Questions in mathematics

Questions in mathematics

📝 Answered - What values of [tex]$c$[/tex] and [tex]$d$[/tex] would make the following expression represent a real number? [tex]$i(2+3 i)(c+d i)$[/tex] A. [tex]$c=2, d=3$[/tex] B. [tex]$c=-3, d=-2$[/tex] C. [tex]$c=3, d=-2$[/tex] D. [tex]$c=-2, d=3$[/tex]

📝 Answered - What number should be added to both sides of the equation to complete the square? [tex]x^2+3 x=6[/tex] A. [tex]\frac{3}{2}[/tex] B. [tex]\left(\frac{3}{2}\right)^2[/tex] C. 3 D. [tex]6^2[/tex]

📝 Answered - Evaluate $f(3)$ for the piecewise function: $f(x)=\left\{\begin{array}{l} \frac{3 x}{2}+8, x<-6 \\ -3 x-2,-4 \leq x \leq 3 \\ 4 x+4, x>3 \end{array}\right.$ Which value represents $f(3)$? A. -11 B. 8 C. 12.5 D. 16

📝 Answered - A family knows two babysitters they can hire. One charges $6 an hour and the other charges $7. The family can't afford more than $42 a week for babysitting. Write the system of inequalities. $\begin{array}{l} 7 x-6 y \leq 42 \\ x \geq 0 \\ y \geq 0 \end{array}$ $\begin{array}{l} 7 x+6 y \geq 42 \\ x \geq 0 \\ y \geq 0 \end{array}$ $7 x+6 y \leq 42$ $\begin{array}{l} x \geq 0 \\ y \geq 0 \end{array}$

📝 Answered - Simplify [tex]$16^{-\frac{1}{2}} \times 4^{\frac{1}{2}} \times 27^{\frac{1}{3}}$[/tex]

📝 Answered - $\begin{array}{l}x=0.7 \\ x \cdot 10^1=0 . \overline{7} \cdot 10^1 \\ 10 x=7.7 \\ 10 x-x=7.7 - 0.7\end{array}$

📝 Answered - f) [tex]\frac{\left(\frac{2}{5}\right)^{-2}}{\left(\frac{5}{2}\right)\left(\frac{5}{2}\right)} \times 2[/tex] R. [tex]\frac{1}{4}[/tex] g) [tex]\frac{25^{-1}}{5^{-2}}+\frac{0,05^{-2}}{0,1^{-3}} \uparrow[/tex] E. 1

📝 Answered - Multiply: $2 \times(-21) \times 7$ A) -273 B) -7 C) -294 D) 294

📝 Answered - What is the following quotient? $\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3}}$

📝 Answered - Cory writes the polynomial [tex]x^7+3 x^5+3 x+1[/tex]. Melissa writes the polynomial [tex]x^7+5 x+10[/tex]. Is there a difference between the degree of the sum and the degree of the difference of the polynomials? A. Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7. B. Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5. C. Adding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5. D. Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.