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3 years ago

What is the sum of the zeros of the function: y= x^2 - 5x + 6?

Mathematics

1 answer:

yawa3891 [41]3 years ago

7 0

Answer:

Step-by-step explanation:

The zeros are the values of x for which y = 0

Quadratic formula

x = [5 ± √(5² – 4·1·6)] / [2·1]

= [5 ± √1] / 2

= [5 ± 1] /2

= 2, 3

sum of zeros = 5

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Which values are solutions to the inequality? 5r≤6r−8 Select each correct answer. r = 7 r = 8 r = 9 r = 10

Ratling [72]

Answer:

r = 8,9,10

Step-by-step explanation:

The given inequality is :

5r≤6r−8 ...(1)

We need to find the value of r.

Subtracting 5r to both sides of the inequality .

5r-5r≤6r-5r−8

0≤r−8

r ≥ 8

Hence, the values of r are 8,9,10.

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3 years ago

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Use the rules for multiplication by powers of 10 to calculate 3 x 100

Yakvenalex [24]

300

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3 years ago

Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C' (C' = kC)

taking exponents of both sides, we have

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$