Answer:
x=4
Step-by-step explanation:
In triangle MLK
- it is a equilateral triangle
- Hence
- ML=LK=MK=5
Now come to triangle MKJ
- It is a isosceles triangle
- Hence
- MJ=Mk
MK=5
Hence
In the image, as denoted by similar sides OP and MN, we can conclude that the 2 triangles are similar triangles. To look for the value of x (which we can substitute later to find the length of segment LP), we relate the relations of segments LO and LP to segments LM and LN. This relation is shown below:
LO/LP = LM/LN
22 / x+12 = 30 / x+12 + 5
22 / <span>x+12 = 30 / x+17
</span>
Cross-multiplying:
30x + 360 = 22x + 374
Isolating x to one side of the equation by subtracting 22x and 360 from both sides:
30x + 360 - 360 - 22x = 22x + 374 - 360 - 22x
8x = 14
x = 1.75
Since we now have the value of x, we substitute this to the equation of LP:
LP = x + 12
LP = 1.75 + 12
LP = 13.75
Therefore the value of LP is 13.75 in.
2 yards = 72 inches
3 ft = 36 inches
72 - 36 = 36
She still needs 36 inches of fabric.
Step-by-step explanation:
<u>Given</u>
- x + 2y = 3 and xy = 2
- show that x³ + 8y³ + 9 = 0
<u>Solution in steps:</u>
- (x + 2y)³ = 3³
- x³ + 3x²(2y) + 3x(2y)² + (2y)³ = 27
- x³ + 6x(xy) + 12y(xy) + 8y³ = 27
- x³ + 8y³ + 6(x + 2y)xy = 27 ⇒ Substitute values
- x³ + 8y³ + 6*3*2 = 27
- x³ + 8y³ + 36 - 27 = 0
- x³ + 8y³ + 9 = 0
Done
