Let x and y be the numbers;
We have x + 2y = 9 and 2x + y = 21;
Then, x = 9 - 2y;
Finally, 2(9-2y) + y = 21 ;
18 - 4y + y = 21;
18 - 3y = 21;
-3y = 3;
y = - 1;
x = 9 - 2× (-1);
x = 9 + 2 ;
x = 11;

7 0

3 years ago

1. Exercise 18, section 5.4. Compute 90, 91, 92, 93, 94 and 95. Make a conjecture about the units digit of 9n where n is a posit

Burka [1]

Answer:

n is a positive integer and here 90, 91, 92, 93, 94 and 95 is 9⁰ = 1

9¹ = 9

9² = 81

9³ = 729

9⁴ = 6561

9⁵ = 59049

so mathematical induction is prove given below.

Step-by-step explanation:

9⁰ = 1

9¹ = 9

9² = 81

9³ = 729

9⁴ = 6561

9⁵ = 59049

lets us consider by P (n) for the base case n = 0 then 9⁰ = 1 So P (1) is true

k ≥ 1so consider all integers

1≤l≤ k

There is a need to prove P (k+1)

if k is odd

$9^k^+^1$ = $9^k$ .9.

$9^k$ is 9 so

$9^k$ = 9 +10m

then

$9^k^+^1$ = 9 ( 9 + 10m)

=81 + 10 (9m)

so digit is 1 and k +1 is even

3 0

3 years ago

Evaluate √x^2 − y^2 when x^2 =33 and y^2 =15

Andre45 [30]

Answer:

3√2

Step-by-step explanation:

In this question, we are asked to get the value of √ ( x²-y² ), while the value of x² and y² are given to be 33 and 15 respectively.

Hence, x² =33 and y² = 15.

Putting the values of x² and y² in the above expression we get,

√ ( x²-y² ) = √ ( 33-15) = √18 =3√2. (Answer)

3 0

3 years ago