Elena went to a sporting goods store that

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c

natali 33 [55]

Answer: By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

Since, And, D and E are the mid points of the line segments AB and BC respectively.

Therefore, By mid point theorem,

coordinate of D are $(\frac{2+6}{2} , \frac{2+8}{2} ) = (\frac{8}{2} , \frac{10}{2} )= (4,5)$

Coordinate of E are $(\frac{2+8}{2} , \frac{2+4}{2} ) = (\frac{10}{2} , \frac{6}{2} )= (5,3)$

By the distance formula,

$DE=\sqrt{(5-4)^2+(3-5)^2}=\sqrt{5}$

$AC=\sqrt{(8-6)^2+(4-8)^2}=2\sqrt{5}$

By the slope formula,

Slope of AC = $\frac{4-8}{8-6} = \frac{-4}{2} = -2$

Slope of DE = $\frac{3-5}{5-4} = \frac{-2}{1} = -2$

Statement Reason

1. The coordinate of D are (4,5) and 1. By the midpoint formula

the coordinate of E are (5,3)

2. The length of DE = √5 2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the 3. By the slope formula

slope of AC = -2

4. DE║AC 4. Slopes of parallel lines are equal

7 0

3 years ago

Read 2 more answers

Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an eye patient

KonstantinChe [14]

First, you must find the total number of people. Add together 32, 54, 78, 112, and 96 to get 372. Next, add the number of diabetic patients with the number of patients with eye problems (54 + 112 = 166).

Your fraction is now 116/372. Simplify this to get your answer, 29/93 or 0.31.

6 0

2 years ago

Need help also if you can can you do it step-by-step explanation please thank you 3(c + 8) = 28<br>

skelet666 [1.2K]

Answer:

c = 4/3

Step-by-step explanation:

3(c + 8) = 28

Since we have paranthesis, first use the dsitributive property [multiply 3 by c and 8]

3(c + 8) = 28

3c + 24 = 28

To find the value of c, you must have c alone on one side, so subtract 24 from both sides

3c + 24 = 28

3c = 4

Now, divide by 3 to both sides to get your answer

3c = 4

c = 4/3

Therefore, the answer is 4/3!

I hope this helps! :)

3 0

3 years ago

Read 2 more answers

The diameters of ball bearings are distributed normally. The mean diameter is 83 millimeters and the standard deviation is 3 mil

Alenkinab [10]

Answer:

0.2514 = 25.14% probability that the diameter of a selected bearing is greater than 85 millimeters.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this question, we have that:

$\mu = 83, \sigma = 3$