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lions [1.4K]
3 years ago
12

In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in. Show with work

Mathematics
1 answer:
otez555 [7]3 years ago
3 0

Call the point where BK intersects AM point X. BX is the altitude of ∆ABM, and it is also the angle bisector of angle ∠ABM. Hence ∆ABM is isosceles, and AB ≅ MB.

M is the midpoint of BC, which is 12 inches long. Hence MB is half that length, or 6 inches.

Since AB is the same length as MB, which is 6 inches, ...

... AB is 6 inches.

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Which product is positive?
Natalija [7]

Option D:

\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right) is positive product.

Solution:

<em>If the negative sign is in even number of times then the product is positive.</em>

<em>If the negative sign is in odd number of times then the product is negative.</em>

To find which product is positive:

Option A:

$\left(\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)

Here, number of negative signs = 3

3 is an odd number.

So, the product is negative.

Option B:

$\left(-\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)

Here, number of negative signs = 3

3 is an odd number.

So, the product is negative.

Option C:

$\left(\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(-\frac{2}{7}\right)

Here, number of negative sign = 1

1 is an odd number.

So, the product is negative.

Option D:

$\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)

Here, number of negative sign = 2

2 is an odd number.

So, the product is positive.

Hence option D is the correct answer.

\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right) is positive product.

4 0
3 years ago
Help me please !!?????????? Question 4
Ne4ueva [31]

from question d = 16t^2 = 56-4t

=》 16t^2 -56 + 4t =0

=》 4t^2 - 14 + t = 0

=》 (4t-7)(t+2) =0

=》 t = 1.75 seconds

4 0
3 years ago
19. Suppose the diameter of a circle is 10 inches long and a chord is 6 inches long, Find the distance between the chord and the
mihalych1998 [28]

Answer:

10 m

Step-by-step explanation:

x2 + 242 = 262

x2 + 576 = 676

x2 = 100

x = 10

The chord is 10 m from the center of the circle.

3 0
3 years ago
PLEASE SHOW YOUR WORK
lakkis [162]

Answer:

ok

Step-by-step explanation:

5 0
3 years ago
N over 7= 20<br> solve for N
Blababa [14]

Answer:

N = 140

Step-by-step explanation:

N/7 = 20

Inverse operation of division: multiplication

N/7 = 20

becomes:

N = 7 x 20

N = 140

Thus, the value of N is 140.

6 0
3 years ago
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