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Marianna [84]
3 years ago
8

The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possibl

e values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Mathematics
1 answer:
True [87]3 years ago
5 0

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

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3 years ago
Find X, AB, BC, AC if B is the midpoint of AC
Artemon [7]

Step-by-step explanation:

it all starts with the understanding that "midpoint" means that the line segments on both sides have the exact same length.

this is the same as "cut a pizza or a cake in half".

therefore, we know

10x + 1 = 8x + 13

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7 0
1 year ago
Please help! i can’t seem to find a answer to the this question.
DiKsa [7]

Answer:

B (6,0) because when graphed it would make a 90° angle

8 0
2 years ago
Read 2 more answers
URGENT DUE BY 2:30 WILL RATE GOOD:)
Dmitry [639]
Areashaded=areabigcircle-areasmallcircle


areacircle=pir^2
d/2=r

big diameter=20.4, so radius i 20.4/2=10.2cm

small is 10.8/2=5.4


so
big-small
pi10.2^2-pi5.4^2
pi(104.04-29.16)
pi(74.88)
using 3.14=pi
235.1232 cm^2


answer is B

7 0
3 years ago
Read 2 more answers
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