If log10(2) = 0.3010, what is log10(8)? A. 0.9030 B. 0.3010 C. 0.6020 D. 0.9040 7. Find the value of x if 2x + 3y = 11 and x + y = 5 A. 1 B. 2 C. 3 D. 4 8. What is the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...? A. 155 B. 160 C. 165 D. 170 9. If P = x: x is a prime number < 10, Q = x: x is an odd number < 10, find P ∩ Q A. 1, 3, 5, 7 B. 2, 3, 5, 7 C. 3, 5, 7 D. 2, 3, 5, 7, 9 10. Find the equation of the circle with centre (2, 3) and radius 4 A. (x - 2)2 + (y - 3)2 = 16 B. (x + 2)2 + (y + 3)2 = 16 C. (x - 2)2 + (y - 3)2 = 4 D. (x + 2)2 + (y + 3)2 = 4

You're on a roll — let's tackle these math problems! 6. If _10(2) = 0.3010, what is _10(8)? Step 1: Express 8 as a power of 2. 8 = 2^3 Step 2: Use the logarithm property _b(M^p) = p _b(M). _10(8) = _10(2^3) = 3 _10(2) Step 3: Substitute the given value of _10(2). 3 × 0.3010 = 0.9030 The correct option is A. A. 0.9030 7. Find the value of x if 2x + 3y = 11 and x + y = 5. Step 1: From the second equation, express y in terms of x. x + y = 5 y = 5 - x Step 2: Substitute this expression for y into the first equation. 2x + 3(5 - x) = 11 2x + 15 - 3x = 11 Step 3: Simplify and solve for x. -x + 15 = 11 -x = 11 - 15 -x = -4 x = 4 The correct option is D. D. 4 8. What is the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...? Step 1: Identify the first term (a), common difference (d), and number of terms (n). The first term a = 2. The common difference d = 5 - 2 = 3. The number of terms n = 10. Step 2: Use the formula for the sum of the first n terms of an arithmetic progression, S_n = (n)/(2)[2a + (n-1)d]. S_10 = (10)/(2)[2(2) + (10-1)3] S_10 = 5[4 + (9)3] S_10 = 5[4 + 27] S_10 = 5[31] S_10 = 155 The correct option is A. A. 155 9. If P = \x: x is a prime number < 10\, Q = \x: x is an odd number < 10\, find P Q. Step 1: List the elements of set P. Prime numbers less than 10 are numbers greater than 1 that have no positive divisors other than 1 and themselves. P = \2, 3, 5, 7\ Step 2: List the elements of set Q. Odd numbers less than 10 are integers not divisible by 2. Q = \1, 3, 5, 7, 9\ Step 3: Find the intersection P Q, which consists of elements common to both sets P and Q. P Q = \3, 5, 7\ The correct option is C. C. \3, 5, 7\ 10. Find the equation of the circle with centre (2, 3) and radius 4. Step 1: Recall the standard equation of a circle with centre (h, k) and radius r. (x - h)^2 + (y - k)^2 = r^2 Step 2: Substitute the given centre (h, k) = (2, 3) and radius r = 4 into the equation. (x - 2)^2 + (y - 3)^2 = 4^2 (x - 2)^2 + (y - 3)^2 = 16 The correct option is A. A. (x - 2)^2 + (y - 3)^2 = 16 Send me the next one 📸