Answer:
65 pairs
Step-by-step explanation:
Black makes up 5/(5+8) = 5/13 of the total order, so ...
(5/13)(169 pairs) = 65 pairs
Vinny will order 65 pairs of black high tops.
Answer:
4
Step-by-step explanation:
= 4 because the variable y on the numerator and the denominator can cancel out.
Answer:
1/6
Step-by-step explanation:
LCD = 96
2(32) - 16(3)/ 3(32) = 64 - 48/96
= 16/96
Simplify:
16/ 16 = 1
96/16 = 6
2/3 - 16/32 = 1/6
Sorry if my work might seem confusing. If it is, then try searching "fraction calculator." It really helps :)
Answer:
x=15 cm
Step-by-step explanation:
The two triangles in the diagram are:
ABC and BDC
First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.
Hypotenuse is the largest side of a triangle which is usually in front of the right angle.
So in BDC
![Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm](https://tex.z-dn.net/?f=Base%20%3D%20BD%20%3D10cm%5C%5CHypotenuse%20%3D%20BC%20%3D%20%3F%5C%5CPerpendicular%20%3D%20CD%20%3D%202%5Csqrt%7B11%7Dcm)
Applying Pythagoras theorem:
![(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm](https://tex.z-dn.net/?f=%28Hypotenuse%29%5E2%20%20%3D%20%28Base%29%5E2%20%2B%20%28Perpendicular%29%5E2%5C%5CBC%5E2%20%3D%20BD%5E2%20%2B%20CD%5E2%5C%5CBC%5E2%20%3D%20%2810%29%5E2%20%2B%20%282%5Csqrt%7B11%7D%29%5E2%5C%5CBC%5E2%20%3D%20100%2B%282%5E2%20%2A%2011%29%5C%5CBC%5E2%20%3D%20100%2B%284%2A11%29%5C%5CBC%5E2%20%3D%20100%2B44%5C%5CBC%5E2%20%3D%20144%5C%5C%5Csqrt%7BBC%5E2%7D%20%3D%20%5Csqrt%7B144%7D%5C%5CBC%20%3D%2012cm)
Solving for triangle ABC
![Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\](https://tex.z-dn.net/?f=Base%20%3D%20BC%20%3D%2012%20cm%5C%5CPerpendicular%20%3D%20AB%20%3D%209%20cm%5C%5CHypotenuse%20%3D%20AC%20%3D%20x%5C%5C)
Applying Pythagoras theorem
![AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm](https://tex.z-dn.net/?f=AC%5E2%20%3D%20BC%5E2%2BAB%5E2%5C%5Cx%5E2%20%3D%20%2812%29%5E2%20%2B%20%289%29%5E2%5C%5Cx%5E2%20%3D%20144%2B81%5C%5Cx%5E2%20%3D%20225%5C%5C%5Csqrt%7Bx%5E2%7D%20%3D%20%5Csqrt%7B225%7D%5C%5Cx%20%3D%2015cm)
Hence,
x=15 cm
2x+3=17
subtract 3 from both sides
2x=14
divide both sides by 2 and get
x=7