Answer:
k = 33
Step-by-step explanation:
7 + k/3 = 18
=>7 + k/3 -7 = 18 - 7
=>k/3 = 11
=>(k/3) * 3 = 11 * 3
=>k = 33
The rule of 72 says to divide 72 over the interest rate without the percent sign attached to it. This means we divide 72 over 9.6 to get 72/9.6 = 7.5
So the money doubles every 7.5 years. When another 7.5 years rolls around, a total of 2*7.5 = 15 years has gone by. At this point the money is roughly 4 times that of the original amount deposited.
<h3>Answer: choice B</h3>
<span>The easiest way to answer any question like this is to first put your equation in the simplest form 'y = mx + b'
So in this case, f(x) = 3/4(10) - x simplifies to f(x) = 7.5 -x which reordered becomes f(x) = -x + 7.5
So if you imagine this on a graph, you'll have a point on the y axis at 7.5. Then there is a line from there at a slope of -1. So you'll have a point at (0,7.5), (1, 6.5) ... (7.5,0). Now flipping this over the x axis is easy enough. Your first point intercepting the y axis is at -7.5. Then you'll have a line going up at a slope of +1. So your new equation will simply be g(x) = x-7.5. Now simply plug any coordinate in for g(x) and x to see if the equation is true. For example, let's try (1,-6.5). So -6.5 = 1-7.5. ---> -6.5 = -6.5. So (1, -6.5) is a point on g(x)!</span>
Answer:
Option B.
{–9 + i√225 / 24, –9 – i√225 / 24}
Step-by-step explanation:
12a² + 9a + 7 = 0
Using formula method, the solutions to the equation can be obtained as follow:
Coefficient of a² (a) = 12
Coefficient of a (b) = 9
Constant (c) = 7
a = –b ±√(b² – 4ac) / 2a
a = –9 ±√(9² – 4 × 12 × 7) / 2 × 12
a = –9 ±√(81 – 336) / 24
a = –9 ±√(– 225) / 24
Recall
–225 = –1 × 225
Thus,
–9 ±√(– 225) / 24 = –9 ±√(–1 × 225)/24
Recall
√(–1 × 225) = √–1 × √225 = i√225
Thus,
–9 ±√(–1 × 225)/24 = –9 ± i√225/24
Therefore,
a = –9 ± i√225/24
a = –9 + i√225 / 24 or –9 – i√225 / 24
Therefore, the solutions to the equation are:
{–9 + i√225 / 24, –9 – i√225 / 24}
