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prisoha [69]
3 years ago
6

What is the equation of a line that contains the point (2,1) and is perpendicular to the line: y = 3x – 4?

Mathematics
1 answer:
jeka57 [31]3 years ago
8 0
Y = 3x - 4.....the slope here is 3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, u flip the slope and change the sign. So we will need a slope of -1/3...see how I flipped the slope of 3/1 and made it 1/3...and then changed the sign, making it -1/3.

y = mx + b
slope(m) = -1/3
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = -1/3(2) + b
1 = -2/3 + b
1 + 2/3 = b
3/3 + 2/3 = b
5/3 = b

so ur perpendicular equation is : y = -1/3x + 5/3
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Temka [501]

Answer:

x = 13

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = x^2

25+144 = x^2

169 = x^2

Taking the square root of each side

sqrt(169) = sqrt(x^2)

13 =x

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2 years ago
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At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the n
wolverine [178]

Answer:

(1) The probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2) The shop owner has no reasonable chance to expect earning a profit more than $300.

(3) The probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

Step-by-step explanation:

Let <em>X</em> = number of cups of coffee sold and <em>Y</em> = number of donuts sold.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = 320 and <em>σ </em>= 20.

The random variable <em>Y</em> follows a Normal distribution with parameters <em>μ</em> = 150 and <em>σ </em>= 12.

The shop owner opens the shop 6 days a week.

(1)

Compute the probability that the shop owner sells over 2000 cups of coffee in a week as follows:

P(X>2000)=P(\frac{X-\mu}{\sigma}>\frac{2000-(6\times320)}{6\times20})\\=P(Z>0.67)\\=1-P(Z

Thus, the probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2)

The equation representing the profit earned on selling 1 cup of coffee and 1 doughnut in a day is:

P = 0.5<em>X</em> + 0.4<em>Y</em>

Compute the probability that the shop owner earns more than $300 as profit as follows:

P(Profit>300)=P(\frac{Profit-\mu}{\sigma}>\frac{300-((0.5\times320)+(0.4\times150))}{\sqrt{0.5^{2}(20)^{2}+0.4^{2}(12)^{2}}})\\=P(Z>7.21)\\\approx0

The probability of earning a profit more then $300 is approximately 0.

Thus, the shop owner has no reasonable chance to expect earning a profit more than $300.

(3)

The expression representing the statement "he'll sell a doughnut to more than half of his coffee customers" is:

<em>Y</em> > 0.5<em>X</em>

<em>Y</em> - 0.5<em>X</em> > 0

Compute the probability of the event (<em>Y</em> - 0.5<em>X</em> > 0) as follows:

P(Y - 0.5X > 0)=P(\frac{(Y - 0.5X) -\mu}{\sigma}>\frac{0-(150-(0.5\times320}{\sqrt{12^{2}+0.5^{2}20^{2}}})\\=P(Z>0.64)\\=1-P(Z

Thus, the probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

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3 years ago
The data in the table compares x, the number of pages in a chapter, to y, the amount of time, in minutes, spent reading. The fun
Mamont248 [21]

Answer:The answer is A, 15 I believe if i did the math right.

Step-by-step explanation: First you take the equation: f(x)= 0.86x-0.09

Then you plug in x witch in this case is 18 so f(18)=0.86(18)-0.09= 15.39 So round to the nearest whole number and you get 15.

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Answer:

9/10

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Mark as brainliest if this helped

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