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2 years ago

Using the quadratic formula to solve 5x = 6x²-3, what are the values of x?

Mathematics

1 answer:

Salsk061 [2.6K]2 years ago

8 0

Answer:

$\boxed{\sf{x = \frac{5 \pm \sqrt{97} }{12} }}$

Step-by-step explanation:

$\sf{5x = 6 {x}^{2} - 3 }$

$\sf{0 = 6 {x}^{2} - 3 - 5x }$

$\sf{0 = 6 {x}^{2} - 5x - 3 }$

a = 6
b = - 5
c = - 3

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

$\sf{x = \frac{ - ( - 5) \pm \sqrt{ { - 5}^{2} - 4(6)( - 3)} }{2(6)} }$

$\sf{x = \frac{5 \pm \sqrt{ 25 + 72} }{12} }$

$\sf{x = \frac{5 \pm \sqrt{97} }{12} }$

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Which statement best describes the relationship between storage space and number of music files?

Rina8888 [55]

Answer:

As the number of files increases, the storage space used increases.

7 0

3 years ago

The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the

Goshia [24]

Answer:

The passing score is 645.2

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 553, \sigma = 72$

If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 553}{72}$

$X - 553 = 1.28*72$

$X = 645.2$

The passing score is 645.2

6 0

3 years ago

Find the measure of the angle indicated in bold.*

Irina18 [472]

Answer:

131°

Step-by-step explanation:

the equations represent alternate exterior congruent angles so they are equal.

31x + 7 = 32x + 3

simplify:

4 = x

31(4) + 7 = 131°

6 0

3 years ago

How would I do this problem?

Softa [21]

Answer:

Step-by-step explanation:

The sum of the interior angles of an n gon is found by using the following formula.

(n-2)*180 = sum of the interior angles.

(n - 2) * 180 = 3960 Divide by 180

(n - 2) 180/180 = 3960/180 Show the division

n - 2 = 22 Add 2 to both sides.

n -2+2=22+2 Combine

n = 24

======================================

To find the size of each angle, use

(n - 2)*180/n

(24 - 2)*180/24

22 * 180/24

3960/24 = 165

===========

another way

===========

You already know there are 24 sides. You are given the sum of the interior angles as 3960

All you really need to do is 3960/24 = 165

8 0

3 years ago

What is the value of a?

Sindrei [870]

Answer:

a=2

Step-by-step explanation:

Firstly, in order to simplify the expression, we should aim to combine the two terms given. In order to do this, both must have the same denominator. We can give them the same denominator by multiplying the second term $-\frac{2}{x+2}$ by $\frac{x+2}{x+2}$ . This way the fraction value remains the same but now has the same denominator as the first term:

$-\frac{2}{x+2} *\frac{x+2}{x+2} \\\\=\frac{(-2)(x+2)}{(x+2)(x+2)} \\\\=\frac{-2x-4}{(x+2)^{2}}$

From here we can now combine the two terms:

$\frac{2x+6}{(x+2)^{2}} +\frac{-2x-4}{(x+2)^{2}} \\\\= \frac{(2x+6)+(-2x-4)}{(x+2)^{2}} \\\\\\=\frac{2x+6-2x-4}{(x+2)^{2}}\\\\= \frac{2}{(x+2)^{2}}$

Therefore, a = 2.

Hope this helped!

6 0

2 years ago