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1 answer:
Answer:
80 cm
Step-by-step explanation:
The diagonals divide the rhombus into four congruent triangles. The height of each triangle is 18/2 = 9, and the hypotenuse is 41. Using Pythagorean theorem, the width of each triangle is:
c² = a² + b²
41² = 9² + x²
x = 40
Therefore, the longer diagonal is 2×40 = 80.
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Answer:
x= 1.5, y= 3.5
or x= -5, y= 10
Step-by-step explanation:
Let's solve by substitution.
Label the two equations:
y= 2x² +6x -10 -----(1)
y= -x +5 -----(2)
Substitute (2) into (1):
2x² +6x -10= -x +5
2x² +6x +x -10 -5= 0
Simplify:
2x² +7x -15= 0
Factorise:
(2x -3)(x +5)= 0
2x -3= 0 or x +5= 0
2x= 3 or x= -5
x= 1.5
Now that we have found the value of x, we can find the value of y through substitution.
Substitute into (2):
y= -1.5 +5 or y= -(-5) +5
y= 3.5 or y= 10
Supplementary:
Do check out the following should you wish to learn more about solving quadratic equations!
