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3 years ago

11. Find the product of (4x-5) and (2x+7) in simplest form.

Mathematics

1 answer:

vlada-n [284]3 years ago

8 0

8x^2 + 18x - 35

(4x - 5)(2x + 7)

8x^2 + 28x - 10x - 35

8x^2 + 18x - 35

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Find the value(s) of k such that 4x² + kx + 4 = 0 has 1 rational solution

Blababa [14]

Answer:

If you mean only one rational solution, the answer is

$k_1 = 8, k_2 = -8$

If you mean at least 1 rational solution, the answer is

$k\in (-\infty, -8]\cup[8, \infty)$

Step-by-step explanation:

$4x^2 + kx + 4 = 0$

Let's calculate the discriminant.

$\Delta = b^2 - 4ac$

$\Delta = k^2 -4 \cdot 4 \cdot 4$

$\Delta = k^2 -64$

Now, remember that:

$\text{If } \Delta > 0 : \text{2 Real solutions}$

$\text{If } \Delta = 0 : \text{1 Real solution}$

$\text{If } \Delta < 0 : \text{No Real solution}$

Therefore, I will just consider the first two cases.

$k^2 - 64 > 0$

and

$k^2 -64 = 0$

$\boxed{\text{For } k^2 - 64 > 0}$

$k^2 > 64 \Longleftrightarrow k>\pm\sqrt{64} \Longleftrightarrow k\in (-\infty, -8)\cup(8, \infty)$

$\boxed{\text{For } k^2 - 64 = 0}$

$k^2 = 64 \Longleftrightarrow k=\pm\sqrt{64} \implies k_1 = 8, k_2 = -8$

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Consider the sequence of steps to solve the equation: 3(x - 4) + 5x 9x - 36

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Distributive Property

Step-by-step explanation:

You are distributing 3 to x and -4

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What is the reciprocal of two ninths

LenaWriter [7]

<h2>Answer: 9/2</h2>

Step-by-step explanation:

<em>The answer is 9/2 because reciprocal means you just flip the fraction that you are solving. So, the opposite of 2/9 is 9/2 AKA, if you flip 2/9, it would be 9/2.</em>

*<em>Hope this helps:) * Mark me the brainliest !!!</em>

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