Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.
The value is what the Y axis is when X is 8.
Draw a vertical line down from X=8 and see where the line crosses on the Y axis.
See the attached picture. The answer is Y = -4
Answer: 
.
Step-by-step explanation:
We know that 
compresses f(x) vertically such that
- if 0 < a < 1 (a fraction), the graph is compressed vertically by a factor of a units.
- if a > 1, the graph is stretched vertically by a factor of a units.
If we vertically compress the linear parent function, F(x) = x, by multiplying by 
.
Then, the equation of the new function is 
.
i.e. .
<span>You need (8-6) 2 extra gallons to take a bath. With sixty people bathing, you'll need 60*2=120 extra gallons to meet the extra demand for water. Alternatively, you could note that 60 bathers*8 gallons per bath=480 gallons of water would be used for 60 baths and 60*6=360 needed for showers. The difference would be 480-360=120 gallons.</span>
