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Questions in mathematics

[Terjawab] The vertex of this parabola is at $(-3,-2)$. Which of the following could be its equation? A. $y=-2(x-3)^2-2$ B. $y=-2(x+3)^2-2$ C. $y=-2(x-3)^2+2$ D. $y=-2(x+3)^2+2$

[Terjawab] The value of $y$ varies directly with x, and $y = 40$ when $x = 8$. What is y when $x = 7$? $y=[?]$

[Terjawab] Which of the following expressions shows the number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter? a. [tex]$21 \cdot 36^7$[/tex] b. [tex]$26 \cdot 36^7$[/tex] c. [tex]$26^5 \cdot 10^3$[/tex] d. [tex]$36^8$[/tex]

[Terjawab] [tex]\frac{7}{9} \div \frac{35}{45}[/tex]

[Terjawab] The greatest integer function and absolute value function are both examples of functions that can be defined

[Terjawab] Find the 9th term of the AP, $18, 12, 6, 0, -62$

[Terjawab] Try it... 10, 9, 60, 90, 70, 66, ? 1) 88 2) 96 3) 85 4) 91

[Terjawab] Solve the following word problems. a. Alisha has a ribbon that is 12.6 metres long. Shambhvi has a ribbon that is 2.8 metres shorter than Alisha's ribbon. What is the total length of the two ribbons? b. Mohit has a bottle that has 2.17 litres of water and Priya has a jug that has 0.79 litres less water than the bottle. Find the total litres of water in both. c. A coconut tree is 6.6 metres tall and a mango tree is 3.4 metres shorter than the coconut tree. Find the total height of both the trees. d. Sack P contains 34.5 kg of potatoes and Sack Q contains 4.8 kg more potatoes than that of Sack P. Find the total weight of potatoes in both the sacks.

[Terjawab] What is the solution to the equation 2(4 - 3x) + 5(2x - 3) = 20 - 5x? Options: A) x = -13 B) x = 5/4 C) x = 13/2 D) x = 3

[Terjawab] A quadratic polynomial, whose zeroes are -4 and -5, is a) x² - 9x + 20 b) x² + 9x + 20 c) x² - 9x - 20 8. For p(x) = ax² + bx + c, sum of zeroes is equal to a) zero b) c/a c) -b/a 9. Assertion: √2 is an irrational number. Reason: A number is irrational if it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0 a) Both A and R are true, and R is the correct explanation of A. b) Both A and R are true, but R is not the correct explanation of A. c) A is true, but R is false. d) A is false, but R is true. 10. Assertion: If α & β are the zeroes of the quadratic polynomial x² - 7x + 10, then α + β = 7 and αβ = 10. Reason: For a polynomial ax² + bx + c, sum of zeroes = -b/a, and product = c/a. a) Both A and R are true, and R is the correct explanation of A. b) Both A and R are true, but R is not the correct explanation of A. c) A is true, but R is false. d) A is false, but R is true. SECTION - B 11. Find the HCF & LCM of 12, 15, 21 by applying the prime factorization method. 12. Given that HCF(306, 657) = 9, find LCM(306, 657). 13. Find the sum and product of the polynomial 2x² - 9x + 4 = 0. 14. Find the zeroes of the quadratic polynomial x² - 2x - 8, and verify the relationship between the zeroes and its coefficients. 15. If α & β are zeroes of the polynomial x² + 2x - 4, then find the value of 1/α + 1/β.