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kondor19780726 [428]

3 years ago

5

Find the coordinates of the midpoint and the length of the line segment joining these pairs of points. a.(0,0)and(4,-4) b.(1,5)a

nd(3,1) c.(-3,-3)and(0,0) d.(-1,3)and(5,1) e.(-1,6)and(2,-2) f.(-3,4)and(3,-1)

1 answer:

NARA [144]3 years ago

3 0

The answer is (6,7). Hope that helps!! Great problem !!

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What is the relationship between the 5s in the number 755,371

timama [110]

The 5 in the ten thousandths place is 10 times greater than the 5 in the thousandths place.

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4 years ago

Read 2 more answers

Simplify (3-4i/3+4i) + 3+4i/3-4i

notsponge [240]

The answer is 3 / 3

Step-by-step explanation:

Cancel negative with positive then find the answer

7 0

3 years ago

P(A) = 0.75 P(B) = 0.93 P(A and B) = 0.46

kotykmax [81]

A) 0.46/0.93
B) 0.46/0.75
C) These events are dependent

3 0

3 years ago

A certain stock starts the day at $273/8 per share. If it drops $21/2 during the day, what is its closing value? A. $247/8 B. $2

Elza [17]

Answer:

A. $ 24 7/8

Step-by-step explanation:

GIVEN: A stock starts the day at $27 3/8 per share.

Share drops $2 1/2 during the day.

To Find : Closing value

Solution : first we need to find how many 1/8 are there in 1/2

So, $\frac{\frac{1}{2} }{\frac{1}{8} } =4$

when share drops by $2 then share will be :

$27 - $2 =$25

and $\frac{3}{8} - 4(\frac{1}{8})$

⇒ $\frac{3}{8} - \frac{4}{8}$

⇒ $\frac{-1}{8}$

So, $25-\frac{1}{8}$

⇒ $24\frac{7}{8}$

So, its closing value is $24\frac{7}{8}$ .

7 0

4 years ago

Find the three angles of the triangle with the given vertices: P(1,1,1), ????(1,−3,2), and ????(−3,2,5).

velikii [3]

Answer:

The three angles of the triangle are 90, 35.67 and 54.33 degrees.

Step-by-step explanation:

One way to find the angles of the triangle with vertices (1, 1, 1), (1, -3, 2), (-3, 2, 5) is using the definition of the <em>dot product</em> of two vectors, defined as:

a . b = |a| |b| cosФ [1]

Where |a| and |b| are the norms of vectors <em>a</em> and b, and cosФ is the cosine of the angle between either vector <em>a</em> and <em>b</em>.

If a = [ $\\ a_{1}, a_{2}, a_{3}$ ] and b = [ $\\ b_{1}, b_{2}, b_{3}$ ], then the dot product is simply a number (not a vector) obtained from:

a . b = $\\ a_{1}*b_{1} + a_{2}*b_{2} + a_{3}*b_{3}$

The norm of a vector (its length) is, for instance, |a| = $\\ \sqrt{{a_{1}^2 + {a_{2}}^2 + {a_{3}}^2}$ , for a vector in $\\ R^{3}$ .

Having all that into account, we can determine the angles of the triangle for each vertex using equation [1] and solving it for Ф.

<h3>Angle of the triangle for vertex in (1, 1, 1)</h3>

The vectors which form an angle from this vertex are the result of subtracting the vertex (1, 1, 1) to any of the remaining points (1, -3, 2) and (-3, 2, 5):

v(1, 1, 1) - v(1, -3, 2) = $\\ (1 - 1, 1 - (-3), 1 - 2) = (0, 1 + 3, -1) = (0, 4, -1)$

v(1, 1, 1) - v(-3, 2, 5) = $\\ (1 - (-3), 1 - 2, 1 - 5) = (1 + 3, -1, -4) = (4, -1, -4)$

The <em>dot product</em> for these vectors is:

[0, 4, -1] . [4, -1, -4] = [0 * 4 + 4 * -1 + -1 * -4] = 0 - 4 + 4 = 0

The norm for each vector is:

|(0, 4, -1)| = $\\ \sqrt{0^2 + 4^2 + -1^2} = \sqrt{0 + 16 + 1} = \sqrt{17}$

|(4, -1, -4)| = $\\ \sqrt{4^2 + -1^2 + -4^2} = \sqrt{16 + 1 + 16} = \sqrt{33}$

So

a . b = |a| |b| cosФ

$\\ 0 = \sqrt{17} * \sqrt{33} * cos{\theta}$

$\\ \frac{0}{\sqrt{17} * \sqrt{33}} = cos{\theta}$

$\\ cos^{-1}{0}} = cos^{-1}(cos{\theta})$

$\\ 90 = \theta$

In vertex (1, 1, 1) the angle of the triangle is 90 degrees. We have here a right triangle.

We have to follow the same procedure for finding the vectors for angles in vertices (1, -3, 2) and (-3, 2, 5), or better, after finding one of the previous angles, we find the remaining angle subtracting the sum of two angles from 180 degrees to finally obtaining the three angles in question.

Therefore, the other angles are 35.67 degrees and 180 - (90 + 35.67) = 180 - 125.67 = 54.33 degrees.

5 0

3 years ago