Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
Let

be the length of the rectangle and

be the width. In the problem it is given that

. It is also given that the area

. Substituting in the length in terms of width, we have

. Using the zero product property,

. Solving these we get the width

. However, it doesn't make sense for the width to be negative, so the width must be

. From that we can tell the length

.
Answer:
y=1
Step-by-step explanation:
y= 4 - 2x
y= -5 + 4x
4 - 2x = -5 + 4x
4 + 5 = 4x +2x
9 = 6x
9/6 = x
3/2 = x
y= 4 -2(3/2)
y = 4 - 3
y = 1
Answer:
y = 1/3
Step-by-step explanation:
<u>Step 1: Factor</u>
9y^2 - 6y + 1 = 0
(3y - 1)(3y - 1) = 0
(3y - 1)^2 = 0
<u>Step 2: Solve for y</u>
3y - 1 + 1 = 0 + 1
3y / 3 = 1 / 3
y = 1/3
Answer: y = 1/3
Answer:

Step-by-step explanation:


Simplify

If you have any more questions please let me know.