We can figure this out using the explicit formula.
n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.
f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n
Now, we can input 214 for n and solve.
f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646
The 214th term in this sequence is 646.
75x+2=
75x-2=-2. move the 2 to the other side
75x=-2 now divide 75 both sides
75/75x=-2/75
x=-2/75
9514 1404 393
Answer:
y = -4x +2
Step-by-step explanation:
The equation you're writing is in slope-intercept form. The coefficient of x is the slope, which is the "rise"/"run" of the line.
Here, to get from the left point to the right point, you must go down 4 units (rise=-4) and 1 unit to the right (run=1). So, the slope is ...
m = rise/run = -4/1 = -4
The constant in the equation is the y-intercept: the y-coordinate of the point where the line crosses the y-axis. That point is marked as (0, 2), so its y-coordinate is 2.
The equation for the line is ...
y = -4x +2
Answer:
The perimeter and area of the square are 56 units and 196 square units, respectively.
Step-by-step explanation:
The inner right triangle represents a 45-45-90 right triangle, which has the feature of a hypotenuse whose length is 
time the length of any of its legs. If the hypotenuse has a measure of 
, then the legs of the triangle have a measure of 
.
Now, we are aware that the side length of the square is twice the length of the leg of the right triangle. Then, side length of the square is 14 units long.
Lastly, we know from Geometry that the perimeter and area of the square are represented by the following expressions:
Perimeter
(1)
Area
(2)
Where 
is the side length of the square.
If we know that 
, then the perimeter and area of the square are, respectively:
The perimeter and area of the square are 56 units and 196 square units, respectively.
