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1 year ago

Use the distance formula to calculate the length of the leg CD

Mathematics

1 answer:

Karo-lina-s [1.5K]1 year ago

6 0

To calculate the distance between two points on the coordinate system you have to use the following formula:

$d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}$

Where

d represents the distance between both points.

(x₁,y₁) are the coordinates of one of the points.

(x₂,y₂) are the coordinates of the second point.

To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph

C(2,-1)

D(-1,-2)

Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)

$\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}$

The length of CD is √10 units ≈ 3.16 units

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The sum of two prime numbers

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3 years ago

You start driving north for 6 miles, turn right, and drive east for another 19 miles. At the end of driving, what is your straig

Anton [14]

Answer:

Okay, here's the method I'm going to use.

If you drive north 6 miles, and then drive east 19 miles, you are technically making a triangle.

19 miles

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6 milesl

You are just missing the last side of the triangle: the straight line stretching from across your starting point to the ending point. You can find this by using the Pythagorean theorem.

a^2 + b^2 = c^2

6^2 + 19^2 = c^2

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2 years ago

Helppp!!! 0_o 70 pnts!!!

kati45 [8]

Answer:

Option A is correct

Step-by-step explanation:

For the box y=mx+c

Hope this helps

8 0

3 years ago

Read 2 more answers

If m< DBG=58 and mDG =74 , find mGE

mestny [16]

Answer:

Option D: mGE = 190°

Step-by-step explanation:

From the property of angles of secant and tangent lines, we have:

DBG = (mGE - mDG)/2

(That is, the angle in point B is half the difference of the larger arc by the smaller arc defined by the lines)

So, we have that:

58 = (mGE - 74)/2

2*58 = mGE - 74

mGE = 116 + 74 = 190°

So we have that mGE is equal to 190°, correct option: D.

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3 years ago

A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .