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grandymaker [24]
3 years ago
8

Suppose KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. Prove that A is equidistant from LM and KN.

Mathematics
1 answer:
Neporo4naja [7]3 years ago
7 0

Answer:

This is proved by ASA congruent rule.

 Step-by-step explanation:

Given KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. we have to prove that A is equidistant from LM and KN i.e we have to prove that AP=AQ

we know that the diagonals of parallelogram bisect each other therefore the the bisectors of ∠K and ∠L must be the diagonals.

In ΔAPN and ΔAQL

∠PNA=∠ALQ    (∵alternate angles)  

AN=AL   (∵diagonals of parallelogram bisect each other)

∠PAN=∠LAQ      (∵vertically opposite angles)

∴ By ASA rule ΔAPN ≅ ΔAQL

Hence, by CPCT  i.e Corresponding parts of congruent triangles PA=AQ

Hence, A is equidistant from LM and KN.

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This item is $9000 dollar and it is 90% off how much is the item? Step by step?
Daniel [21]

Answer:

The item costs $900 after the 90% off.

Step-by-step explanation:

After the 90% off discount, the item costs (100% - 90%) the cost of the original price.

Hence, \$9000 \cdot (100\% - 90\%)

= \$9000 \cdot 10\%

= \$900

Hope this helped!

5 0
3 years ago
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A community service group organizes a car wash that raises 7c - 18 dollars and a spaghetti dinner that raises 6s - 45 dollars. W
love history [14]

Answer:

7c + 6s - 63

Step-by-step explanation:

7c - 18 + 6s - 45

Combine like terms

7c + 6s - 63

3 0
2 years ago
Write and solve the equations. A number y is five less than thirteen.
Genrish500 [490]

We can follow the following steps to make an equation and solve it.

Step 1:

five less than 13 means we have to subtract 5 from 13

so it becomes 13-5

Step 2:

A number y is five less than thirteen.

Now in algebraic expressions, "is" stands for "="

So we have:

y=13-5

Step 3:

Solving the equation to find y.

y=13-5

Subtracting 5 from 13, we get :

y=8

Answer:

For the given equation the solution is y=8.

4 0
3 years ago
Question number 1: 5/8 (16b+24) -1/2b<br><br> Question number 2: 3/4 (16/64 + 12a) -9a
Sophie [7]

Answer:

Problem 1. <em>(19/2)b + 15</em>

Problem 2. <em>3/16</em>

Step-by-step explanation:

Question number 1

5/8 (16b+24) -1/2b  =

= (5/8) * (16/1) * b + (5/8) * 24 - (1/2)b

= 10b + 15 - (1/2)b

= (20/2)b - (1/2)b + 15

= (19/2)b + 15

Question number 2

3/4 (16/64 + 12a) -9a =

= (3/4) * (16/64) + (3/4) * 12a - 9a

= (3 * 16)(4 * 64) + (3/4) * (12/1) * a - 9a

= (3 * 1)(4 * 4) + (3 * 12)/(4 * 1) * a - 9a

= 3/16 + (3 * 3)/(1 * 1) * a - 9a

= 3/16 + 9a - 9a

= 3/16

5 0
3 years ago
Can someone help me with this right answer only and please explain it too
sineoko [7]

Answer:

g(6) = 71

f(11) = 62

Step-by-step explanation:

Let's solve g(6) first

Plug 6 into x

g(6) = 2(6)^2 - 1

g(6) = 2(36) - 1

g(6) = 72 - 1

g(6) = 71

Now let's solve f(11)

f(11) = 5(11) + 7

f(11) = 55 + 7

f(11) = 62

<em>Thus, out answers are 71 and 62 respectively</em>

5 0
3 years ago
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