Questions in mathematics

Questions in mathematics

[Free] Divide ₹1100 among A, B, and C so that A shall receive [tex]\frac{3}{7}[/tex] of what B and C together receive and B may receive [tex]\frac{2}{9}[/tex] of what A and C receive.

[Free] The average cost per fruit of 5 apples and 4 mangoes is ₹48 and the average cost per fruit of 7 apples and 8 mangoes is ₹60. Find the total cost of 24 apples and 24 mangoes. A. ₹1332 B. ₹2424 C. ₹2664 D. ₹3996

[Free] Q.1) In the following, circle the polynomials: (i) [tex]\[\sqrt{x} + 2\][/tex] (ii) [tex]\[t^2 + 5t - 1\][/tex] (iii) [tex]\[\sqrt{3}x^2 - 2x\][/tex] (iv) [tex]\[8\][/tex] (v) [tex]\[1 - \sqrt{2}x\][/tex] (vi) [tex]\[\frac{t}{4}\][/tex] (vii) [tex]\[0\][/tex] (viii) [tex]\[y^{\frac{3}{2}} + 3y + 2\][/tex] Q.2) Mark as right (✔) or wrong (x): 1) [tex]\[x^2 + y + 3\][/tex] is a polynomial in one variable. 2) Number of terms in a polynomial is almost two. 3) 0 is a polynomial. 4) [tex]\[x + \frac{1}{x}\][/tex] is a polynomial.

[Free] Find the difference quotient of [tex]$f$[/tex]; that is, find [tex]$\frac{f(x+h)-f(x)}{h}, h \neq 0$[/tex], for the following function. Be sure to simplify. [tex]$f(x)=2 x^2-x-3$[/tex] [tex]$\frac{f(x+h)-f(x)}{h}= \square$[/tex] (Simplify your answer.)

[Free] Perform the indicated operations on the following polynomials. Add: [tex]3 x^3+4 x^2-x+8[/tex] and [tex]x^3-7 x^2+2 x-16[/tex]

[Free] Fatima wants to find the value of [tex]$\sin \theta$[/tex], given [tex]$\cot \theta-\frac{4}{7}$[/tex]. Which identity would be best for Fatima to use? [tex]$\cos \theta=\frac{1}{\sec \theta}$[/tex] [tex]$\sin ^2 \theta+\cos ^2 \theta=1$[/tex] [tex]$\csc \theta=\frac{t}{y}$[/tex] [tex]$1+\cot ^2 \theta=\csc ^2 \theta$[/tex]

[Free] Solve the system by the addition method. [tex]\begin{array}{l} x+y=6 \ x-y=4\end{array}[/tex] Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is $\square$ \}. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

[Free] 22. Show that (i) [tex]$\binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\cdots\binom{n}{n}=2^n$[/tex] (ii) [tex]$\binom{n}{0}-\binom{n}{1}+\binom{n}{2}-\cdots-\binom{n}{n}=0$[/tex] 23. When [tex]$(1-2 x)^p$[/tex] is expanded, the coefficient of [tex]$x^2$[/tex] is 40. Given that [tex]$p\ \textgreater \ 0$[/tex], use this to find (i) the value of the constant [tex]$p$[/tex] (ii) the coefficient of [tex]$x$[/tex] (iii) the coefficient of [tex]$x^2$[/tex]

[Free] If [tex]f(x)=3 x+2[/tex] and [tex]g(x)=x^2+1[/tex], which expression is equivalent to [tex](f \circ g)(x)[/tex]? A. [tex](3 x+2)(x^2+1)[/tex] B. [tex]3 x^2+1+2[/tex] C. [tex](3 x+2)^2+1[/tex] D. [tex]3(x^2+1)+2[/tex]

[Free] Determine the slope of the tangent to the curve [tex]y=x^2[/tex] at the point with [tex]x[/tex]-coordinate 11. A. 22 B. 1 C. 33 D. 11