6. 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

Question

6. 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

Asked on April 11, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-11T23:46:40.534Z

You're on a roll — let's tackle these math problems! 6. If $\log_{10}(2) = 0.3010$, what is $\log_{10}(8)$? Step 1: Express 8 as a power of 2. $$8 = 2^3$$ Step 2: Use the logarithm property $\log_b(M^p) = p \log_b(M)$. $$\log_{10}(8) = \log_{10}(2^3) = 3 \log_{10}(2)$$ Step 3: Substitute the given value of $\log_{10}(2)$. $$3 \times 0.3010 = 0.9030$$ The correct option is A. $$\boxed{\text{A. } 0.9030}$$ 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 $x$. $$x + y = 5 \implies y = 5 - x$$ 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. $$\boxed{\text{D. } 4}$$ 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, $S_n = \frac{n}{2}[2a + (n-1)d]$. $$S_{10} = \frac{10}{2}[2(2) + (10-1)3]$$ $$S_{10} = 5[4 + (9)3]$$ $$S_{10} = 5[4 + 27]$$ $$S_{10} = 5[31]$$ $$S_{10} = 155$$ The correct option is A. $$\boxed{\text{A. } 155}$$ 9. If $P = \{x: x \text{ is a prime number } < 10\}$, $Q = \{x: x \text{ is an odd number } < 10\}$, find $P \cap Q$. 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 $P \cap Q$, which consists of elements common to both sets $P$ and $Q$. $$P \cap Q = \{3, 5, 7\}$$ The correct option is C. $$\boxed{\text{C. } \{3, 5, 7\}}$$ 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. $$\boxed{\text{A. } (x - 2)^2 + (y - 3)^2 = 16}$$ Send me the next one 📸

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