Find cos (330°). Your answer MUST be in radical form.

when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3>Solution:</h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = $a^2$

6 is subtracted from the square of a number = $a^2 - 6$

5 times the number = $5 \times a$

So we can frame a equation as:

6 is subtracted from the square of a number = 5 times the number

$a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0$

Let us solve the above quadratic equation

For a quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here in this problem,

$a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6$

Substituting the values in above quadratic formula, we get

$\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}$

We have two solutions for "a"

$\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}$

We have asked negative solution. So a = -1

Thus the negative solution is -1

6 0

3 years ago

One eighth of Tony's books are mystery books He has 3 Mystery books how many books does Tony have in all

kolezko [41]

The answer to One eighth of Tony's books are mystery books He has 3 Mystery books how many books does Tony have in all is 24

5 0

2 years ago

Read 2 more answers

1 saa ite 5. Count by tens. What is the next number? 20, 30, 40, 50,

OleMash [197]

Answer:

60

Step-by-step explanation:

I would assume you want the answer step-by-step:

We can count carefully and read the question again.

It is asking for us to count by tens or add ten to the most recent integer in the pattern.

In that case, we can see that our answer will by 50 + 10 = 60.

Also, note, that this question is not very intellectually challenging! Next time ask a question like "What do they mean when they say this?" If you don't understand the wording.

7 0

2 years ago

Read 2 more answers

What is (14x^2– 27x+9) / (7x-3)? A. 7x-3 B. 2x-3 C. -211x+9 D. 2x-33

Yakvenalex [24]

Answer:

B. 2x - 3

Step-by-step explanation:

$\rm \frac{ {14x}^{2} - 27x + 9}{7x - 3}$