Simplify 8x2(2x2+3y), find the value of x if 10 x = 4, find x and y if x+10y=6 and x-10y=4, and make g the subject of T = 2((h2+R2)/(g))

Here are the solutions to your questions: 1. Simplify 8x^2(2x^2+3y) Step 1: Distribute 8x^2 to each term inside the parenthesis. 8x^2(2x^2+3y) = (8x^2 · 2x^2) + (8x^2 · 3y) Step 2: Multiply the terms. = 16x^4 + 24x^2y The simplified expression is 16x^4 + 24x^2y. 2. Find the value of x if _10 x = 4 Step 1: Convert the logarithmic equation to an exponential equation. _10 x = 4 10^4 = x Step 2: Calculate the value of x. x = 10 × 10 × 10 × 10 x = 10000 The value of x is 10000. 3. Find the value of x and y if x+10y=6 and x-10y=4 Let the given equations be: (1) x+10y=6 (2) x-10y=4 Step 1: Add equation (1) and equation (2) to eliminate y. (x+10y) + (x-10y) = 6+4 2x = 10 Step 2: Solve for x. x = (10)/(2) x = 5 Step 3: Substitute the value of x=5 into equation (1). 5+10y=6 10y = 6-5 10y = 1 Step 4: Solve for y. y = (1)/(10) The values are x=5, y=(1)/(10). 4. Make g the subject of the formula T = 2((h^2+R^2)/(g)) Step 1: Divide both sides by 2. (T)/(2) = sqrt((h^2+R^2)/(g)) Step 2: Square both sides. ((T)/(2))^2 = (h^2+R^2)/(g) (T^2)/(4^2) = (h^2+R^2)/(g) Step 3: Multiply both sides by g. g (T^2)/(4^2) = h^2+R^2 Step 4: Isolate g by multiplying both sides by (4^2)/(T^2). g = (h^2+R^2) (4^2)/(T^2) g = (4^2(h^2+R^2))/(T^2) The formula with g as the subject is g = (4^2(h^2+R^2))/(T^2). 5. Factorize 4y^2+15y=3y Step 1: Move all terms to one side to set the equation to zero. 4y^2+15y-3y=0 4y^2+12y=0 Step 2: Factor out the common term, which is 4y. 4y(y+3)=0 The factored expression is 4y(y+3). 6. Construct angle 75^ To construct a 75^ angle: • Draw a line segment AB. • At point A, construct a 90^ angle (e.g., using a compass to draw perpendicular bisector of an arc). Let the perpendicular line be AC. • At point A, construct a 60^ angle (e.g., using a compass to mark an arc from A, then another arc from the intersection point on AB with the same radius). Let this line be AD. • Bisect the angle between the 60^ line (AD) and the 90^ line (AC). The angle between them is 30^. Bisecting it gives 15^. • The angle formed by the 60^ line and the bisector will be 60^ + 15^ = 75^. **7. Construct angle $15