Answer: 1/2
<u>Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD</u>
(2/12*1/1) + (1/3+4/4)
<u>Complete the multiplication and the equation becomes
</u>
2/12+4/12
<u>The two fractions now have like denominators so you can add the numerators.</u>
2+4/12 = 6/12
<u>This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor </u>
6/12 ÷ 6/6 = 1/2
<u>Therefore:
</u>
2/12 + 1/3 = 1/2
Answer:
144yd^2
Step-by-step explanation:
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Answer:
x=3
Step-by-step explanation:
We have to use the fact that all angles of a triangle add up to 180 and two supplementary angles add up to 180.
First,QRS forms a line, so angle QRT and angle TRS add up to 180 or, if we call angle TRS y for the sake of having it as a variable, 45x+y=180 or y=180-45x
Now we have all three angles of the triangle, and we know all three add up to 180, so startign with our newly found angle, (180-45x)+(25x)+(57+x)=180
180-45x+25x+57+x=180
237 - 19x = 180
57 = 19x
x=3
Let me know if you need any further explanation.
Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Is there any more to the question than this?
