[Given]
{ x + y = 6
{ x = y + 4
[Plug-in our x value & solve]
[Given] x + y = 6
[ Plug-in] (y + 4) + y = 6
[Distribute] y + 4 + y = 6
[Combine like terms] 2y + 4 = 6
[Subtract 4 from both sides] 2y = 2
[Divide both sides by 2] y = 1
[Answer]
Third option - (5, 1)
-> You do not need to solve for x since this is the only option that has y = 1, but to solve for x we would do y + 4 = 1 + 4 = 5, so this answer fully checks correctly
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Your answer is, ( - 7 , 2), ( 0 , 0), (3 , 4), (0 , - 4), (3 , -6), and ( - 7 , - 3).
The figure ABCDEF below represents a roof of a house. The figure ABCDEF below represents a roof of a house. AB = DC = 12m, BC = AD = 6m, AE = BF = CF = DE = 5m and EF=8m.
It is given that ABCDEF is a regular hexagon in which all the sides are equal and all the angles are also equal. Hence, ABCDEF is a symmetrical figure due to which we can break it down into identical figures.
Answer:
Yes you can have some peace of mind, because your house is safe. Since, the flagpole is only 14.85 feet, is shorter than the 18 feet of distance from its base to your home.
Step-by-step explanation:
What you need to do is to estimate the height of the pole using its shadow, and the relationship between the height of the fence and it respective shadow:
- <em>For a rectangle triangle, the proportion of its shorter sides are constant</em>.
- <em>The shadows of the fence and of the pole, both form two rectangle triangle.</em>
- <em>The first triangle</em>, the smaller one, <em>has a base of 7 feet</em> (the shadow of the fence), <em>and a height of 4 feet</em> (the corresponding height of the fence)
- <em>The second</em> one, a bigger one, <em>has a base of 26 feet</em> (the shadow of the flagpole), <em>and an unknown height</em> (the height of the pole that its worrying you).
- Then, as stated, the proportion for both triangles remains constant. So:
, where<em> x is the height of the pole.</em> - x is solved as:
. Meaning that the flagpole has 14.85 feet of height. - Then when the height is compared to the distance from its base to your home, it is found that the pole is shorter then, there is no risk of the pole falling into your house.