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3 years ago

The graphs of the equation y = 4x + 1 and y - kx = 10 are perpendicular when k = _______?

Mathematics

1 answer:

Ann [662]3 years ago

3 0

Answer:

$k=-\frac{1}{4}$

Step-by-step explanation:

we have

Line 1

$y=4x+1$

Equation in slope intercept form

The slope is equal to

$m_1=4$

Line 2

$y-kx=10$

$y=kx+10$

Equation in slope intercept form

The slope is equal to

$m_2=k$

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

$m_1*m_2=-1$

substitute

$(4)(k)=-1$

$k=-\frac{1}{4}$

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What is the sample space for a 5 sided number cube?

grigory [225]

Answer:

{1, 2, 3, 4, 5}

Step-by-step explanation:

Sample space is the set of all possible outcomes. Supposing that the 5 sided number cube has numbers one to five on its sides, the possible outcomes are the numbers that can be rolled, then its sample space is: {1, 2, 3, 4, 5}

3 0

3 years ago

I have no clue how to solve this.

expeople1 [14]

Answer: 36.6

Step-by-step explanation: 2x+1+3x-4=180

add 2 & 3 to get 5x

subtract 1 from 1 & 180
so u would have 5x-4=179

+4 to 179

then 5x=183

divide by 5

x=36.6

hope it helps

7 0

2 years ago

The total land area of the world is about fifty-seven million, two hundred eighty thousand square miles. Write that number

expeople1 [14]

The total land area of the world is about fifty-seven million, two hundred eighty thousand square miles is 57, 280, 000 square miles

<em><u>Solution:</u></em>

Given that, we have to write the given words in number

The total land area of the world is about fifty-seven million, two hundred eighty thousand square miles

The number of zeros in million is 6

Here given that 57 million

So, 57 million means 57, followed by 6 digits

two hundred eighty thousand means 280 followed by 3 zeros

two hundred eighty thousand = 280 thousand

Thus the number is: 57, 280, 000

5 0

3 years ago

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 15 years, and standard deviation of 3

Gala2k [10]

Answer:

The probability that their mean life will be longer than 13 years = .9943 or 99.43%

Step-by-step explanation:

Given -

Mean $(\nu )$ = 15 years

Standard deviation $(\sigma )$ = 3.7 years

Sample size ( n ) =22

Let $\overline{X}$ be the mean life of manufacturing items

the probability that their mean life will be longer than 13 years =

$P(\overline{X}> 13)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}> \frac{13 - 15 }{\frac{3.7}{\sqrt{22}}})$ $(Z =\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}})$