Do each equation individually and compare if they are the same end answer in each question. which ever one is unequal than that is the answer
Call the number : x
(1/3)x + 5 = x-6
=> (1/3)x + 5 - (x-6) = 0
=> (1/3)x + 5 - x + 6 = 0
Group (1/3)x with -x, 5 with 6
=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
=> x = -11 : (-2/3) = 33/2.
Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2
33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)
<span>3 = log(8) + log(x³) </span>
<span>When adding logs, you are multiplying the terms altogether. </span>
<span>3 = log(8x³) </span>
<span>Then, by log_a b = n ==> aⁿ = b: </span>
<span>10³ = 8x³ [Since the base is not given, I assume that the base is 10] </span>
<span>1000 = 8x³ </span>
<span>Finally, solve for x. </span>
<span>1000/8 = x³ </span>
<span>x³ = 125 </span>
<span>x = (125)^(1/3) . . .Set both sides to the power of 1/3. </span>
<span>x = 5 </span>
<span>Hence, x = 5. </span>
Answer
<em>TV screens are measured on the diagonal </em>
<em>. In this specific case the TV is shaped like a rectangle , whose diagonal is 40 i n c h e s and its width is 24 i n c h e s : w =
</em>
<em>24 i n d = 40 i n </em>
<em>Then , the sides of the rectangle and its diagonal form a right triangle . </em>
<em>Therefore , we can determine the height ( l ) </em>
<em>if we can apply the Pythagorean theorem: d 2 = l 2 + w 2 </em>
<em>So , solving for l : l = √ d 2 − w 2 </em>
<em>Thus , substituting: l = √ ( 40 ) 2 − ( 24 ) 2 </em>
<em>Simplifying: d = √ 1024 = 32 i n </em>
<em>Therefore </em>
<em>, the height of the TV is: </em>
<em>32 i n
</em>
