQZ9/tJ56nP8N82uG2VEJdN0hVSL+PrvcK4mIekdWGeyhL5Tuaeq0n/SYXvzpO+MfxrIK+tUuNi3GxCXVzs6LSS8/ebBQ174I7FSuQl0odA/qt2mDHDvxbGAftVlbgskH5ojMtuZuoxyRfS3MTvN0hPIl+Re5kRtUn/VTrMUsHUsldwRWgzeW2VFpc593/sffJFjXH5XXLsAumR+/lcwBFrWqD2Avn/30Q+RPpk0oWhaf7bTlFbpcQlyegus1+pSmTLkLRq0tXJWc+TlqeQiRzD/xHSG9J5rR2G2VaJcbnsBp1VjXEpmwIZN4LZBoZ8zlbX1Lqqf98r8oLr2Ise/tvKtLZKisskMy6Z1cVlWDIF/PvM0E6D+kISObso0aR/nw5zgvSMdJhxP9n2xS5OW6XEJQ+Vi5BFjwnsiPvWBcuOYp8ZU6AQibzuPIfwz+0wdiHlJekg47NZ/22D21YJccnDzgB2FMYl98H9UZPuiJk8wZdMumEjdiJzNoTU5Z/bYd65qxSHtm884LZVQlzs5pWrbtA5YNKdXj9J1xXGZZ/tiXsVe6/wmnQs53MvTLri2GQCly1iFG2li+2fuwijYSugz4JT7LisuIFn7LTpBg6jMC7/pht4aSKef60gLhG4ZWRvUbP3L2uK/WsFcQGd556T7zGg5F7FZ/MFaF8yI4kBaHkyI4mB19UcCiduMg89khjntSUxxtS6e1dln0QGAGBqDQBoKokNkhkAHUlcJZlR8jiufwAqg917cf2DGuCWRdUMSh7Xi92znXj4BzXgUxZVIyh5XC/29cvvJW1Q8SZVSJooi6oRlDyutw89NWnFz4TpXzVSy6JqBCWP6+tDyxPeEqZ/9Ugsi6oRlDyupw9ZD7YQ//yU72oseVyK1LKo2kDJ43r60CAzxU+Y/juBxLKoXUrkGDGoM5FD+bePlEYebehcIksri9q1qXXVGMSeWofqQ7avLDK/27mptcSyqFpnPSh5XK0P+VzFO7XYJbUsqkZQ8riZPpQw/atFcllUjaDkcdhE7sSGEMllUTWDksdhBiNs0QSNgpcm4voHoDZQ8jiuf/MH1r/ShOT0pPYAAAHadEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4zPC9tbj48L21yb3c+PC9tZnJhYz48bW8+JiN4RDc7PC9tbz48bWZyYWM+PG1yb3c+PG1uPjI8L21uPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4zPC9tbj48bW8+KTwvbW8+PC9tcm93Pjxtcm93Pjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PG1vPik8L21vPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj40PC9tbj48bW8+KTwvbW8+PC9tcm93PjwvbWZyYWM+PC9tYXRoPtFQQTYAAAAASUVORK5CYII=)
![equals fraction numerator 2 left parenthesis x plus 2 right parenthesis over denominator x plus 4 end fraction](data:image/png;base64,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)
Thus, the quotient of the expression is:
.
Division of two expressions is the same as taking the reciprocal of the second expression and multiplying it with the first expression.
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The cost of 4.25 m of cloth is 38.25. Find the cost of cloth per meter ?
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Taylor uses tape to mark a square play area in the basement for her daughter. The area measures 28 sq.ft . Is the side length of the square rational or irrational ? Explain.
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Maths-General
Maths-
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
Find the approximate annual interest rate for a five year auto loan of $40,000 that has monthly payments of $750.
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
Find the approximate annual interest rate for a five year auto loan of $40,000 that has monthly payments of $750.
Maths-General
Maths-
Order from least to greatest ![29 over 12 comma 2.4444 horizontal ellipsis comma square root of 5.65](data:image/png;base64,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)
Order from least to greatest ![29 over 12 comma 2.4444 horizontal ellipsis comma square root of 5.65](data:image/png;base64,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)
Maths-General
Maths-
Find the Quotient and the domain .
![fraction numerator 25 straight x squared minus 4 over denominator straight x squared minus 9 end fraction divided by fraction numerator 5 straight x minus 2 over denominator straight x plus 3 end fraction](data:image/png;base64,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)
Find the Quotient and the domain .
![fraction numerator 25 straight x squared minus 4 over denominator straight x squared minus 9 end fraction divided by fraction numerator 5 straight x minus 2 over denominator straight x plus 3 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Order from least to greatest
0.363636..... , √15 , ![square root of 17 over 3 end root](data:image/png;base64,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)
Order from least to greatest
0.363636..... , √15 , ![square root of 17 over 3 end root](data:image/png;base64,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)
Maths-General
Maths-
Becky is competing in an 8-mi road race. She runs at a constant speed of 6 mi/h. Write an in slope-intercept form to represent the distance Becky has left to run.
Becky is competing in an 8-mi road race. She runs at a constant speed of 6 mi/h. Write an in slope-intercept form to represent the distance Becky has left to run.
Maths-General
Maths-
Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
![13.9 comma space square root of 49 comma space minus 48](data:image/png;base64,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)
Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
![13.9 comma space square root of 49 comma space minus 48](data:image/png;base64,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)
Maths-General
Maths-
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
a. Find the approximate annual interest rate for a four year signature loan $20,000 that has monthly payments of $500.
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
a. Find the approximate annual interest rate for a four year signature loan $20,000 that has monthly payments of $500.
Maths-General
Maths-
The line
passes through the points
.Find b, n, and p.
The line
passes through the points
.Find b, n, and p.
Maths-General
Maths-
Find the Quotient and the domain .
![fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction divided by fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAsCAYAAACzKYDtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAA2pJREFUeNrtW79rFUEQPkQeKUQIIiJ2IsEihAeSQuQhAbEQCwmkEJEgQhAJIvYWYhNSiP+AiNhZigQhBAkhBEGsgxBSib2IPIKwzsKEHMvevb3c7szsvfngK3J3hLlv52b2x/uKojswyAPgNvBSoWDDY+CKsJhWMK4qnMD733X4eDAD3BEa2zbGV4ehDiHf4PSFxnYFuFVz/zpwkym2OeAa8C8m7w/ga+AZRr3IYupj4kjGFiaQi/MY+0WmuL4A54E9R8/PjFqRxbQKXBaeOE88868p4CdMHmn4nWhBIComm4mD0t8TON+54Dx3FvgN78fAJHC/YsL70ymtV4EbTqWx5fi0wKSx1W83gZ4mUkxNdB+ZiT3n2jQOTBn2674ZWeR14Kxz7Qbwo3Ot53wxNrbLwhLmHPABziluJdDTRIwpVPda/Ku4vlxaCi8C3ycQ+6GnBb0D3vU8e+CI6JILbhxPE+lpIsbURPfGiWPxAVctewElzATQ1672nMryx1MB3cSRCPsud4BfUTMOPUNjaqJ7o1Z1iAEO2FJCwddLWwH2S3zreaaXaMKZAqdwoGLraSLHFKL7yIG7VjFZssvge9iPU8GWzZelWHx9350cS8cwgZ4mckwhuh9rOf4CJ1YW93ETKVWJ38WV0q+a+cFqJkkzg5PR2HqayDGF6F4L3wbgLPbjMl7hC6dqV29qxKzaAOSG3bFeAJ7EijKHS93FBHqayDGF6D4SO8XRedAE/sNJz3Nr2DZStCvjWSIWxegjB04MsO0MkXbX9rbzDLWeITGF6B5cyjgPOfsV5b0owg45FfF1D8ajgu9nFc+AzyvmX0s6vuS6ZwNbyrl+jMW9gTiuumePcU4chYL2K+sy2777OGunVVih0DmOQhNHoVAoyKobp5FQzYwZQ4KRUM2MGWOoMYSVSMUROI2EJDFQ2Tui2TYyALeRkCwGKntHFNuGcEgwEpLGQGHviGLbEF5puI2ELDFIsstIQZNWntJIGNrqWcyMFPaO1rYNBoS28tQHiSGtnvwwk8re0dq2wQQK52uWrZ7K3tHatsGIJq08RK/sWz2lveOw0rSybTCBwvmaTauXZpeRCirna1dbfRREsW1k1spjrq5ybfWtkZttg9r52tVWH+XFcznu52jlXWz1Cm31Cm31Cm31x8V/7WnI+Q/pF0kAAAI7dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbz4oPC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+eTwvbWk+PG1zdXA+PG1vPik8L21vPjxtbj4yPC9tbj48L21zdXA+PC9tcm93Pjxtcm93PjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj54PC9taT48bW8+KzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPnk8L21pPjwvbXJvdz48L21mcmFjPjxtbz4mI3hGNzs8L21vPjxtZnJhYz48bXJvdz48bW4+MzwvbW4+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4rPC9tbz48bW4+MzwvbW4+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPnk8L21pPjwvbXJvdz48bXJvdz48bXN1cD48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtc3VwPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj55PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjwvbWF0aD5RvvzEAAAAAElFTkSuQmCC)
Find the Quotient and the domain .
![fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction divided by fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction](data:image/png;base64,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)
Maths-General
Maths-
For What value of X is
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For What value of X is
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Maths-General
Maths-
Give an example of two irrational numbers whose product is rational .
Give an example of two irrational numbers whose product is rational .
Maths-General
Maths-
Find the Quotient and the domain .
![fraction numerator y squared minus 16 over denominator y squared minus 10 y plus 25 end fraction divided by fraction numerator 3 y minus 12 over denominator y squared minus 3 y minus 10 end fraction](data:image/png;base64,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)
Find the Quotient and the domain .
![fraction numerator y squared minus 16 over denominator y squared minus 10 y plus 25 end fraction divided by fraction numerator 3 y minus 12 over denominator y squared minus 3 y minus 10 end fraction](data:image/png;base64,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)
Maths-General