Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

ratio 5:2

105, ___

5x = 105 → x = 21

2x = ____ → 2(21) = 42

Result: 42°

Answer:

x=9,-1 and

Explanation:

We are given the quadratic equation

, which we then compare with the standard form of a quadratic. The general quadratic is identified as

. From our given equation, it follows that a=1,b=-8,c=-9

. To calculate the discriminant, we insert these values into the formula

. Now, to find the value of x

The formula is

. The resulting equation will be obtained by rewriting the original equation through rearranging 9 to the right side and applying negative signs within brackets to convert the expression into the form of

Explanation:

Step-by-step clarification:

Referring to step 6

(b² — 4ac) / 4a² = (x + b/2a)²

The mistake in the question is that it should be (x + b/2a)²

According to step 7

±√(b² —4ac) /2a = x + b/2a

The error in the question is that it should be divided by 2a, not 1a.

1. The transition from step 6 to step 7 involves taking the square roots of both sides

(b² — 4ac) / 4a² = (x + b/2a)²

Taking the square of both sides

√(b²—4ac) / √4a² = √(x + b/2a)²

√(b²—4ac) / 2a = x + b/2a

This forms step 7 correctly.

Next, subtracting b/2a from both sides

√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a

√(b²—4ac) / 2a — b/2a = x

(√(b²—4ac)  — b)/2a = x

x = [—b ± √(b²—4ac)] / 2a

This gives the desired formula.

The discriminant is D = b²—4ac.

Answer:

The hourly rate for lectures is $7.33

Step-by-step explanation:

* Let's break down how to tackle the problem.

- For the level 3 course, examination hours are priced at double that of workshop hours.

- Workshop hours cost twice the rate of lecture hours.

- The total includes examination, workshop, and lecture hours.

- Examination lasts 3 hours, workshops 24 hours, and lectures 12 hours.

* Let’s denote the cost of lecture hours as $x per hour.

∴ The lectures cost $x per hour.

∵ Workshop charge is twice that of lectures

∴ Workshop hours cost 2(x) = 2x per hour.

∵ Examination fees are double that of workshop hours

∵ The workshop cost is 2x

∴ Examination fees are 2(2x) = 4x per hour.

- Combining costs for level 3 gives us the total of lecture, workshop, and examination hours.

∵ 12 hours for lectures

∵ 24 hours for workshops

∵ 3 hours for examinations

∵ Thus the total cost for level 3 = 12(x) + 24(2x) + 3(4x).

∴ Total cost for level 3 = 12x + 48x + 12x.

∵ Therefore, total cost = $528.

∴ 12x + 48x + 12x = 528.

∴ 72x = 528; hence we divide both sides by 72.

∴ x = 7.33.

∵ x represents the cost of lecture hours per hour.

∴ Therefore, the hourly price for lectures is $7.33.

Here’s a counterexample: consider

Select the subsets in the following manner:

It's accurate that and and that , but