AdamTaurus

\(\frac{11}{12}+\frac{7}{8}\)

First, the denominators must be the same.

\(2(\frac{11}{12})+3(\frac{7}{8})\)

Simplify.

\(\frac{22}{24}+\frac{21}{24}\)

Combine.

\(\frac{43}{24}\)

You cannot simplify any further, so 43/24 is your final aswer.

\(m^2-7m-60\)

First, multiply a by c.

The base forula for an equation like this is ax²+bx+c.

So, a*b=1*-60=-60

Now, find two factors of 60 that add to -7 and multiply to -60.

In this case, it would be 5 and -12.

\((m+5)(m-12)\)

First, they must have a common denominator.

\(2(\frac{4x-1}{5})+5(\frac{x+4}{2})=3\)

\(\frac{8x-2}{10}+\frac{5x+20}{10}=3\)

Now you can combine the two.

\(\frac{8x-2+5x+20}{10}=3\)

Combine like terms.

\(\frac{13x+18}{10}=3\)

To cancel the fraction, multiply both sides by 10.

\(13x+18=30\)

Subtract 18 from both sides.

\(13x=12\)

Divide each side by 13.

\(x=\frac{12}{13}\)

3x(x+1) + 7(x+1)

Since both of the values in the parenthesis are equal, we can combine.

(3x+7)(x+1)

Notice the parenthesis. If i had just done 3x+7(x+1), then only 7 would be multiplied by x+1.

So (3x+7)(x+1) is your final answer.

What is 10+6d?

To begin, you have to realize that d is a variable. This means d can be any number.

In this equation, d is multiplied by 6. So you must think about order of operations.

If you have 2 numbers multiplied by each other, you have to find their product before you can add any other numbers.

Ex- d=4

If d equals 4, you plug in anywhere there is a d.

10+6(4)

Notice my use of parenthesis. If the number were negative, you would want to make sure the negative is inside the parenthesis.

Simplify.

6*4=24

10+24=?

10+24=34

A good way to remember order of operations is PEMDAS.

Some people use PEMDAS as the acronym Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) in that order. For example, you would have to do parenthesis before exponents, or multiplication before addition.

Hope this explanation helps!

Thanks!

\(\frac{\frac{2}{3}(5*4)}{3+\frac{6}{7}}\)

Is this the correct format?

Let's say x is the mystery number.

So first you have x.

Then you take away 5/7 of x.

\(x-\frac{5}{7}x\)

That equals 30.

\(x-\frac{5}{7}x=30\)

This is the same as 2/7x equals 30.

\(\frac{2}{7}x=30\)

You divide both sides by 2/7.

\(x=\frac{30}{\frac{2}{7}}\)

But when you divide by a fraction, it is the same as multiplying by the reciprocal.

\(x=30*\frac{7}{2}\)

Simplify.

\(x=\frac{30*7}{2}\)

\(x=\frac{210}{2}\)

\(x=105\)

A good way to test this is by plugging it into the original equation.

\(x-\frac{5}{7}x=30\)

Substitute each x for 105.

\(105-\frac{5}{7}(105)=30\)

\(105-\frac{525}{7}=30\)

\(105-75=30\)

\(30=30\)

This is true, so your mystery number is 105.

\(2.[3-2.(2-6)]+1 = ?\)

I do not see how this problem is possible as 2-6=-4 and a decimal cannot be negative.

\(-6(6u-2v-3)\)

When you use the distributive property, the value outside the parenthesis, in this case -6, is multiplied by every value inside the parenthesis. 

\(-6(6u-2v-3)\Rightarrow -36u+12v+18\)