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 slope is a zero slope. This means that the line is a straight, horizontal line.
Step-by-step explanation:
Use the slope formula.
5-5/-18-18 = 0/-36
Answer:
3n-8
Step-by-step explanation:
Let n be our number
3 times n
3n
eight less than
3n-8
Answer:
In geometry, the area of a two dimensional object is the amount of space an area takes up. A square unit is a square with sides of length one unit.
The answer is: [C]: Two angles form [a] linear pair if and only if the angles are adjacent.
_____________________________
{Your answer choice is correct! Good job!}.
_______________________________________
Explanation:
__________________
Consider the answer choice given in: "Answer choice: [C]" :
_______________________
"<span>Two angles form linear pair if and only if the angles are adjacent."
</span>_____________________________
Then, consider the following:
__________________
1) "Two angles that are supplementary form a linear pair."
Is this true? Yes, but not always. (In other words, "sometimes"). A "linear pair" of angles IS supplementary (by definition); however, NOT ALL supplementary pairs of angles are linear angles. Supplementary pairs of angles must ALSO be ADJACENT in order to be "linear angles" as well.
2) "Two angles that are vertical are adjacent." Is this true? No; this is NEVER true
_____________
As such, this biconditional is NOT a good definition; and by examining all the other answer choices given, we see that this answer choice "C" is correct.
__________________
Consider the other answer choices given:
_________________________________________
Answer choice: [A]: "T<span>wo angles are supplementary if and only if the sum of their angles measures 180." ;
</span> is INCORRECT because it is a good definition:
1) If 2 angles are supplementary, then the sum of their measures is 180 degrees.
2) If the sum of the measures of two angles is 180 degrees, then the angles are supplementary.
___________________________________
Answer choice: [B]: "<span>Two angles are vertical angles only if they are not adjacent to each other and are formed by two intersecting lines.";
is INCORRECT because it is a good definition:
1) </span>If two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.
<span> 2) If two angles are nonadjacent angles formed by two intersecting lines, then the angles are vertical angles.
_____________________________________
Answer choice: [D]: "The sum of two angles is 90 if and only if those angles are complementary" ;
is INCORRECT because it is a good definition:
1) </span>If two angles are complementary, then the sum of their measures is 90 degrees.
<span> 2) f the sum of [the measures of] two angles is 90 degrees, then the angles are complementary.
_______________________________________________</span>
