It is given that the general term of a quadratic number pattern is \( T_{n}=2 n^{2}+b n+5 \) and the first term of the first differences is 2 4.1 Show that \( b=-4 \)

expunencial \( \left.\left(4^{2}\right)\left(2^{3}\right)^{2 x-5}\right)=8 \)

42. Julio paid \( 7 \frac{3}{4} \% \) sales tax on an item he bought. He figured that if he had bought the item in a neighboring state where the sales tax is \( 8 \frac{1}{4} \% \), he would have paid \( \$ 75 \) more. What was the cost of the item before tax? (C) \( \$ 15,000.00 \) (IS) \( \$ 3,750.00 \) (C) \( \$ 1,500.00 \) (D) \( \$ 150.00 \) (F) \( \$ 37.50 \)

f) \( (-15 a b c+12 a b-9 a c-3 a) \div(-3 a) \)

-простіть вираз: \( \begin{array}{ll}15 \mathrm{~m}^{2} \cdot\left(4 \mathrm{~m}^{3}\right)^{2} ; & \text { 2) }-0,5 \mathrm{~m}^{5} \cdot\left(2 \mathrm{~m}^{3}\right)^{4} \\ \left.-3 \mathrm{a}^{3} \mathrm{~b}^{4}\right)^{4} \cdot\left(-\frac{1}{8} a^{3} b\right) ; & \text { 4) }\left(-\frac{4}{5} m n^{4}\right)^{3} \cdot 25 m^{4} \mathrm{n}\end{array} \)

Find \( x \). \( \frac{x-1}{3}=\frac{5}{x}+1 \) A. 6.36 OR -2.36 (B) 6.36 (C) 5.46 OR 2.36 (D) No real roots