Answer:
x⁴ - 81 factors: x + 3, x - 3, x + 3i, x - 3i
x³ - 2x² + 9x - 18 factors: x - 3i, x + 3i, x - 2
x⁴ + 5x² - 36 factors: x - 2, x + 2, x + 3i, x - 3i
Answer:800
Step-by-step explanation:
Given a percentage, convert to decimal and put it over 100. (69/100)
Then we perform "cross multiplication" where we try to find our b if (a/b = c/d [and our c/d is our percentage*]).
So ([552]/b)= (69/[100])
We obtain (ad/b) = c, which is (55200/b)=69.
We then divide ad by our c, (55200/69=800), our b=800.
Therefore, 552 is 69% of 800.
Answer:
7. -37/36 or -1 1/36
8. -3/10
9. 1/24
10. -118/21 or -5 13/21
11. 97/12 or 8 1/12
12. 49/8 or 6 1/8
Step-by-step explanation:
To subtract fractions, they must have the same denominator. The common denominator will be the LCM (lowest common multiple) of the two denominators. Then, combine the fractions and simplify.
7. Find a common denominator
Combine the fractions
Answer. Already in lowest terms.
Keep a negative number. 37 goes into 36 one time, leaving 1 remainder (becomes numerator)
8. Find a common denominator
Combine the fractions
Answer in simplest form.
9. Find common denominator
Combine the fractions
Answer in simplest form
10. Translate to improper fraction
Multiplied each whole number with base, added to numerator
Found common denominator
Combined fractions
Answer in improper form
Answer as a mixed number
11. Convert to improper fraction
Two minuses make a plus
Find common denominator
Combined fractions
Answer as improper fraction
Answer as mixed fraction
12. Convert to improper fraction
Find common denominator
Combined fractions
Answer as improper fraction
Answer as mixed number
For this case we have the following expression:
Applying distributive property to the terms within parentheses we have:
We add similar terms on both sides of equality considering that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
We add 7.5x to both sides of equality:
We subtract 72 from both sides of equality:
We divide between 3 on both sides of equality
ANswer:
Distributive property
Add similar terms
Equality property of the sum
Equality subtraction property
Equality property of the division
If you look at the attached graphic, you will see that the altitude (or height) of an equilateral triangle is:
Height = side length * sq root (3) / 2
Area = side^2 * sq root (3) / 4