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:
1.922 miles is equivalent to 3.1 kilometers.
Step-by-step explanation:
Given:
1 km = 0.62 miles.
3.1 km = ? miles
Now, in order to find the number of miles equivalent to 3.1 km, we use unitary method with the help of the conversion factor.
From the conversion factor, we can conclude that kilometer is a smaller unit compared to that of mile.
So, conversion factor = 
The formula to transform 'n' kilometers to miles is given as:
Therefore, 3.1 km = 
3.1 km = 
miles
Therefore, 1.922 miles is equivalent to 3.1 kilometers.
Answer:
A.
Step-by-step explanation:
6^(1-1) + 6^(2-1) + 6^(3-1) + 6^(4-1)
= 1 + 6 + 36 + 216
= 259.
Answer:
is 200 times larger than 
Step-by-step explanation:
To compare both values we divide the exponents
6 divide by 3 is 2
for simplify exponents we use exponential property
a^m / a^n = a^(m-n)
is 200 times larger than
Answer:
B. m ∠ 1 = 90° and m ∠ 2 = 90°
Step-by-step explanation:
For most situations, the conjecture would probably be true, but there is one exception that makes this statement false.
When two right angles are supplementary, none of them is acute.
For an angle to be acute it needs to be lesser than 90°, and for a pair of angles to be supplementary they should add up to exactly 180°.
With a pair of right angles (90° each), their sum adds up to 180° but neither of them are acute.
Therefore, the answer is B. m ∠ 1 = 90° and m ∠ 2 = 90°
