A different piggy bank contains quarters, dimes and nickels. The value of the coins is $13.85 and there are 18 dimes and 6 nickels. How many quarters are in the piggy bank? Let q represent the number of quarters.
Write an equation that can be used to solve for q.

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Ответ:

nataliasol73341

07.05.2023

Mathematics

Step-by-step explanation:

If CD is the altitude, then AB is the base. The area of a triangle is

$A = \frac{1}{2}\times\text{base}\times\text{height}$

The distance between two points (x_1, y_1) and (x_2, y_2) is

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The base is the length of AB

= $\sqrt{(-7-(-1))^2+(-1-5)^2}$

= $\sqrt{(36+36)}=\sqrt{72}=6\sqrt{2}$

The height is the length of CD

= $\sqrt{(0-(-3))^2+(0-3)^2}$

= $\sqrt{(9+9)}=\sqrt{18}=3\sqrt{2}$

The area of triangle ABC is

$A = \frac{1}{2}\times6\sqrt{2}\times3\sqrt{2} = \dfrac{18\times2}{2}=18$

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A different piggy bank contains quarters, dimes and nickels. The value of the coins is $13.85 and there are 18 dimes and 6 nickels. How many quarters are in the piggy bank? Let q represent the number of quarters. Write an equation that can be used to solve for q.