What is the product of ( x + 3) ( x - 4)?

Mathematics

1 answer:

Lelechka [254]3 years ago

7 0

Answer: x² - x - 12

Step-by-step explanation: When multiplying two binomials together, we can use the F.O.I.L. method.

First, Outer, Inner, Last.

We take the product of the first terms which is x² plus the product of the outer terms which is -4x plus the product of the inner terms which is 3x plus the product of the last terms which is -12.

So we have x² - 4x + 3x - 12.

Simplifying from here by combing the middle terms, we have x² - x - 12.

Pay very close attention to your positives and negatives as you F.O.I.L. because this is the area where most mistakes occur.

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10/3 * 3^x -3^(x-1) = 81 Solve for x.

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Answer:

$x=3$

Step-by-step explanation:

$~~~~~~~\dfrac{10}{3} \cdot 3^x - 3^{x-1} = 81\\\\\\\implies 10 \cdot 3^{x-1} - 3^{x-1} = 81~~~~~~~~~~~~~~~~~~~~;\left[\dfrac{a^m}{a^n} =a^{m-n} \right]\\\\\\\implies 9\cdot 3^{x-1} = 81\\\\\\\implies 3^{x-1} = \dfrac{81}{9}\\\\\\\implies 3^{x-1} = 9\\\\\\\implies 3^{x-1} = 3^2\\\\\\\implies x -1 = 2\\\\\\\implies x = 2+1\\\\\\\implies x = 3$