To solve the previous problem, we can split the triangle into two right triangles, each having a base of 10 cm and a hypotenuse of 18 cm. The measure of the longer side is necessary to determine the height of the isosceles triangle. By applying the Pythagorean theorem, a² + b² = c², we have a² + (10cm)² = (18cm)², leading to a² = 324 cm² - 100 cm², thus a² = 224 cm². This results in a = √224 cm², which is approximately a = 14.97 cm. The area is then given by A = 1/2 * base * height, or A = 1/2 * 20 cm * 14.97 cm, yielding A = 149.70 cm². Using the formula A = r/2 * p, we derive 149.70 cm² = r/2 * (18cm + 18cm + 20cm), simplifying to 149.70 cm² = r/2 * 56 cm. This results in 149.70 cm² ÷ 56 cm = r/2. Consequently, r/2 equals 2.67 cm, and thus r is 5.34 cm. In conclusion, the final answer is that the radius is approximately 5.35 cm.
Response: the equations are
0.02x + 0.07y = 156
y = 300 + x
Step-by-step explanation:
Let x denote the dollar amount from phone sales made by Josiah.
Let y indicate the dollar amount from his computer sales.
Josiah receives a 2% commission on his phone sales total and 7% on his computer sales. He accumulated a total of $156 in commission, leading to the equation
0.02x + 0.07y = 156 - - - - - - - - - - -1
Furthermore, it’s given that Josiah had $300 more in computer sales than in phone sales, expressed as
y = 300 + x
To solve this problem, I would add 7 to obtain...
... 2x² = 16
Next, I would divide by 2 to yield
... x² = 8
I would then take the square root, noting that both positive and negative solutions exist.
... x = ±√8
This root can be simplified to give...
... x = ±2√2
_____
This method appeared to be the most straightforward to me. Although one could apply the quadratic formula, that entails more steps.
... 2x² -16 = 0.... continuing by subtracting 9
... x = (-0 ± √(0² -4·2·(-16)))/(2·2).... inserting the coefficients into the formula
... x = ±(√128)/4 = ±√8 = ±2√2..... simplifying the final expression
Response:
Detailed explanation:
Considering the given algebraic expression:
The task is to remove the negative exponents and derive the new expression.
Applying the Negative Exponent Rule: 
Utilizing the Division Law for Exponents: 
Consequently:
