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Questions in mathematics

📝 Answered - Select the correct answer. Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop. Which equation represents this situation, and after how many months, $t$, will Jane have enough money to purchase the bike? A. $3(2)^t=1,536 ; t=11$ B. $3(1.2)^t=1,536: t=35$ C. $(3 cdot 2)^t=1,536 ; t=9$ D. $3(2)^t=1,536 ; t=9

📝 Answered - Evaluate the function [tex]f(x)=5 x+1[/tex] at the given values of the independent variable and simplify. a. [tex]f(-1)[/tex] b. [tex]f(x+5)[/tex] c. [tex]f(-x)[/tex] a. [tex]f(-1)=[/tex] (Simplify your answer.)

📝 Answered - Faelyn grouped the terms and factored the GCF out of the groups of the polynomial $6 x^4-8 x^2+3 x^2+4$. Her work is shown. Step 1: $\left(6 x^4-8 x^2\right)+\left(3 x^2+4\right)$ Step 2: $2 x^2\left(3 x^2-4\right)+1\left(3 x^2+4\right)$ Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next? A. Faelyn should realize that her work shows that the polynomial is prime. B. Faelyn should go back and regroup the terms in Step 1 as $\left(6 x^4+3 x^2\right)-\left(8 x^2+4\right)$. C. In Step 2, Faelyn should factor only $2 x$ out of the first expression. D. Faelyn should factor out a negative from one of the groups so the binomials will be the same.

📝 Answered - Thomas was selling tickets to his school play. The tickets cost $[tex]$5.00$[/tex] for adults and $[tex]$2.00$[/tex] for children. He sold 200 tickets and collected $[tex]$610$[/tex]. Which system represents the number of adult and child tickets that Thomas sold? [tex] \begin{array}{r} x+y=200 \\ 5 x+2 y=610 \end{array} [/tex] [tex]$x+y=610$ $5 x+2 y=200$[/tex] [tex] \begin{array}{r} x+y=200 \\ x+2 y=610 \end{array} [/tex] [tex]$x+y=200$ $5 x+y=610$[/tex]

📝 Answered - 1. 22,482 + 4,225 = 4,225 + 22,482 A. 21,534 B. 4,225 C. 0 D. 1 2. 3,456 + ... = 3,456 A. 1 B. 0 C. 3,456 D. 3,451 3. 72,132 ÷ 100 gives Q = 121 and R = 32 A. 72,132 B. 721,32 C. 7,2132 D. 7213,2 4. 4,22,11,333 - 84,43,553 = ... A. 2,37,66,789 B. 3,37,66,780 C. 3,37,67,781 D. 3,37,67,780 5. Find the product of the greatest 5-digit number and the greatest 1-digit even number. A. 1,99,999 B. 2,00,000 C. 1,99,987 D. 7,99,992

📝 Answered - [tex]\int \frac{y^2}{2\sqrt{y^3+5}} \, dx[/tex] [tex]\int \frac{5}{x} \cot(\ln x^3) \, dx[/tex] [tex]\int \frac{e^{x^2-2x}(2x-5)}{e^{1+3x}} \, dx[/tex] [tex]\int \frac{dz}{z^2+6z+5}[/tex] [tex]\int \frac{dx}{3+2^x}[/tex] [tex]\int \frac{5dw}{w\sqrt{9w^6-4}}[/tex]

📝 Answered - Rohan has named the given ray as \overrightarrow{QP}. Is he correct? Why? Explain your answer. ``` P | Q --> ```

📝 Answered - Which pair of equations represents parallel lines? $\begin{array}{l} -\frac{2}{3} x+y=12 \\ y=-\frac{3}{2} x-1 \end{array}$ $\begin{array}{l} 3 x+y=-8 \\ y=3 x-8 \end{array}$ $\begin{array}{l} -2 x+y+2=0 \\ y=-\frac{1}{2} x-4 \end{array}$ $\begin{array}{l} x+2 y=8 \\ -x-2 y=3 \end{array}$

📝 Answered - Evaluate the expression $2 x-(4 y-3)+5 x z$, when $x=-3, y=2$, and $z=-1$. A. 45 B. 16 C. 4 D. -10

📝 Answered - Given: [tex]$\begin{array}{c} A B=12 \ A C=6 \end{array}$[/tex] Prove: C is the midpoint of [tex]$\overline{ AB }$[/tex]. Proof: We are given that [tex]$AB =12$[/tex] and [tex]$AC =6$[/tex]. Applying the segment addition property, we get [tex]$A C+C B=A B$[/tex]. Applying the substitution property, we get [tex]$6+ CB =12$[/tex]. The subtraction property can be used to find [tex]$CB =6$[/tex]. The symmetric property shows that [tex]$6=A C$[/tex]. Since [tex]$C B$[/tex] [tex]$=6$[/tex] and [tex]$6= AC , AC = CB$[/tex] by the property. So, [tex]$\overline{ AC } \cong \overline{ CB }$[/tex] by the definition of congruent segments. Finally, C is the midpoint of [tex]$\overline{ AB }$[/tex] because it divides [tex]$\overline{ AB }$[/tex] into two congruent segments.