Answer:
Given that:
The equation for the future value of a deposit earning compound interest is equation:
.....[1]
where,
P = the initial deposit
t = years invested
r = rate at which interest is compounded annually
.
n = number of times the interest is compounded per year
As per the statement:
After 10 years, a $2,000-dollar investment compounded annually has grown to $3600.
⇒P = $2000 and V(t) = $3600
Substitute in [1] we have;
Divide both sides by 2000 we have;
Taking log base 10 both sides we have;
⇒
Divide both sides by 10 we have;
⇒
Simplify":
Subtract 1 from both sides we have;
or
r = 0.06 = 6%
Therefore, 6% is the interest rate to the nearest whole-number percent
Answer:
The coordinates are (2,8)
Step-by-step explanation:
A hole is where both the numerator and the denominator are zero
f(x)=x^2+4x−12 / x−2
Factor the numerator
f(x) = (x+6) (x-2)/ (x-2)
The hole will occur where x-2 =0
x-2=0
Add 2 to each side
x-2+2 =0+2
x=2
There is a hole at x=2
If we could cancel the x-2 values from the top and bottom, we are left with
f(x) = x+6
At x=2
f(2) = 6+2
f(2) would be 8
The coordinates are (2,8)
There is a hole
I believe the answer is A) 3
Answer:(2,0)
Step-by-step explanation:
5x+2y=10
Verification of points
5(2)+2(0)=10
10=10
LHS=RHS
THUS solution is (2,0)
Explanation:
When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.
The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.
When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.
Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:
- x > ... or x ≥ ... ⇒ shading is to the right of the boundary
- y > ... or y ≥ ... ⇒ shading is above the boundary
Otherwise, the shaded solution space will be below or to the left of the boundary line.
_____
Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.
_____
The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.
