At the end of spring break, Lucy left the beach and drove back towards home, driving at a rate of 40 mph . Lucys friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph . How long did it take Lucys friend to catch up to Lucy? Provide your answer below: hours

Câu 1: Giải tam giác Dạng 1: Cho tam giác ABC có \( \mathrm{AB}=5 \mathrm{~cm}, \mathrm{BC}=7 \mathrm{~cm}, \mathrm{AC}=6 \mathrm{~cm} \). Tính số đo các góc \( \mathrm{A}, \mathrm{B}, \mathrm{C} \).

Solve the following: Show your solutions 1. All items in Store ACE have \( 12 \% \) sales tax inclusive. Ernesto bought a wallet and observed that in his receipt, he paid a total tax of P126 for his purchased wallet. How much is the cost of the wallet? 2. Jha bought a lipstick with tag price of P600 + \( 8 \% \) sales tax. How much should she pay for her purchase? 3. Jena bought some food from a fast-food restaurant. The total amount of her ordered food was P855 plus a \( 12 \% \) VATOHow much was the total amount she paid to the cashier? 4. Cora bought a new laptop computer that costs P28 985 . Looking at her Official Receipt, she found out that a sales tax of P2 318.80 was added to the cost of the laptop she bought. Find the sales tax rate. 5. The sales tax on a P13 800 appliance is P1 656 . What is the rate of sales tax? 6. How much sales tax is charged for an item that costs P250 if the sales tax rate is 6\%? How much is the total price? 7. A set of 6 -piece notebook is sold at P150 and the sales tax is \( 8 \% \). What is the total cost of this set of 6 -piece notebook including the sales tax? 8. The cost of a watch including a tax of \( 20 \% \) is Php1344. What is the price without the tax?

In a laboratory setup, a block of ice of mass mi at an initial temperature of \( -15^{\circ} \mathrm{C} \) is needed to transform 0.5 kg of steam contained in a sealed glass container from \( 110^{\circ} \mathrm{C} \) into water at \( 15^{\circ} \mathrm{C} \). The specific heat capacity of ice, \( \underline{\text { water and }} \) steam are respectively \( \mathrm{Ci}=2090 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C}, \mathrm{Cw}=4186 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C} \) and \( \mathrm{Cs}=2010 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C} \), the steam and the glass container are in thermal equilibrium Fusion point of water (or melting point of ice) \( 0^{\circ} \mathrm{C} \) Vaporization point of water \( 100^{\circ} \mathrm{C} \) The latent heat of condensation steam Lc= \( 2.26 \times 10^{\wedge} 6 \mathrm{~J} / \mathrm{kg} \) Latent heat of Fusion of ice \( \mathrm{Lf}=3.36 \times 10^{\wedge} 5 \mathrm{~J} / \) kg The amount of heat Qg gained during the

н) \( \left(\sqrt{\left|a_{1}\right|}-a_{1}\right)^{2}+\ldots+\left(\sqrt{\left|a_{n}\right|}-a_{n}\right)^{2} \)

Now subtract \( 5 x \) from each side of the equation and solve for \( x \) \[ \begin{array}{l}22 x=5 x \\ 22 x-5 x=5 x-5 x \\ \text { Enter an exact number. }\end{array} \] \( x=\square \)