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Answer: Choice C. 4*sqrt(6)</h3>
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Explanation:
Each cube has a side length of 4. Placed together like this, the total horizontal side combines to 4+8 = 8. This is the segment HP as shown in the diagram below. I've also added point Q to form triangle HPQ. This is a right triangle so we can find the hypotenuse QH
Use the pythagorean theorem to find QH
a^2 + b^2 = c^2
(HP)^2 + (PQ)^2 = (QH)^2
8^2 + 4^2 = (QH)^2
(QH)^2 = 64 + 16
(QH)^2 = 80
QH = sqrt(80)
Now we use segment QH to find the length of segment EH. Focus on triangle HQE, which is also a right triangle (right angle at point Q). Use the pythagorean theorem again
a^2 + b^2 = c^2
(QH)^2 + (QE)^2 = (EH)^2
(EH)^2 = (QH)^2 + (QE)^2
(EH)^2 = (sqrt(80))^2 + (4)^2
(EH)^2 = 80 + 16
(EH)^2 = 96
EH = sqrt(96)
EH = sqrt(16*6)
EH = sqrt(16)*sqrt(6)
EH = 4*sqrt(6), showing the answer is choice C
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A shortcut is to use the space diagonal formula. As the name suggests, a space diagonal is one that goes through the solid space (rather than stay entirely on a single face; which you could possibly refer to as a planar diagonal or face diagonal).
The space diagonal formula is
d = sqrt(a^2+b^2+c^2)
which is effectively the 3D version of the pythagorean theorem, or a variant of such.
We have a = HP = 8, b = PQ = 4, and c = QE = 4 which leads to...
d = sqrt(a^2+b^2+c^2)
d = sqrt(8^2+4^2+4^2)
d = sqrt(96)
d = sqrt(16*6)
d = sqrt(16)*sqrt(6)
d = 4*sqrt(6), we get the same answer as before
The space diagonal formula being "pythagorean" in nature isn't a coincidence. Repeated uses of the pythagorean theorem is exactly why this is.
Answer:
Step-by-step explanation:
To start, lets form our polynomial factors from our zeroes.
x = -2
x + 2 = 0
x = 5
x - 5 = 0
Now lets put these into factored form by moving them into parenthesis and multiplying them with each other!
(x+2)(x-5)
We can start moving them out! I am going to use FOIL, but you could also use distributive or any other method/property.
x · x = x²
x · -5 = -5x
x · 2 = 2x
2 · 5 = 10
Now lets put our terms into our polynomial function, based on the order of the powers.
We are done! Hope this helps!
65 is the answer,I just put it into a calculator,but all that really is is multiplying,a negative times a negative equals a positive so you would take -6.5×2=-13
-13×-5=65
Before going to the range, it's better to discuss first about the symbols used in inequality expressions. These equations contain <, >, ≤ and ≥ in their equations. That is why there are solid and hollow figure when they are graphed. If the line is solid, that means points along that line are part of the solution. If not, then they are not part of the solution. The same applies for solid points and hollow points.
Now, the domain and range of a given function is basically the coverage of their x and y values that are part of the solution. If the point is along the solid lines and points, the domain or range is expressed either in [ or ], depending where it starts and ends. If the point is along the hollow lines and points, the domain or range is expressed either in ( or ), depending where it starts and ends. The ∪ symbol is added to connect domains and ranges through discontinuities.
Looking at the leftmost line, it starts from the hollow point (-7,-4) and ends on the solid point (-3,3). The range for this part is expressed as (-4,3]. Looking the rightmost line, it starts from the hollow point (-1,-3) and ends at the solid point (2,-8). The range for this part is expressed as (3,8]. Connecting the two ranges, the answer would be <span>(-4,3)U(3,8].</span>
