The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for

Determining the answer here is quite straightforward. Ella has a total of $2.16, and we need to ascertain the cost per piece of gum.
It is known that if the gum cost one cent less, she would have acquired three more pieces.
 Currently, with 8 pieces priced at 27 cents each, a reduced price would allow her to have 8.64 pieces. This outcome, even after rounding, is incorrect as it does not yield 11.
 For 9 pieces at 24 cents each, a cheaper price would mean she could have 9.39 pieces, which still does not round to 12, indicating it's incorrect.
 At 16 pieces costing 13.5 cents each, at one cent less, she would acquire 17.28 pieces, which also confirms it's wrong because rounding does not yield 19.
 When purchasing 24 pieces at 9 cents each, with the cheaper price, she could buy 27 pieces, which is valid since 27-24 equals 3.
 Therefore, the correct answer is D) 24

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

.

The elements that are visible include A, B, and C.

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.

Response:

x ≥ 4

Step-by-step breakdown:

Given

- 4(8 - 3x) ≥ 6x - 8 ← distribute the term in parentheses on the left side

- 32 + 12x ≥ 6x - 8 (subtract 6x from both sides)

- 32 + 6x ≥ - 8 (add 32 to both sides)

6x ≥ 24 (divide both sides by 6)

Thus, x ≥ 4