Questions in mathematics

Questions in mathematics

📝 Answered - A lighthouse is located at $(1,2)$ in a coordinate system measured in miles. A sailboat starts at $(-7,8)$ and sails in a positive $x$-direction along a path that can be modeled by a quadratic function with a vertex at $(2,-6)$. Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse? $\left\{\begin{aligned}(x-1)^2+(y-2)^2 & =5 \\ y & =\frac{14}{81}(x-2)^2-6\end{aligned}\right.$ $\left\{\begin{aligned}(x-1)^2+(y-2)^2 & =25 \\ y & =\frac{14}{81}(x-2)^2-6\end{aligned}\right.$ $\left\{\begin{aligned}(x-1)^2+(y-2)^2 & =5 \\ y & =-\frac{14}{81}(x+7)^2+8\end{aligned}\right.$ $\left\{\begin{aligned}(x-1)^2+(y-2)^2 & =25 \\ y & =-\frac{14}{81}(x+7)^2+8\end{aligned}\right.$

📝 Answered - Write the equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form.

📝 Answered - MATHEMATICS PAPER 2 (THEORY) INSTRUCTION: Answer any three (3) questions, Question One (1) is compulsory. 1. a. The cost of one litre of petrol was N1,100.00. Create a table of values to show the cost of 2, 3, 4, 5 and 6 litres of petrol. b. Use a scale of 2cm to 1 litre on the horizontal axis and a scale of 2cm to #1,000.00 on the vertical axis, draw the graph to illustrate the cost of petrol (N) against the quantity of petrol (litres). c. Extend the line on the graph to determine: i. the cost of 7½ litres of petrol. ii. how many litres of petrol can be bought with N3,500.00 2. a. Using a pair of compasses, ruler and pencil, construct a right-angled triangle with side XY-60mm and XZ-55mm, measure YZ. (Hint: 10mm=1cm). b. A man gets a monthly pay of Nx. His monthly rent is N8,000.00. After paying his rent, he is left with less than N20,000. Find the range of values of x. 10 3. a. If 2 is added to the numerator and denominator of a fraction, it becomes from the same numerator and denominator, it becomes. Find the fraction. b. Write 1011.1012 as base 10 number. and if 3 is subtracted 4. a. A tray of eggs contains 16 large sized eggs and 14 small sized egg. An egg is selected at random. Find the probability of selecting either a small sized or large-sized egg. b. If T² = 4π² (h²+ k²) make 'k' the subject of the formula. hg

📝 Answered - A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? [tex] \begin{array}{l} V=h w h \\ p=2(l+w) \end{array} [/tex] A. [tex]y=5(28-x)(x)[/tex] B. [tex]y=5(28-2 x)(x)[/tex] C. [tex]y=5(14-x)(x)[/tex] D. [tex]y=5(14-2 x)(x)[/tex]

📝 Answered - Simplify the expression: [tex]\begin{array}{c} \left(r^{-4} s^7 t^5\right)^{10} \\ \frac{s^{[?]} t}{r} \end{array}[/tex]

📝 Answered - Which of the following is the formula for the solutions of a quadratic equation [tex]a x^2+ b x+c=0[/tex]? A. [tex]\frac{b \pm \sqrt{b^2-4 a c}}{2 a}[/tex] B. [tex]\frac{b \pm \sqrt{b^2+4 a c}}{2 a}[/tex] C. [tex]\frac{-b \pm \sqrt{b^2+4 a c}}{2 a}[/tex] D. [tex]\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]

📝 Answered - How many solutions exist for the given equation? [tex]3(x+10)+6=3(x+12)[/tex] A. zero B. one C. two D. infinitely many

📝 Answered - i. the cost of $7 \frac{1}{2}$ litres of petrol. ii. how many litres of petrol can be bought with $3,500.00

📝 Answered - $\frac{1}{2} x^2+3 x$

📝 Answered - What is the following sum in simplest form? $\sqrt{8}+3 \sqrt{2}+\sqrt{32}$