Maharashtra Board Class 10 Mathematics — Flashcards

A: Step 1: Substitute x = 3 into 2x - y = 4. 2(3) - y = 4 Step 2: Simplify. 6 - y = 4 Step 3: Subtract 6 from both sides. -y = -2 Step 4: Multiply by -1. y = 2 Answer: y = 2

A: Step 1: Add the equations. (x + y) + (2x - y) = 4 + 2 3x = 6 Step 2: Solve for x. x = 2 Step 3: Substitute x = 2 in x + y = 4. 2 + y = 4 Step 4: Solve for y. y = 2 Answer: x = 2, y = 2

A: Step 1: Choose easy values of x. If x = 0, then y = 4, so one point is (0, 4). Step 2: Choose another value. If x = 2, then y = 2, so another point is (2, 2). Step 3: Check. 0 + 4 = 4 and 2 + 2 = 4. A

A: Step 1: Since PQ is parallel to BC, use the basic proportionality theorem. Step 2: Write the ratio of the divided sides. AP/PB = AQ/QC Answer: The line divides the two sides in the same proportion.

A: Use it when a line is parallel to one side of a triangle and cuts the other two sides at distinct points. Example: If PQ ∥ BC in triangle ABC, then AP/PB = AQ/QC. This helps compare the two divided si

A: Step 1: Use the basic proportionality theorem. AP/PB = AQ/QC Step 2: Substitute the values. 3/6 = 4/QC Step 3: Simplify 3/6 = 1/2. So, 1/2 = 4/QC Step 4: Cross-multiply. QC = 8 cm Answer: QC = 8 cm

A: Step 1: Factorise the quadratic polynomial. x^2 - 4x - 5 = (x - 5)(x + 1) Step 2: Use the zero product property. If product of two numbers is zero then at least one of them is zero. So, x - 5 = 0 o

A: Step 1: Write the quadratic in completed-square form. x^2 + 10x + 2 = (x + 5)^2 - 25 + 2 Step 2: Simplify. (x + 5)^2 - 23 = 0 Step 3: Rearrange. (x + 5)^2 = 23 Step 4: Take square roots. x + 5 = √

A: Yes. Step 1: Check the highest power of x. The maximum index of x is 2. Step 2: Check the coefficient of x^2. Here, a = 1, so a ≠ 0. Step 3: Match the standard form. It fits ax^2 + bx + c = 0. Answ