Answer: B. |x-100| = 25
Explanation:
Draw out a number line. Mark 75, 100 and 125 on the number line as points A, B, and C in that order. Don't worry about the spacing.
The value of x represents where the train is. So if we had say x = 85, then it would be at location 85 on the number line. Writing |x-100| is the distance from x to 100. The absolute value ensures the distance is never negative. We want this distance to be 25 because after traveling 25 cm, the switch is turned, and the train goes the other way.
Factor out the common term; 3
(3(x + 1))^2 = 36
Use the Multiplication Distributive Property; (xy)^a = x^ay^a
3^2(x + 1)^2 = 36
Simplify 3^2 to 9
9(x + 1)^2 = 36
Divide both sides by 9
(x + 1)^2 = 36/9
Simplify 36/9 to 4
(x + 1)^2 = 4
Take the square root of both sides
x + 1 = √4
Since 2 * 2 = 4, the square root of 2 is 2
x + 1 = 2
Break down the problem into these 2 equations
x + 1 = 2
x + 1 = -2
Solve the first equation; x + 1 = 2
x = 1
Solve the second equation; x + 1 = -2
x = -3
Collect all solutions;
<u>x = 1, -3</u>
He actually borrowed P=21349-3000=18349 (present value)
Assume the monthly interest is i.
then future value due to loan:
F1=P(1+i)^n=18349(1+i)^(5*12)=18349(1+i)^60
future value from monthly payment of A=352
F2=A((1+i)^n-1)/i=352((1+i)^60-1)/i
Since F1=F2 for the same loan, we have
18349(1+i)^60=352((1+i)^60-1)/i
Simplify notation by defining R=1+i, then
18349(R^60)-352(R^60-1)/(R-1)=0
Simplify further by multiplication by (R-1)
f(R)=18349*R^60*(R-1)-352(R^60-1)=0
Solve for R by trial and error, or by iteration to get R=1.004732
The APR is therefore
12*(1.004732-1)=0.056784, or 5.678% approx.
Roland’s Boat Tours will make more money if they sell more economy seats, hence the maximum profit is attained if they only sell the minimum deluxe seat which is 6
6*35+ 24*40 = 210+960= $1170
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Given details
To make a complete tour, at least 1 economy seats
and 6 deluxe seats
Maximum passengers per tour = 30
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<em>"Boat Tours makes $40 profit for each </em><em>economy</em><em> seat sold and $35 profit for each deluxe seat sold"</em>
<em> </em>Therefore, to maximise profit, he needs to take more of economy seats
Hence
Let a deluxe seat be x and economy seat be y
Maximise
6 x+ 24y = 30
The maximum profit from one tour is = 6*35+ 24*40 = 210+960= $1170
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brainly.com/question/25828237
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The factored expression would look like this : 3(x+8)(x-8)
