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:
Question 1: (2.2, -1.4). Question 2: (1.33, 1). Providing a detailed analysis, the equations for the given lines are specified as (1) passing through points (0, 2.5) and (2.2, 1.4), and (2) through (0, -3) and (2.2, -1.4). We are tasked with locating a common solution or intersection of these equations. This leads to finding x = 2.2, and consequently y = -1.4. Therefore, the solution set is (2.2, -1.4). For question 2, the equations yield a solution of (1.33, 1).
I believe it's around $62, though I'm uncertain. Sorry for the lack of precision, but wish you all the best in life! <3
Answer: C) HF measures 4 units and GH is 2 units.
Step-by-step explanation:
The SSS similarity theorem asserts that triangles are similar if the lengths of their corresponding sides are in proportion.
For triangles ΔDFE and ΔGFH:
DG equals 15, GF is 5, EH equals 12, and DE is 8.
To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:
Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.
Got it!
There are 2π radians in a complete circle.
Now, let's calculate the circumference.
5/2π = 60/circumference.
Next, solve for the circumference.
By multiplying both sides by 2π, we have: 5 * circumference = 120π.
Now divide both sides by 5, and we find: circumference = 24π.
Using the formula c = 2πr,
we set 24π = 2πr.
Dividing both sides by 2π gives us r = 12. Thus, the radius measures 12cm.
