Question 43 MarksSolve the following inequations graphically in a two-dimensional plane: $\left(\frac{1}{4}\right) x+\left(\frac{1}{2}\right) y \leq 1$View full question & answer→
Question 53 MarksSolve the following inequations graphically in a two-dimensional plane: $4 x+5 y \leq 40$View full question & answer→
Question 63 MarksSolve the following inequations graphically in a two-dimensional plane: $2 x-y \leq-2$View full question & answer→
Question 73 MarksSolve the following inequations graphically in a two-dimensional plane: $x-y \geq 0$View full question & answer→
Question 83 MarksSolve the following inequations graphically in a two-dimensional plane: $y-5 x \geq 0$View full question & answer→
Question 93 MarksSolve the following inequations graphically in a two-dimensional plane: $y \leq-2 x$View full question & answer→
Question 103 MarksSolve the following inequations graphically in a two-dimensional plane: $y \geq 3$View full question & answer→
Question 113 MarksSolve the following inequations graphically in a two-dimensional plane: $x \leq-4$View full question & answer→
Question 123 MarksFind all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.AnswerLet $2 n, 2 n+2$ be two positive consecutive integers where $n \geq 1 \in Z$.Given that $2 n>5$ and $2 n+2>5$$\begin{aligned}& \therefore n>\frac{5}{2} \text { and } 2 n>3 \\& \therefore n>\frac{5}{2} \text { and } n>\frac{3}{2} \\& \therefore n>\frac{5}{2} \ldots . . . \text { (i) }\end{aligned}$Also $(2 n)+(2 n+2)<23$$\begin{aligned}& \therefore 4 \mathrm{n}+2<23 \\& \therefore 4 \mathrm{n}<21 \\& \therefore \mathrm{n}<\frac{21}{4} \ldots . . . \text { (ii) }\end{aligned}$From (i) and (ii)$\begin{aligned}& \frac{5}{2}<n<\frac{21}{4} \text { and } n \text { is an integer. } \\& \therefore n=3,4,5 \\& n=3 \text { gives } 2 n=6,2 n+2=8 \\& n=4 \text { gives } 2 n=8,2 n+2=10 \\& n=5 \text { gives } 2 n=10,2 n+2=12\end{aligned}$$\therefore$ The pairs of positive even consecutive integers are $(6,8)(8,10),(10,12)$View full question & answer→