Questions in mathematics

Questions in mathematics

📝 Answered - Solve $3^{x+1}=2^x+4$ graphically.

📝 Answered - Question 2: Sum of the first 3 terms of an AP is \(\frac{2}{9}\) times the sum of first 6 terms of the same AP. Find the ratio of the first term to the common difference of the same AP.

📝 Answered - Convert the following fractions into percentages: [tex]\frac{22}{100}[/tex] [tex]\frac{3}{4}[/tex] [tex]\frac{28}{24}[/tex]

📝 Answered - 8. Simplify. (i) (21.6 ÷ 1.2) × 3.9 (ii) (2.8 × 1.6) ÷ 12.8 (iii) (12.8 ÷ 0.125) ÷ 3.2 9. The product of two decimals is 0.252. If one of them is 0.72, find the other. 10. A bar of chocolate costs ₹10.50 and a packet of chips costs ₹6.75. What will be the total cost of 8 bars of chocolate and 5 packets of chips? 11. Eight copies of a book cost ₹523.60. What is the cost of a copy of the book? 12. If 40 vessels of equal capacity can be filled with 186 litres of water, find the capacity of each vessel. 13. A certain sum of money is distributed among 26 people. If each person receives ₹6.45 and ₹2.30 is left in the end, what was the initial sum of money?

📝 Answered - (a) By rounding each number in the calculation correct to 1 significant figure, work out an estimate for the value of A. A = (136 + 47.2) / (62.9 - 18.1) Show all your working. (b) Use your calculator to find the actual value of A, correct to 4 significant figures. (c) Write 2.37 × 10^6 as an ordinary number. (d) Write 0.00045 in standard form. (e) Calculate 3.5 × 10^7 + 4.4 × 10^5. Give your answer in standard form.

📝 Answered - A sailboat that is 2 km due west of a lighthouse sends a signal to the lighthouse that it is in distress. The lighthouse quickly signals a rescue plane that is 7 km due south of the lighthouse. What heading from due north should the plane take in order to intercept the troubled sailboat? Round your answer to the nearest degree. [tex] \begin{array}{c} \Rightarrow a=2 km \\ b=7 km \\ \angle \theta=? \\ \tan \theta=\frac{2}{7} \\ \theta=\tan ^{-1}\left(\frac{2}{7}\right) \end{array} [/tex]

📝 Answered - Anya graphed the line $(y-2)=3(x-1)$ on the coordinate plane. What is the slope of Anya's line? A. -3 B. -1 C. 1 D. 3

📝 Answered - Perform the elementary row operation $-\frac{1}{3} R_2 \rightarrow R_2$ on the given matrix. Write numbers as integers or simplified fractions. $\left[\begin{array}{ccc:c} 3 & 5 & 1 & 4 \\ 1 & 3 & 1 & 5 \\ 1 & 3 & 0 & 10 \end{array}\right]$ Resulting matrix:

📝 Answered - Consider the following function: r(x)=(x-4)^2-4 Find two points on the graph of the parabola other than the vertex and $x$-intercepts.

📝 Answered - The point-slope form of the equation of the line that passes through $(-9,-2)$ and $(1,3)$ is $y-3=\frac{1}{2}(x-1)$. What is the slope-intercept form of the equation for this line? A. $y=\frac{1}{2} x+2$ B. $y=\frac{1}{2} x-4$ C. $y=\frac{1}{2} x+\frac{5}{2}$ D. $y=\frac{1}{2} x-\frac{7}{2}$