To start, our equation will look like this:
(2 1/4 + 1/2)/ 3/4 = b
To make it easier convert the 2 numbers inside the parentheses into improper fractions, and then multiply them by their least common denominator to add.
(9/4 + 1/2)
(18/8 + 4/8)
(22/8)/ 3/4 = b
Now, to divide 22/8 cups of grapes into bags with 3/4 cup of grapes, multiply 22/8 by 4/3.
(22/8)(4/3)=b
3 2/3 = b
So, if Ari has a bag with 2 1/4 cups of red grapes and 1/2 cup of green grapes, and he divides it into bags with 3/4 cup each, he will have about 3 full bags.
The difference between
i) <span>14k+2(3k+5)-5=10 and
ii) </span><span>14k+6k+10-5=10
is the equality </span>2(3k+5)=6k+10
The property used here, can be described for any numbers a, b and c as:
This is called the DISTRIBUTIVE PROPERTY
Answer: DISTRIBUTIVE PROPERTY
Short Answer x = - 6
Remark
You gave the second best answer.
The trick here is not to divide both sides by 2. Solve the problem this way.
log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2 Expand the equation
x^2 + 2x + 1 = 25 Subtract 25 from both sides.
x^2 + 2x - 24 = 0 Factor
(x + 6)(x - 4) = 0 Find the zeros.
x + 6 = 0
x = - 6 <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem
x - 4 = 0
x = 4 This is a legitimate result to the original equation.
Peyton is 28 years old
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