Answer:
w= 9
Step-by-step explanation:

Square both sides:
-4w +61= (w -4)²

Expand:
-4w +61= w² -2(w)(4) +4²
-4w +61= w² -8w +16
Simplify:
w² -8w +16 +4w -61= 0
w² -4w -45= 0
Factorize:
(w -9)(w +5)= 0
w -9= 0 or w +5= 0
w= 9 or w= -5 (reject)
Note:
-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.
<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>
When solving an equation such as x²= 4,
we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.
In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.
However, back to our question, we did not introduce the square root so we should not consider the negative square root value.
Answer:
Step-by-step explanation:
Your "y=2xsquared-12x+10" translates into y = 2x^2 - 12x + 10. This factors into y = 2(x^2 - 6x + 5).
Setting this = to 0 results in y = 2(x - 5)(x - 1) = 0, so that the x-intercepts are (5, 0) and (1, 0). The x-coordinate of the vertex lies halfway between x = 1 and x = 5, that is, at x = 3. Using synthetic division to evaluate y = 2x^2 - 12x + 10 at x = 3, we get
3 2 -12 10
6 -18
------------------
2 -6 -8
Therefore, the vertex is located at (3, -8).
Setting x = 0 results in the y-intercept: y = 2(0)^2 - 12(0) + 10 => (0, 10)
Answer: 9
Step-by-step explanation: 3 blocks tall multiplied by 3 blocks wide makes 9