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3 years ago

Use synthetic division and the Remainder Theorem to find f(4) if f(x) = – 2x3 + 9x2

Mathematics

1 answer:

Elis [28]3 years ago

6 0

Step-by-step explanation:

Let's see. f(4) makes the divisor x-4

4|-2 9 -6 7

| 8 -68 296

-2 17 -74 2072

The quotient is -2x²+17x-74 with a remainder of 2072

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Solve 5x^2 - 7x + 2 = 0 by completing the square.

Reika [66]

Answer: The correct option is (c) $\dfrac{49}{100}.$

Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square:

$5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)$

Also, we are to find the constant added on both sides to form the perfect square trinomial.

We have from equation (i) that

$5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.$

So,

$x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.$

Thus, the required solution is $x=1,~-\dfrac{2}{5}.$ and the value of the constant added is $\dfrac{49}{100}.$

Option (c) is correct.

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3 years ago

Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 5% annual interest; the other paid 9% a

Alex17521 [72]

Answer:

Step-by-step explanation:

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3 years ago

Find the value of X in the triangle below

melomori [17]

Answer:

x=9+4

x=13

option b is the correct answer

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3 years ago

You are on a road trip and need to travel 300 km. The speed limit is 80 km/hr. How

notsponge [240]

Answer:

3 3/4 or 3.75 hours.

Step-by-step explanation:

If you need to travel 300 km, assuming you are going at the speed limit, you take the total amount and divide it by that.

300 / 80 = 3.75 hours

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3 years ago

Write down the integer values satisfied by the diagram

____ [38]

Answer:

{0, 1, 2, 3}

Step-by-step explanation:

<u>The diagram includes the interval:</u>

(-1, 3]

<u>The integer values in the given interval are:</u>

{0, 1, 2, 3}

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3 years ago

Read 2 more answers