Answer:
7/3 =x
Step-by-step explanation:
2x+3=5x-4
Subtract 2x from each side
2x-2x+3=5x-2x-4
3 = 3x -4
Add 4 to each side
3+4 = 3x
7 = 3x
Divide by 3
7/3 =3x/3
7/3 =x
Answer:AC = 20
BK = 9.6
Step-by-step explanation:
AC is found using the Pythagorean theorem in the usual way:
AC² = AB² + BC²
AC² = 12² + 16² = 144 +256 = 400
AC = √400
AC = 20
You may recognize this is a 3-4-5 triangle scaled by a factor of 4.
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Then BK is found using similar triangles. All of the triangles in the figure are similar*, so ...
long side / hypotenuse = BC/AC = BK/AB
BK = AB(BC/AC) = 12(16/20) = 12×0.8
BK = 9.6
By pythagoras theorem,
cb^2 = ac^2 + ab^2
5^2 = ac^2 + 3^2
ac^2 = 5^2 - 3^2 = 16
ac = squareroot 16 = 4cm