The quadratic equation x^{2}-6x=12 is rewritten in the form (x+p)^2=q, where q is a constant. What is the value of p ?

Given the quadratic functions expressed as;

x² - 6x = 12

The value of p given the quadratic expression is -3

Complete the square at the left hand side of the equation.

Add the square of the half of coefficient of x to both sides.

coefficient of x = -6

Half of coefficient of x = -6/2 = -3

Square of the result = (-3)² = 9

Add 9 to both sides of the equation

x² - 6x + 9 = 12 + 9

Factoring the left hand side

(x-3)² = 21

Comparing the result with (x+p)² = q

The value of p wil be -3

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p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.