Question

Quick Answers
7. If 9 is subtracted from thrice of a number, we get 14. Find the number.
& Three-fifth of x gives 18. Find x.
9. Two-third of y gives 2.4. Find y.
10. Three-fourth of x is subtracted from
gives
7
6
Find x.
6
1
11. One-fifth of x gives
Find x.
25
12. 99 subtracted from 2a gives 283. Find a.​

Answer 1

$7. Let \: a \; number = x$

/* According to the problem given ,

9 is subtracted from thrice of a number, we get 14.

$3x - 9 = 14$

$\implies 3x = 14 + 9$

$\implies 3x = 23$

$\implies x = \frac{23}{3}$

Therefore.,

$\red{ Required \: number }\green { = \frac{23}{3}}$

$9. Given \: Three - fifth \: of \: x \: gives \: 18$

$\frac{3}{5} x = 18$

$\implies x = 18 \times \frac{5}{3}$

$\implies x = 6 \times 5$

$\implies x = 30$

$\green { Value \: of \:x } \green { = 30}$

•••♪

Answer 2

→ Given, O is the origin, So O is ( 0, 0)

→Co-ordinates : A is (x₁, y₁), B is (x₂, y₂)

⊕ In vector form,

→OA = x₁ i + y₁ j

→OB = x₂ i + y₂ j

→Let's say OA, OB are represented by Vectors a, b.

⇒ So,

⇒a. b = ( x₁ i + y₁ j) (x₂ i + y₂ j)

⇒ a. b = x₁x₂ + y₁y₂ - - - - (1)

→By definition of Dot product,

⇒ a. b = |a| |b| cos(a, b)

⇒a. b = OA × OB ×cos ( ∠AOB) - - - - (2)

→Now, From (1) & (2)

→OA × OB × cos ( ∠AOB) = x₁x₂ + y₁y₂

∴Hence proved

hope it helps

:)