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<span><span> 8x24-27y6</span> </span>Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
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Step by step solution :<span> Step 1 :</span>Skip Ad
<span>Equation at the end of step 1 :</span><span><span> (8 • (x24)) - 33y6
</span><span> Step 2 :</span></span><span>Equation at the end of step 2 :</span><span> 23x24 - 33y6
</span><span> Step 3 :</span>Trying to factor as a Difference of Squares :
<span> 3.1 </span> Factoring: <span> 8x24-27y6</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
<span> A2 - B2</span>
</span>Note : <span> AB = BA </span>is the commutative property of multiplication.
Note : <span> - AB + AB </span> equals zero and is therefore eliminated from the expression.
Check :<span> 8 is not a square !!
</span>Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor as a Difference of Cubes:
<span> 3.2 </span> Factoring: <span> 8x24-27y6</span>
Theory : A difference of two perfect cubes, <span> <span>a3</span> - <span>b3</span> </span> can be factored into
<span> (a-b) • (a2 +ab +b2)</span>
Proof : <span> (a-b)•(a2+ab+b2) =
<span>a3</span>+<span>a2b</span>+<span>ab2</span>-<span>ba2</span>-<span>b2a</span>-<span>b3</span> =
<span>a3</span>+(<span>a2b</span>-<span>ba2</span>)+(<span>ab2</span>-<span>b2a</span>)-<span>b3</span> =
<span>a3</span>+0+0+<span>b3</span> =
<span>a3</span>+<span>b3</span></span>
Check : 8 is the cube of 2
Check : 27 is the cube of 3
Check :<span> x24</span> is the cube of <span> x8</span>
Check :<span> y6</span> is the cube of <span> y2</span>
<span>Factorization is :
</span> <span> <span>(2x8 - 3y2)</span> • </span><span> (4x16 + 6x8y2 + 9y4)</span>
Trying to factor as a Difference of Squares :
<span> 3.3 </span> Factoring: <span> 2x8 - 3y2</span>
Check :<span> 2 is not a square !!
</span>Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor a multi variable polynomial :
<span> 3.4 </span> Factoring <span> 4x16 + 6x8y2 + 9y4</span>
Try to factor this multi-variable trinomial using trial and error<span>
</span>Factorization fails
Final result :<span> (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
</span>
Answer:
explained
Step-by-step explanation:
Ramon wants to report the number of years whose temperature was higher than the previous year’s temperature. This can be done by him as
The random variable is the number of years in which the temperature increased from the previous year.
Its possible values are {0,1,2,3,4,5}.
Answer:
P=0.954 or 95.4%
Step-by-step explanation:
Using the formula for the standardized normal distribution to find Z:
Where μ is the mean (μ=20) and σ is the standard deviation (σ=2.6).
In the table of the normal distribution, we can look for positive values z, and these values are going to represent the area under the curve between z=0 and the values searched. the negatives values are found by symmetry (with the corresponding positive value but remember this area is under the left side of the curve). To find a value in the table, find the units in the first column and the follow over the same row till you find the decimals required.
represents the probability of length being between 14.8 and 20 (the mean) and 
represents the probability of length being between 20 and 25.2, The requested probability is the sum of these two.
F(10) = (10)^2 + 1
= 100 + 1
= 101
101 is the answer
Answer: y = -2x - 7
Step-by-step explanation:
The equation for a perpenducular line has a slope that is the negative inverse of the reference line, in this case x - 2y = 6.
Let's put this equation into standard slope-intercept form, y = mx+b, where m is the slope and b the y-intercept (the value of y when x is 0).
x - 2y = 6
- 2y = 6 - x
y = (1/2) x -3
The slope is (1/2), so a perpendicular line will have a slope of -2.
y = -2x + b
We can find b by using the given point ((-3,-1), a known solution):
-1 = -2*(-3) + b
-1 = 6 + b
b = -7
The perpendicular equation is y = -2x - 7
y = -2x
