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3 years ago

Five times a certain number, minus 5 is equal to 7 more than three times the number

1 answer:

3 0

Let’s start with putting the unknown to x, in this case it is the number.

5x-5=7+3x, so now we just solve this equation.

5x-3x=7+5
2x=12
x=6

the number is 6

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Solve the system of linear equations by substitution.<br> y=X-4<br> - 2x+y= 18

11Alexandr11 [23.1K]

Answer:

] y=x-4

-2x+y=18

y - x = -4

y - 2x = 18

equation [2] for the variable y

[2] y = 2x + 18

// Plug this in for variable y in equation [1]

[1] (2x+18) - x = -4

[1] x = -22

// Solve equation [1] for the variable x

[1] x = - 22

// By now we know this much :

y = 2x+18

x = -22

// Use the x value to solve for y

y = 2(-22)+18 = -26

Step-by-step explanation:

please mark me as brainlist please

4 0

1 year ago

Write the quadratic equation that has roots -1-rt2/3 and -1+rt2/3 if its coefficient with x^2 is equal to 1

weeeeeb [17]

The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9

<h3>How to determine the quadratic equation?</h3>

From the question, the given parameters are:

Roots = (-1 - √2)/3 and (-1 + √2)/3

The quadratic equation is then calculated as

f(x) = The products of (x - roots)

Substitute the known values in the above equation

So, we have the following equation

$f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})$

This gives

$f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})$

Evaluate the products

$f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})$

Evaluate the like terms

$f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}$

So, we have

f(x) = x²+ 2/3x - 1/9

Read more about quadratic equations at

brainly.com/question/1214333

#SPJ1

7 0

1 year ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are

Degger [83]

Answer:

y = -2/3x - 11/3

Step-by-step explanation:

7 0

3 years ago

The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Pr

aniked [119]

Answer:

(a) $E(X) = 0.383$

The expected number in the sample that treats hazardous waste on-site is 0.383.

(b) $P(x = 4) = 0.000169$

There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

Step-by-step explanation:

Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.

N = 209

Only eight of these facilities treated hazardous waste on-site.

r = 8

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?

n = 10

The expected number in the sample that treats hazardous waste on-site is given by

$E(X) = \frac{n \times r}{N}$

$E(X) = \frac{10 \times 8}{209}$

$E(X) = \frac{80}{209}$

$E(X) = 0.383$

Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site

The probability is given by

$P(x = 4) = \frac{\binom{r}{x} \binom{N - r}{n - x}}{\binom{N}{n}}$

For the given case, we have

N = 209

n = 10

r = 8

x = 4

$P(x = 4) = \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}}$

$P(x = 4) = \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}}$

$$ P(x = 4) = \frac{70 \times 84944276340}{35216131179263320}$

$P(x = 4) = 0.000169$

Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

8 0

2 years ago

Find the inverse function (on the given interval, if specified)

Zinaida [17]

Step-by-step explanation:

f(x) = x² + 1, where x >= 0.

Let y be f(x).

=> y = x² + 1

=> x² = y - 1

=> x = √(y - 1) because x is non-negative.

Hence f^-1(x) = √(x - 1), where x >= 1.

5 0

2 years ago