Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
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To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4
(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3
Answer:
Step-by-step explanation:
9 - x ≤17
At some point you are going to have to turn the equation around. This would not normally be your first step, but this time it is better to start with it.
We won't do it directly. The best way to do it is to add x to both sides before you do anything else. This is not the usual way to solve these equations, but it's a good time to learn.
Inequality Rule: you must always solve for x. If it is -x then you are going to have to make an adjustment to get the x to be positive.
9 - x ≤ 17 Add x to both sides
9 - x+x ≤ 17 + x Combine
9 ≤ 17 + x Subtract 17 from both sides.
9 - 17 ≤ 17 - 17 + x
8 ≤ x
Notice that you have effectively changed the ≤ sign around, not because you have, but because the x reads differently now. It started out 9 - x ≤ 17 and when you finish solving it you get 8 is less than or equal to x. Entirely different.
Answer:
Decimal: 1.82. Percent: 182%
Step-by-step explanation:
