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k0ka [10]
3 years ago
6

Keith needs to read 2 novels each month.

Mathematics
1 answer:
garik1379 [7]3 years ago
7 0
*2(M)=N

*2(19)=N
38=N

..........................
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5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9) ​
Irina-Kira [14]

Label the points A,B,C

  • A = (1,2)
  • B = (4,5)
  • C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\

Segment AB is exactly 3\sqrt{2} units long.

Now let's find the distance from B to C

B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\

Segment BC is exactly 4\sqrt{2} units long.

Adding these segments gives

AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\

AC is exactly 7\sqrt{2} units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0
2 years ago
Apply the distributive property to factor out the greatest common factor.<br> 45e -27f
mojhsa [17]

Answer:

9 (5e - 3f)

Step-by-step explanation:

45e -27f

45e = 9*5*e

27f = 9*3*f

The common factor is 9

9*5*e -  9*3*f

9 (5e - 3f)

8 0
3 years ago
Read 2 more answers
D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF? A. 30° B. 45° C. 60° D. 90°
viva [34]
D hope this helps man
4 0
2 years ago
Simplify completely the quantity 4 times x to the third power plus 5 times x to the 2nd power plus 3 times x all over x. (2 poin
ikadub [295]

Answer:   4x² + 5x + 3

<u>Step-by-step explanation:</u>

\dfrac{4x^3+5x^2+3x}{x}\\\\\\=\dfrac{x(4x^2+5x+3)}{x}\qquad \text{factored out the common term from the numerator}\\\\\\=4x^2+5x+3\qquad \text{canceled out x from numerator and denominator}

8 0
3 years ago
Simplify your answer as much as possible.<br><br> -27=5v-2
Vinil7 [7]

hello there

the answer is ..... down below

I did the math for ya

hope this helps

thank you

best regards Queen Z

7 0
3 years ago
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