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3 years ago

Determine the equation of the line that is perpendicular to the line y = 3x + 4 and passes through the point (6, 2).

Mathematics

1 answer:

fomenos3 years ago

3 0

Answer:

y = -1/3x + 4

Step-by-step explanation:

Perpendicular lines: Their gradients are reciprocals.

This means:

-1 ÷ Gradient 1 = Gradient 2
Gradient 1 * Gradient 2 = -1

Gradient of the given equation is 3.

-1 / 3 = -1/3

Gradient of the equation we're finding is -1/3

y = -1/3x + c

Substitute the coordinates in to find the value of c

2 = -1/3(6) + c

2 = -2 + c

2 + 2 = c

4 = c

y = -1/3x + 4

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P(x)=(x-2)(x-4)(x-5)

Cerrena [4.2K]

The constants of a polynomial is the term that has no variable attached to it.

<h3>The constant term</h3>

To determine the constant, we simply multiply the constant term in each factor of the polynomial.

So, we have:

<h3 /><h3>Polynomial P(x) = (x-2)(x-4)(x-5)</h3>

$Constant = -2 \times -4 \times -5$

$Constant = -40$

Hence, the constant is -40

<h3>Polynomial P(x) = (x-2)(x-4)(x+5)</h3>

$Constant = -2 \times -4 \times 5$

$Constant = 40$

Hence, the constant is 40

<h3>Polynomial P(x) =1/2(x-2)(x-4)(x+5)</h3>

$Constant = \frac 12 \times -2 \times -4 \times 5$

$Constant = 20$

Hence, the constant is 20

<h3>Polynomial P(x) = 5(x-2)(x-4)(x+5)</h3>

$Constant = 5 \times -2 \times -4 \times 5$

$Constant = 200$

Hence, the constant is 200

$Constant = -5 \times -2 \times -4 \times 5$

$Constant = -200$

Hence, the constant is -200

Read more about polynomials at:

brainly.com/question/2833285

5 0

2 years ago

6.Suppose the Gallup Organization wants to estimate the population proportion of those who think there should be a law that woul

drek231 [11]

Answer:

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that $n = 1012, \pi = \frac{374}{1012} = 0.3696$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}$

$E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}$

$\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

$n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

4 0

3 years ago

What is two mixed numbers that have the sum of 3

Juli2301 [7.4K]

Mixed numbers are a mix of a whole number and a fraction
a easy one is
1 and 1/4+1 and 3/4
1 and 1/2 +1 and 1/2
1 and 9/10 and 1 and 1/10
etc

6 0

3 years ago

SHAYNA FREEL PLANS TO BUY $17.45 WORTH OF STATIONERY SUPPLIES. IF THE SALES TAX IS 13%, HOW MUCH WILL SHAYNA PAY?

Rainbow [258]

9514 1404 393

Answer:

$19.72

Step-by-step explanation:

The sales tax is 13% of $17.45:

0.13 × $17.45 = $2.27 . . . . . . rounded (up) to the nearest cent

Then the total Shayna will pay is ...

$17.45 +2.27 = $19.72

7 0

3 years ago

The relationship between the number of months and cumulative cell phone cost is represented by the scatter plot shown.

Elza [17]

Answer:

C. $940

Step-by-step explanation:

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3 years ago

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