Work out ( 5 × 10 − 8 ) 2 Give your answer in standard form.

If using the method of completing the square to solve the quadratic equation

lara [203]

Answer:

x² + 7x + 10 = 0

Subtract 10 from both sides

x² + 7x = -10

Use half the x coefficent (7/2) as the complete the square term

(x + 7/2)² = -10 + (7/2)²

note: the number added to "complete the square" is (7/2)² = 49/4

(x + 7/2)² = -10 + 49/4

(x + 7/2)² = 9/4

Take the square root of both sides

x + 7/2 = ±3/2

Subtract 7/2 from both sides

x = -7/2 ± 3/2

x = {-5, -2}

6 0

3 years ago

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Two hoses are filling a pool the first hose fills at a rate of x gallons per minute the second hose fills at a rate of 15 gallon

Zielflug [23.3K]

Answer:

B. (0, 5]∪(15,30] only (15,30] contains viable rates for the hoses.

Step-by-step explanation:

The question is incomplete. Find the complete question in the comment section.

For us to meet the pool maintenance company's schedule, the pool needs to fill at a combined

rate of at least 10 gallons per minute. If the inequality represents the combined rates of the hoses is 1/x+1/x-15≥10 we are to find all solutions to the inequality and identifies which interval(s) contain viable filling rates for the hoses. On simplifying the equation;

$\frac{1}{x} + \frac{1}{x-15} \geq \frac{1}{10}\\\\ find\ the \ LCM \ of \ the function \ on \ the \ LHS\\\\\frac{x-15+x}{x(x-15)} \geq \frac{1}{10}\\\\\frac{2x-15}{x(x-15)} \geq \frac{1}{10}\\\\10(2x-15)\geq x(x-15)\\\\20x-150\geq x^2-15x\\\\collect \ like \ terms\\-x^2+20x+15x - 150\geq 0\\$

$-x^2+35x-150 \geq 0\\\\multipply \ through \ by \ minus\\x^2-35x+150 \leq 0\\\\(x^2-5x)-(30x+150) \leq 0\\\\x(x-5)-30(x-5) \leq 0\\\\$

$(x-5)(x-30) \leq 0\\\\x-5 \leq 0 and x - 30 \leq 0\\\\x \leq 5 \ and \ x \leq 30$

The interval contains all viable rate are values of x that are less than 30. The range of interval is (0, 5]∪(15,30]. Since the pool needs to fill at a combined rate of at least 10 gallons per minute for the pool to meet the company's schedule, this means that the range of value of gallon must be more than 10, hence (15, 30] is the interval that contains the viable rates for the hoses.