gibsonj338

or x=6

\({x}^{2}+4x=60\)

Two ways to do it

Way One: factoring

\({x}^{2}+4x-60=0\)

\((x+10)(x-6)=0\)

\(x=-10\) or \(x=6\)

Way Two: completing the square

\({x}^{2}+4x+4=64\)

\({(x+2)}^{2}=64\)

\(x+2=±8\)

\(x=-2±8\)

\(x=-10\)​ or 

Nice way to get to the answer.  My way of getting to the answer, completing the square, works too, but your way envolves fewer steps which I did not see.  I wish I would have thought of it first.

\(48T=48{T}^{2}\)

\(48T-48{T}^{2}=0\)

\(-48{T}^{2}+48T=0\)

\({T}^{2}-T=0\)

\({T}^{2}-T+\frac{1}{4}=\frac{1}{4}\)​

\({(T-\frac{1}{2})}^{2}=\frac{1}{4}\)

\(T-\frac{1}{2}=±\frac{1}{2}\)

\(T=\frac{1}{2}±\frac{1}{2}\)

\(T=\frac{1}{2}+\frac{1}{2}\)

\(T=\frac{2}{2}\)

\(T=1\)

\(T=\frac{1}{2}-\frac{1}{2}\)

\(T=\frac{0}{2}\)

\(T=0\)

Do you know about order of operations?  There is an acronym Please Excuse My Dear Aunt Sally (PEMDAS). If you take the first letter of each word in the acronym and replace it with the correct mathematical operation and do the operations in the order of the acronym, you wlll get to the answer.

P - Parenthesis

E - Expoents

M - Multiplication

D - Division

A - Addition

S - Subtraction

\(7(23-18)/(12-5)\)

The acronym says to do what is inside the parenthesis first.  Follow the rest of the acronym within the parenthesis.

\(7(5)/(12-5)\)

\(7(5)/7\)

The acronym says to do the expoents next.  There are no expoents so this we can skip.

Even though the acronym says to do multiplication next, in actuality, you do multiplication and division at the same time in order from left to right

\(35/7\)

\(5\)

Even though the acronym says to do addition next, in actually, you do addition and subtracton at the same time in order from left to right.  Because there is no addition or subtraction to do, you leave as is which is your answer.

\(5\)

x-15%=100

\(x-0.15=100\)

\(x=100.15\)

\(tan(x)=\frac{2.2}{9.6}\)

\(tan(x)=\frac{22}{96}\)

\(tan(x)=\frac{11}{48}\)

\(tan(x)= 0.2291666666666666...\)

\({tan}^{-1}(tan(x))= {tan}^{-1}(0.2291666666666666...)\)

\(x≈ 0.225276779214\)

\(x= 0.2291666666666666...+\pi\)

\( x≈0.2291666666666666...+ 3.1415926535897932...\)

\(x≈3.3707593202564599\)

\(x≈ 0.225276779214\) or \(x≈3.3707593202564599\)

\({({y}^{2}-x)}^{2}\)  \(y=1\) and \(x=2\)

Two ways to solve this

The short way

Subsitute \(1\) for \(y\) and \(2\) for \(x\) and solve

\({({1}^{2}-2)}^{2}\)

\({(1-2)}^{2}\)

\({(-1)}^{2}\)

\(1\)

The long way

Subsitute \(1\) for \(y\) and \(2\) for \(x\), expand the expression and solve

\({({1}^{2}-2)}^{2}\)

\(({1}^{2}-2)({1}^{2}-2)\)

\((1-2)({1}^{2}-2)\)

\((1-2)(1-2)\) 

\(1-2-2+4\)

\(-1-2+4\)

\(-3+4\)

\(1\)

OR

\({({1}^{2}-2)}^{2}\)

\(({1}^{2}-2)({1}^{2}-2)\)

\({1}^{4}+{1}^{2}(-2)+(-2)({1}^{2})+4\)

\(1+{1}^{2}(-2)+(-2)({1}^{2})+4\)

\(1+1(-2)+(-2)({1}^{2})+4\)

\(1+(-2)+(-2)({1}^{2})+4\)

\(1+(-2)+(-2)(1)+4\)

\(1+(-2)+(-2)+4\)

\(-1+(-2)+4\)

\(-3+4\)

\(1\)

Two examples

\(\frac{4}{2}\)

Take the reciprocal of the number in the denominator and multiply the two numbers

\(4\times\frac{1}{2}\)

\(\frac{4}{2}\)

\(2\)

\(\frac{\frac{1}{2}}{\frac{2}{3}}\)

Take the reciprocal of the number in the denominator and multiply the two numbers

\(\frac{1}{2}\times \frac{3}{2}\)

\(\frac{3}{4}\)

If you know the base and the height of the parallelogram, you can calculate the area: \(A=b\times h\)

If you know the lengths of adjacent sides and one of the angeles, you can calculate the area: \(A=absinC;\) where where \(a\) and \(b\) are adjacent sides and \(C\) is the given angle.