Explanation

Solve 7n + 12 = 4n + 27

= 7n - 4n + 12 - 27

= 3n + 12 

= 3n - 15 

15 = 3n

15/ 3 = n 

n =  5 

Explanation

Address the formula, input parameters & values.

Input parameters & values:

The number series 1, 3, 5, 7, 9, .  .  .  .  , 139.

The first term a = 1

The common difference d = 2

Total number of terms n = 70

step 2

apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 70/2 x (1 + 139)

= (70 x 140)/ 2

= 9800/2

1 + 3 + 5 + 7 + 9 + .  .  .  .   + 139 = 4900

Therefore, 4900 is the sum of first 70 odd numbers.

Explanation

1+2 = 3
3x2 = 6+2 =8
8x2 = 16+3 =19
19x2 = 38+4 = 42
42x2 = 84+5 = 89

Explanation

A perfect square is a number that is the square of a whole number.

7 × 7 = 49, so 49 is a perfect square.

Explanation

The homogeneous equation ax² + 2hxy + by² = 0 represents:

• A pair of real and distinct straight lines through the origin if h² − ab > 0
• A pair of coincident lines if h² − ab = 0
• A pair of imaginary lines if h² − ab < 0

So, the correct answer is: h² − ab > 0

Explanation

Explanation

To evaluate the expression 2 - 1/3, we need to subtract 1/3 from 2.

First, convert the whole number 2 to a fraction with a denominator of 3:

2 = 6/3

Now, subtract 1/3 from 6/3:

6/3 - 1/3 = 5/3

Explanation

Explanation

Explanation

Solution:

The ratio of two numbers is 

35:49

5:7

and the sum of two numbers is 

35+49=84

if if 5 subtracted from the sum of these two numbers

84-5=79