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.
Answer:
B. 30
Step-by-step explanation:
2m^2 + 12
m = 3
2(3)^2 + 12
3 squared is 9
2(9) + 12
2 times 9 is 18
18 + 12 = 30
2m^2 + 12 = 30
Answer:
x is about 5.67
Step-by-step explanation:
Steps:
Divide each side by three:
17x = 3 → x = 5.67
The point-slope form of a line is:
y-y1=m(x-x1), where m=slope and (x1,y1) is any point on the line
First we need to find the slope, which is (y2-y1)/(x2-x1)
m=(4--1)/(8-2)
m=5/6 and we can use either point, I'll use (8,4)
y-4=(5/6)(x-8)
That is your equation in point-slope form.
Now the standard equation of a line is ax+by=c
y-4=(5/6)(x-8) we can perform the indicated multiplication on the right side
y-4=(5x-40)/6 multiply both sides by 6
6y-24=5x-40 add 24 to both sides
6y=5x-16 subtract 5x from both sides
-5x+6y=-16 and by convention, the standard equation of a line should be expressed with a positive coefficient for x, so multiply both sides by -1
5x-6y=16
