Decrease 140g by 25%
2 answers:
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Answer:
1. 0
2. 18 th term
3. 209
4. 670
Step-by-step explanation:
1. n^th term of an A.P = a + (n - 1)d , where n is the term
6 = a + (5 - 1)d ... (i)
5 = a + (6 - 1)d ... (ii)
a + 4d = 6 ... (i)
a + 5d = 5 ... (ii)
Subtracting (ii) - (i) we get;
0 + d = -1 , d = -1
So the common difference (d) = -1
And first term (a);
a + 4(-1) = 6
a = 6 + 4 = 10
11^th term will be;
= 10 + -1(11 - 1) = 10 - 10 = 0
2. The A.P is;
1, 4, 7, 10, 14, ....
The first term (a) = 1
The common difference (d) = 3
= a + (n - 1)d
52 = 1 + (n - 1)3
3n - 3 + 1 = 52
3n = 52 + 2 = 54
n = 54/3 = 18 th term
3. The A.P is;
4, 9, 14, ... , 254
The first term (a) = 4
The common difference (d) = 5
= a + (n - 1)d
To find what term number 254 is;
254 = 4 + (n - 1)5
5n - 5 + 4 = 254
5n = 254 + 1 = 255
n = 255/5 = 51
The 10^th term from the end of the AP is the 42^nd term.
= 4 + (42 - 1)5 = 4 + 205 = 209
4. The A.P is;
5, 8, 11, 14, ...
The first term (a) = 5
The common difference (d) = 3
Sum of n terms in an A.P is given by;
=
(2a + (n - 1)d)
=
(10 + 19(3) = 10(10 +57) = 670
Answer:
The length of side AC is 5 units.
The areas of triangle ABC is 10 square units.
Step-by-step explanation:
From point A (1,3) to point C (1,-2) is 5 units
To check this:
3 - (-2) = 3 + 2 =5
We're subtracting since the point went down (from positive 3 to negative 2)
Now for the area:
Area formula for a triangle: bh =
⋅b⋅h
We already found the height (length) : 5
The base is from point C (1,-2) to point B (5,-2), which is 4 units
To check this:
5 - 1 = 4
Now that we have found the base and height, Let's solve:
⋅4⋅5 =
⋅20 = 10
Our area is 10 square units.
Hope that helps :)