Answer:
The resulting graph is 
.
Step-by-step explanation:
The resulting function is of the form:
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Amplitude, dimensionless.
- Midpoint value, dimensionless.
The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: 
. According to the graph, the function is bounded between 5 (
) and -5 (
), and the midpoint value () is 0. The amplitude is determined by the following calculation:
If 
and 
, then:
The resulting graph is .
You deposit some money into a bank account paying 8% simple interest per year. You received $500 in interest after 2 years. How much the deposit (principal) was?
Result
The principal was $3125.
Explanation
Find principal by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this example I = $500, i = 8% and t = 2 years, so
IPPP=P⋅i⋅t=Ii⋅t=5000.08⋅2=3125
If "a" and "b" are two values of x-coordinate, and "m" is the midpoint between them, it means the distance from one end to the midpoint is the same as the distance from the midpoint to the other end
... a-m = m-b
When we add m+b to this equation, we get
... a+b = 2m
Solving for m gives
... m = (a+b)/2
This applies to y-coordinates as well. So ...
... The midpoint between (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2)
_____
Jennifer had (x1, y1) = (-4, 10) and (x2, y2) = (-2, 6). So her calculation would be
... midpoint = ((-4-2)/2, (10+6)/2) = (-6/2, 16/2) = (-3, 8)
Brandon had (x1, y1) = (9, -4) and (x2, y2) = (-12, 8). So his calculation would be
... midpoint = ((9-12)/2, (-4+8)/2) = (-3/2, 4/2) = (-1.5, 2)
Answer:
∠ 1 = ∠ 3 = 33°
Step-by-step explanation:
∠ 3 and ∠ 6 are same- side interior angles and are supplementary , thus
∠ 3 + ∠ 6 = 180° , that is
∠ 3 + 147° = 180° ( subtract 147° from both sides )
∠ 3 = 33°
∠ 1 and ∠ 3 are vertical angles and congruent, thus
∠ 1 = ∠ 3 = 33°
