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patriot [66]
3 years ago
14

Find the point, M, that divides segment AB into a ratio of 5:5 if A is at (0, 15) and B is at (20, 0).

Mathematics
2 answers:
Debora [2.8K]3 years ago
7 0

Answer:

Option C). (10, 7.5)

Step-by-step explanation:

We have to find the coordinates of point M that divides the segment AB into a ratio of 5:5.

Vertices A and B are (0, 15) and (20, 0)

Ratio 5:5 is simply the ratio 1:1 means point M is the midpoint of segment AB.

So x-coordinate of M will be \frac{(20+0)}{2}=10

and y - coordinate will be = \frac{(15+0)}{2}=7.5

Therefore Option C. (10, 7.5) are the coordinates of point M.

Airida [17]3 years ago
5 0

C

a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment

using the midpoint formula

M = [\frac{1}{2} (0 + 20 ), \frac{1}{2} (15 + 0)] = (10, 7.5 )


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Step-by-step explanation:

As i previously explained,

The general form of equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.

h and k are the co-ordinates of the center of circle and r is the radius

Here, We have (2,1) as the co-ordinates of the center of circle

Now,

( x - h )^2 + ( y - k )^2 = r^2

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The radius of the circle is 1 units(from figure)

So, put that in, we get

( x - 2 )^2 + ( y - 1 )^2 = 1^2

or, ( x - 2 )^2 + ( y - 1 )^2 = 1

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The cost per hour of running an assembly line in a
nlexa [21]

Answer:

the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Step-by-step explanation:

if there is no mistake in the problem description, I read the following function :

C(x) = y = 0.3x² - 1.2x + 2

I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.

the first derivative of C(x) is

0.6x - 1.2 = y'

0.6x - 1.2 = 0

0.6x = 1.2

x = 2

C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8

so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

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3 years ago
Today only, a table is being sold at a 62% discount. The sale price is $144.40.
Korolek [52]
  • Answer:

<em>$ 232.90</em>

  • Step-by-step explanation:

<em>62% ........... $144.40</em>

<em>100% ..........$ x</em>

<em>x = 144.40×100/62</em>

<em>= 14440/62</em>

<em>= $ 232.90</em>

3 0
3 years ago
Find the smallest number which when divided by 12,15,18&amp;27 leaves as remainder 8,11,14,23 respectively.
Free_Kalibri [48]

Answer:

\boxed{ \bold{ \huge{  \boxed{ \sf{536}}}}}

Step-by-step explanation:

Solution :

Here, 12 - 8 = 4

15 - 11 = 4

18 - 14 = 4

27 - 23 = 4

Thus, every divisor is greater than its remainder by 4. So, the required smallest number is the difference of the L.C.M of the given number and 4

<u>Finding </u><u>the</u><u> </u><u>L.C</u><u>.</u><u>M</u>

First of find the prime factors of each numbers

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18 = 3 × 3 × 3

27 = 3 × 3 × 3

Take out the common prime factors : 3 , 3 and 3

Also take out the other remaining prime factors : 2 , 2 and 5

Now, Multiply those all prime factors and obtain L.C.M

L.C.M = Common factors × Remaining factors

= 3 × 3 × 3 × 2 × 2 × 5

= 540

L.C.M of 12 , 15 , 18 and 27 = 540

So, The required smallest number = 540 - 4

= 536

Hope I helped!

Best regards!!

3 0
3 years ago
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