Explanation

Square of x is x².

Last verified on 10-02-2026

Explanation

Let Farha's age = x

Sanam's age = x + 13

After 3 years:

Farha = x+3

Sanam = x+13+3 = x+16

Sum = (x+3) + (x+16) = 33

2x + 19 = 33

2x = 14

x = 7

Farha = 7

Sanam = 7+13 = 20

Sanam's age after 3 years = 20 + 3 = 23

Last verified on 09-02-2026

Explanation

Items = [8 14]

Costs = [15; 10]

Total cost = [8 14] [15]

[10]

= 8(15) + 14(10)

= 120 + 140 = 260

Matrix representation:

[8 14] × [15; 10] = [260]

Last verified on 08-02-2026

Explanation

(4i)(-3i) = -12i² = -12(-1) = 12

Last verified on 08-02-2026

Explanation

In the quadratic expression ax² + bx + c, x is the only variable.

a, b, c are constants (parameters), not variables.

Last verified on 08-02-2026

Explanation

(x, 8) = (4, y-2)

⇒ x = 4 and 8 = y-2

⇒ y = 8+2 = 10

x + y = 4 + 10 = 14

Last verified on 07-02-2026

Explanation

Additive inverse of a number x is a number y such that x + y = 0.

For 2/3, the additive inverse is -2/3 because 2/3 + (-2/3) = 0.

Last verified on 07-02-2026

Explanation

In (a + b)^n, the total number of terms is n + 1.

Last verified on 07-02-2026

Explanation

Explanation

Given:

$$X : Y = 3 : 4 quad text{and} quad Y : Z = 5 : 8$$

Step 1: Make Y common

• From $X:Y=3:4$, let$X=3k$, $Y = 4k$

• From $Y:Z = 5:8$, let $Y = 5m$, $Z=8m$

Step 2: Equate Y

$$4k = 5m implies k = frac{5}{4} m$$

Then:

$$X = 3k = 3 cdot frac{5}{4} m = frac{15}{4} m$$ $$Y = 4k = 5m$$$$Z = 8m$$

Step 3: Compute the expression

$$frac{2Y}{3X - Y + 2Z} = frac{2 cdot 5m}{3 cdot frac{15}{4} m - 5m + 2 cdot 8 m}$$3X−Y+2Z​=2⋅5m/ 3⋅15​/4m−5m+2⋅8m​

Numerator: $2\cdot 5m=10m$

Denominator:

3⋅15/4​m=45​/4m
45/4​m−5m+16m=45/4​m−20​/4m+64/4​m=89/4​m$$frac{2Y}{3X - Y + 2Z} = frac{10 m}{frac{89}{4} m} = frac{10 cdot 4}{89} = frac{40}{89}$$3X−Y+2Z​=10m​/89/4=10⋅4/89​=40/89​