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:
The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.
Customers served in 0.5 hours : 3.6 versus x customers served in 7.5 hours
-------------------- = --------------------
0.5 hours 7.5 hours
Applying cross multiplication:
3.6 multiplied by 7.5 equals x times 0.5
Dividing both sides by 0.5:
x = (3.6 * 7.5) / 0.5
x = 54
So, you assisted 54 customers in 7.5 hours.
<span>Which formula can be applied to find the side length of the rhombus?
The correct answer is the first choice: 10/Cos(30°) Explanation:
1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:
Cos(</span>α)=Adjacent side/Hypotenuse
<span>
</span>α=30°
<span> Adjacent side=(20 in)/2=10 in
Hypotenuse=x
2. Inputting these numbers into the equation yields:
</span>
Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x
3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:
x=10/Cos(30°)
</span>
