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Questions in mathematics

📝 Answered - Evaluate each function for the given value. 1) f(x) = 4x + 2; Find f(0) 2) f(x) = -2x + 2; Find f(-3) 3) f(x) = 2x; Find f(-9/5) 4) f(x) = -3x; Find f(3/5) 5) f(x) = 3x - 4; Find f(0.2) 6) f(x) = x + 6; Find f(3.8)

📝 Answered - If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {1, 2, 4, 6, 7}, then find: 1) A ∪ B 2) B ∪ C 3) (A ∪ B) ∪ C 4) A ∩ (B ∪ C) 5) A ∩ (B ∩ C) 6) A ∪ (B ∪ C) What is your observation?

📝 Answered - Solve the literal equation for $y$. Simplify your answer. $\frac{1}{y}=\frac{1}{z}$

📝 Answered - Identify the inverse [tex]g(x)[/tex] of the given relation [tex]f(x)[/tex]. [tex] \begin{aligned} f(x)= & \{(8,3),(4,1),(0,-1),(-4,-3)\} \ & g(x)=\{(-4,-3),(0,-1),(4,1),(8,3)\} \ & g(x)=\{(-8,-3),(-4,1),(0,1),(4,3)\} \ & g(x)=\{(8,-3),(4,-1),(0,1),(-4,3)\} \ & g(x)=\{(3,8),(1,4),(-1,0),(-3,-4)\} \end{aligned} [/tex]

📝 Answered - Which of the following is equal to $\sqrt{9 \cdot 4}$? A. $\sqrt{9} \cdot \sqrt{4}$ B. 18 C. $\sqrt{\frac{9}{4}}$ D. 36

📝 Answered - Solve for x: [tex]\frac{1}{3} x-\frac{1}{2}=\frac{3}{4} x[/tex]

📝 Answered - Assessment 6 1. The coordinates of line [tex]$AB$[/tex] are [tex]$A(5,4)$[/tex] and [tex]$B(-2, t)$[/tex]. The line is perpendicular to a line whose gradient is [tex]$-\frac{1}{2}$[/tex]. Determine the value of [tex]$t$[/tex]. 2. The coordinates of line [tex]$AB$[/tex] are [tex]$A(3,6)$[/tex] and [tex]$B(1,1)$[/tex]. Determine the gradient of a line perpendicular to line [tex]$AB$[/tex]. 3. Without drawing, determine whether each of the following pairs of lines are perpendicular or not. (a) [tex]$y=-3 x+4$[/tex] and [tex]$y=\frac{1}{3} x+12$[/tex] (b) [tex]$y=\frac{3}{5} x+3$[/tex] and [tex]$y=5 x-12$[/tex] (c) [tex]$y=\frac{1}{7} x-9$[/tex] and [tex]$y=-\frac{1}{7} x+11$[/tex] 4. Chebet drew line [tex]$NM$[/tex] with coordinates [tex]$N(3,5)$[/tex] and [tex]$M(1,-1)$[/tex]. Magera drew line [tex]$CD$[/tex] with coordinates [tex]$C(3,6)$[/tex] and [tex]$D(4,3)$[/tex]. Determine whether line [tex]$NM$[/tex] is perpendicular to line [tex]$CD$[/tex] or not.

📝 Answered - Which linear function represents the line given by the point-slope equation $y-8=\frac{1}{2}(x-4)$? A. $f(x)=\frac{1}{2} x+4$ B. $f(x)=\frac{1}{2} x+6$ C. $f(x)=\frac{1}{2} x-10$ D. $f(x)=\frac{1}{2} x-12$

📝 Answered - Shakira has a balance of $202.86 in her checking account on Saturday morning. She uses her debit card to pay her cell phone bill of $80.73 over the phone. She then picks up her dry cleaning, dog food at the pet store, and groceries for debits of $16.89, $35.24, and $113.92. Shakira's bank uses a balance system of deducting highest transactions first. The bank will not return amounts up to a total of $50 in overdrafts, but they do charge a fee for each overdraft. How many overdraft fees will Shakira incur? A. 1 B. 2 C. 3 D. 4

📝 Answered - Which statement best describes how to determine whether [tex]f(x)=9-4 x^2[/tex] is an odd function? A. Determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]9-4 x^2[/tex]. B. Determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4 x^2)[/tex]. C. Determine whether [tex]9-4(-x^2)[/tex] is equivalent to [tex]9+4 x^2[/tex]. D. Determine whether [tex]9-4(-x^2)[/tex] is equivalent to [tex]-(9+4 x^2)[/tex].