Answer:
84 square units.
Step-by-step explanation:
If LM - KN = 4, then denote KN = x and LM = x+4.
1. Consider right triangle KLM. By the Pythagorean theorem,
![KL^2 =ML^2+MK^2,\\ \\15^2=(x+4)^2+MK^2.](https://tex.z-dn.net/?f=KL%5E2%20%3DML%5E2%2BMK%5E2%2C%5C%5C%20%5C%5C15%5E2%3D%28x%2B4%29%5E2%2BMK%5E2.)
2. Consider right triangle KMN. By the Pythagorean theorem,
![MN^2 =NK^2+MK^2,\\ \\13^2=x^2+MK^2.](https://tex.z-dn.net/?f=MN%5E2%20%3DNK%5E2%2BMK%5E2%2C%5C%5C%20%5C%5C13%5E2%3Dx%5E2%2BMK%5E2.)
Subtract these two equations:
![15^2-13^2=(x+4)^2-x^2,\\ \\225-169=x^2+8x+16-x^2,\\ \\56=8x+16,\\ \\8x=56-16,\\ \\8x=40,\\ \\x=5\ un.](https://tex.z-dn.net/?f=15%5E2-13%5E2%3D%28x%2B4%29%5E2-x%5E2%2C%5C%5C%20%5C%5C225-169%3Dx%5E2%2B8x%2B16-x%5E2%2C%5C%5C%20%5C%5C56%3D8x%2B16%2C%5C%5C%20%5C%5C8x%3D56-16%2C%5C%5C%20%5C%5C8x%3D40%2C%5C%5C%20%5C%5Cx%3D5%5C%20un.)
Then
![13^2=5^2+MK^2,\\ \\MK^2=169-25,\\ \\MK^2=144,\\ \\MK=12\ un.](https://tex.z-dn.net/?f=13%5E2%3D5%5E2%2BMK%5E2%2C%5C%5C%20%5C%5CMK%5E2%3D169-25%2C%5C%5C%20%5C%5CMK%5E2%3D144%2C%5C%5C%20%5C%5CMK%3D12%5C%20un.)
The area of KLMN is
![A_{KLMN}=\dfrac{LM+KN}{2}\cdot MK=\dfrac{5+9}{2}\cdot 12=14\cdot 6=84\ un^2.](https://tex.z-dn.net/?f=A_%7BKLMN%7D%3D%5Cdfrac%7BLM%2BKN%7D%7B2%7D%5Ccdot%20MK%3D%5Cdfrac%7B5%2B9%7D%7B2%7D%5Ccdot%2012%3D14%5Ccdot%206%3D84%5C%20un%5E2.)
Answer:
5.1
Step-by-step explanation:
-10.3 +y= -5.2
y=-5.2+10.3
y=5.1
16(x+2)-8 = 16x+24
16x + 32-8 = 16 x + 24
16x + 24 = 16x + 24
Every x is a solution. How many is that?
An uncountably infinite number of solutions.
Answer: 123 crackers
Step-by-step explanation:
If 1/3 of the box contains sesame seed crackers, then, 2/3 of the box contains whole wheat and cheese flavored crackers.
Total number of whole wheat and cheese flavored crackers = 53 + 29 = 82
Let x be the total number of crackers in the box, so we will have the equation
2/3 x= 82
x = 82 ÷ 2/3; we will get
X =82 x 3/2
X = 123 crackers