Questions in mathematics

Questions in mathematics

📝 Answered - Factor the quadratic $4 x^2-7 x-2$ List ONLY ONE of the factors with parentheses and no spaces. Example: $(x+1)$

📝 Answered - Determine whether the point with coordinates $(1,6)$ lies on the line with equation $y=2x+6$.

📝 Answered - Suppose you need 10.0 m of Grade 70 tow chain, which has a diameter of [tex]$3 / 8^{\prime \prime}$[/tex] and weighs [tex]$2.16 kg / m$[/tex], to tow a car. How would you calculate the mass of this much chain? Set the math up, but don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols. [tex]$\text { mass of chain }=$[/tex]

📝 Answered - What is the range of the function [tex]g(x)=|x-12|-2[/tex]? [tex] \{y \mid y\ \textgreater \ -2\} [/tex] [tex] \{y \mid y \geq-2\} [/tex] [tex] \{y \mid y\ \textgreater \ 12\} [/tex] [tex] \{y \mid y \geq 12\} [/tex]

📝 Answered - 5. a) Given that [tex]$U =\{1,2, \ldots, 10\}$[/tex] is a universal set. [tex]$A =\{ x : x \leq 5, x \in U \}, B =\{ y : y$[/tex] odd number, [tex]$y \in U \}$[/tex] and [tex]$C =\{ z : z$[/tex] is a prime number, [tex]$z \in U \}$[/tex]. (i) What is the cardinality of set A? (ii) How many elements are there in [tex]$A \cap B \cap C$[/tex]? (iii) Show the relation of the sets [tex]$U , A , B$[/tex] and C in a Venn-diagram and prove [tex]$n(A \cup B \cup C)=n(A)+n(B)+n(C)-n(A \cap B)-n(B \cap C)-n(C \cap A)+n(A \cap B \cap C)$[/tex] (iv) Find the percentage of [tex]$n _0(A)$[/tex].

📝 Answered - Given the equation [tex]F=\frac{9}{5} C+32[/tex] where [tex]C[/tex] is the temperature in degrees Celsius and [tex]F[/tex] is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs: [tex]\left(-10, F_1\right),\left(-30, F_2\right)[/tex] Step 1 of 2: Compute the missing [tex]y[/tex] values so that each ordered pair will satisfy the given equation.

📝 Answered - a) Find the value of $\sqrt[3]{8^3 \times \sqrt{\frac{1}{64}}}$

📝 Answered - Explain how the procedure for changing $\frac{5}{9}$ to $\frac{10}{18}$ requires the use of the multiplicative identity element, 1. Choose the correct choice below. A. One must add $\frac{5}{9}$ to 1 to obtain $\frac{10}{18}$. B. One must multiply the reciprocal of $\frac{5}{9}$ by 1 in the form of a fraction, $\frac{2}{2}$, to obtain $\frac{10}{18}$. C. One must multiply $\frac{5}{9}$ by 1 in the form of a fraction, $\frac{2}{2}$, to obtain $\frac{10}{18}$. D. One must divide $\frac{5}{9}$ by the reciprocal of $\frac{10}{18}$ to obtain 1. E. One must subtract $\frac{5}{9}$ from 1 to obtain $\frac{10}{18}$.

📝 Answered - The point $(0,0)$ is a solution to which of these inequalities? A. $y-6<2 x-7$ B. $y+7<2 x+6$ C. $y+7<2 x-6$ D. $y-7<2 x-6$

📝 Answered - Solve the equation by using the quadratic formula. [tex]25 x^2+60 x=-36[/tex] a. [tex]x=\frac{5}{6}[/tex] b. [tex]x=\frac{6}{5}[/tex] c. [tex]x=-\frac{6}{5}[/tex] d. [tex]x=-\frac{5}{6}[/tex]