The perimeter of angle ABC is 98 centimeters. If the radius circle A is twice the radius of circle C and the radius of circle B
is four times the radius of circle C, then find the radius of circle C.
1 answer:
Answer: Circle C has a radius of 7 cm.
Explanation:
Referring to the illustration below:
Let's denote the radius of circle C as x.
Circle A's radius can be represented as 2x.
Circle B's radius can be expressed as 4x.
The length of side AC in triangle ΔABC becomes x + 2x = 3x.
For side BC of triangle ΔABC, we get 4x + x = 5x.
Similarly, for side AB of triangle ΔABC, it is 4x + 2x = 6x.
Given that the perimeter of triangle ΔABC totals 98 cm.
Remember, the perimeter refers to the total length around the triangle.
Hence, Perimeter = 6x + 5x + 3x = 98 cm.
Thus, 14x = 98.
From this, we find x = .
Therefore, x = 7.
This concludes that the radius of circle C is 7 cm.
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Answer:
To find the number of genuine solutions for a system of equations consisting of a linear equation and a quadratic equation
1) With two variables, say x and y, rearrange the linear equation to express y, then substitute this y in the quadratic equation
After that, simplify the resulting equation and determine the number of real roots utilizing the quadratic formula, for equations of the type 0 = a·x² - b·x + c.
When b² exceeds 4·a·c, two real solutions emerge; if b² equals 4·a·c, there will be a single solution.
Step-by-step explanation:
Answer: y²z⁴ / x¹²
- The exponent for x is 12
- The exponent for y is 2
- The exponent for z is 4
Explanation:
1) The expression to simplify:
2) Rule: power of a power:
3) Rule: product of powers with identical bases
4) Add up the exponents
5) Transfer the negative exponent to the denominator:
The exponent attached to x is 12, for y it is 2, and for z it is 4.