-5x+y=6 -3x+6y=-12 Solving systems of equations by substitution
1 answer:
if you isolate y in the top equation to get y=5x+6 then you can substiture y for 5x+6 in the bottom equation because thats what y equals
as of now you have -3x+6(5x+6)=-12 but if you use the distrubite property you would get -3x+30x+36=-12
then if you subtract 36 from both sides you would get -3x+30x=-48 then combine like terms to get 27x=-48 then divide both sides by 27 to get or x≈1.8
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Answer:
The value of is -30.
Step-by-step explanation:
Let , we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:
(1)
(2)
(3)
From (3) we find the least root:
By (2) we have the value of :
Answer:
84 feet
Step-by-step explanation:
This problem involves several steps. The first step is to realize that the given figure does not show the required number of vertical stringers. It shows 5, but there will be 7 of them. The given diagram is helpful in that it shows a vertical stringer on the centerline of the arches.
The second step is to write a function that will tell you how long the stringer will be. I find it convenient to write the equation for an arch shape such as this using the parent function h(x) = 1-x^2. This parent function gives an arch of height 1 and width 1 from center (a total width of 2). You want an arch that is 16 ft high and 40 ft wide (one side from center), so you must scale this parent function both horizontally (by 40) and vertically (by 16). It becomes ...
H(x) = 16(1 -(x/40)^2)
The taller arch is twice this height, so the length of a vertical stringer at position x is
vertical length = 2H(x) -H(x) = H(x)
That is, the function H(x) we defined can be used to find the length of the stringers.
The third step is to find the stringer lengths. It can save some energy if you realize that the problem is symmetrical, so that the stringer at x=-30 is the same length as the one at x=30. We need to find stringer lengths every 10 feet from -40 feet to +40 feet. Of course, the ones at ±40 feet are zero length, because that is where the two arches meet.
H(-30) = 16(1 -(3/4)^2) = 7
H(-20) = 16(1 -(1/2)^2) = 12
H(-10) = 16(1 -(1/4)^2) = 15
H(0) = 16
Then the fourth step is to add up the stringer lengths, rounding the result as required.
7 +12 +15 +16 +15 +12 +7 = 16 + 2(34) = 84 . . . . feet (no rounding needed)
Finally, you need to answer the question asked:
The sum of vertical stringer lengths is 84 feet.
Answer:
<em>$2,025.78 </em>
Step-by-step explanation:
I = Prt ⇒ P =
2.25% = 0.0225
P = 45.58 ÷ ( 0.0225 × 1 ) ≈ <em>$2,025.78</em>