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3 years ago

Calculate the distance between the points Q = (2, -1) and K = (6,-9) in the coordinate plane.

Mathematics

1 answer:

White raven [17]3 years ago

3 0

Answer:

Sqrt 80 = 8.94

Step-by-step explanation:

d = sqrt[(x-x)^2 + (y-y)^2]

d = sqrt [(6-2)^2 + (-9 - - 1)^2]

d = sqrt [(4)^2 + (-8)^2]

d = sqrt (16 + 64)

d = sqrt 80

d = 4 sqrt 5 = 8.94

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Need to find the value of y

alexgriva [62]

Answer:

√55

Step-by-step explanation:

Notice that the small triangle in the bottom corner shares an angle with the overall triangle. Also, they are both right triangles. Therefore, they are similar triangles.

Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle. Therefore it is also similar to the overall triangle and the smaller triangle.

Writing a proportion between the small and large triangles:

y / 11 = 5 / y

y² = 55

y = √55

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3 years ago

Find the slope of the line that passes through the points (-8, 3) and (7, 3)

taurus [48]

Answer:

slope : 1/15

Step-by-step explanation:

slope = change in y / change in x

change in y = 1 / change in x = 15

therefore, 1/15 = slope

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3 years ago

1/2 x 2/4 x 3/6 x 4/8 x 5/10 x 6/12 simplified

Talja [164]

Answer: 3

Step-by-step explanation: Because, 1/2=2/4=3/6=4/8=5/10=6/12 are all the same. You can test is out by simply factoring out the biggest factor on both sides. For example, 2/4 can be simplified to 1/2, because 2/4=(2/2)/(4/2) you can divide both sides by two. Hope this helps, <3!

8 0

3 years ago

A corporate team-building event costs $19plus an additional $1 per attendee. How many attendees can there be, at most, if the bu

Mars2501 [29]

Answer:

There can be at most $12$ attendees in a corporate team-building event.

Step-by-step explanation:

Let $x$ denotes number of attendees in a corporate team-building event.

Fixed cost = $19

Cost charged per attendee = $1

Budget for the corporate team-building event = $31

Therefore,

$19+1(x)\leq 31\\19+x\leq 31\\x\leq 31-19\\x\leq 12$

So, there can be at most $12$ attendees in a corporate team-building event.

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3 years ago

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken

mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

$X=1$ number of citrus trees that are infected with the citrus red mite.

$n=5$ random sample taken

$\hat p=\frac{1}{5}=0.2$ estimated proportion of citrus trees that are infected with the citrus red mite.

$p$ true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values would be given by: