7 self study question with answer--21

Question 1

(17)^3.5 × (17)^? = (17)^8

  2.29

  2.75

  4.25

  4.5

It's '4.5 '
Explanation:
Let (17)^3.5 × (17)^x = 17⁸
Then, (17)^3.5+x = 17⁸
3.5 + x = 8
x = (8 - 3.5)
x = 4.5

Question 2

If (a/b)^(x-1) = (b/a)^(x-3), then evaluate for x?

  1/2

  1

  2

  7/2

It's '2 '
Explanation:
Given (a/b)^(x-1) = (b/a)^(x-3)
(a/b)^(x-1) = (a/b)^(3-x)
x-1 = 3-x
2x = 4
x = 2

Question 3

If x = (8+3√7), what is the value of (√x- 1/√x)?

  √13

  √14

  √16

  √15

It's '√14 '
Explanation:
(√x-1/√x)²
= x-2+ 1/x
= x+ 1/(x )-2
= (8+3√7 + 1/(8+3√7)) -2
= (8+3√7) + (8-3v7)/(8+3√7)8-3√7) - 2
= (8+3√7) + (8-3√7)8^2)/3√7)^2 - 2
= (8+3√7) + (8-3√7)/(64-63) -2
= (8+3√7) + (8-3√7)/1 -2
= 8+3√7 + 8-3√7-2
= 14
as (√x - 1/√x)^2
= 14
so, (√x - 1/√x)
= √14

Question 4

Solve the equation 1/(1+a^(n-m)) + 1/(1+a^(m-n)) = ?

  1

  2

  3

  4

It's '1 '
Explanation:
= 1/(1+(a^m/a⁽ⁿ⁾)) + 1/(1+(aⁿ/a^(m)))
= a^(m)/(a^m+aⁿ) + a⁽ⁿ⁾/(a^m+aⁿ) = a^(m)+a⁽ⁿ⁾/(a^m+aⁿ)
= 1

Question 5

p * q = 2p – 3q + pq, then 3*5 + 5*3 = ?

  20

  21

  22

  23

It's '22 '
Explanation:
= 2(3)-3(5) + (3*5) + 2(5)-3(3)+(5*3)
= 6-15+15+10-9+15
= 31-9
= 22

Question 6

What fraction of 4/7, should be added to itself to become 1 1/14

  7/8

  7/9

  7/10

  7/11

It's '7/8 '
Explanation:
= 4/7 x + 4/7 = 154
= 4/7 x = 15/4- 4/7
= 4/7 x = 7/14
= x = 1/2 * 7/4
= 7/8

Question 7

If x = 3+2√2, then solve for √x - 1/√x?

  3√3

  2√2

  2

  1

It's '2 '
Explanation:
(√x - 1/√x)² = x + 1/ x – 2
= (3 + 2√2) + 1 / (3+2√2) – 2
= (3 + 2√2) + 1/ (3+2√2) * (3+2√2)/(3 - 2√2) – 2
= (3 + 2√2) + (3 - 2√2) – 2 = 4
= (√x - 1/√x) = 2