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3 years ago

Factor the trinomial x^2-5x-6

Mathematics

1 answer:

sasho [114]3 years ago

7 0

Answer: (x - 6)(x + 1)

Step-by-step explanation: This trinomial has an x² term, an x term and a constant term so it can be factored as the product of two binomials.

So starting with our two sets of parentheses, x² factors as x multiplied by x. Now we want to find factors of the constant term that add to the coefficient of the middle term. So we're looking for factors of -6 that add to -5.

A negative number factors into the product of a positive and a negative. So our factors of -6 are 6 × -1, -6 × 1, 3 × -2, or -3 × 2.

This is a trick problem because many of these pairs of factors look like they could add to -5 but the only one that does is -6 × 1.

So our answer is (x - 6)(x + 1).

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A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati

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The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

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$T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20$

We also know that at t=2, T=55°F

$T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08$

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

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The question states the congruent images:

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The order of the letters matters.

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From the images, the square ABCD is just shifted 9 units down to form the square FGHI. No refelection is needed.

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