For a quadratic equation ax^2 + bx + c = 0, the discriminant is given by b^2 - 4ac
Thus for a^2 - 2a + 5 = 0,
a = 1, b = -2 and c = 5
b^2 - 4ac = (-2)^2 - 4(1)(5) = 4 - 20 = -16
Answer:
Base 5
Step-by-step explanation:
We want to determine the base at which:
113 X 2 =231
We consider the last number of the result (231).
The base must be a number such that:
3 X 2 will have a remainder of 1.
3 X 2 = 6 = 5 Remainder 1
Therefore:
113 X 2 =231 in positive integral number base 5.
The number 0.0000012 in scientific notation is 1.2 x 10⁶ (the 6 should be negative as the decimal must move to the right.
Answer:
31.4
Step-by-step explanation:
So a really easy way to solve this is as goes
--> 3.14 x (20 x 1/2)
--> 3.14 x (10)
Now multipling by 10 is just moving the deciaml place one spot to the right
=> thus, we get 31.4
Hope this helps!
I'll do problem 1 to get you started.
The vertical sides are 3 and x for the left and right figures.
The horizontal sides are 15 and 60 for the left and right figures.
The corresponding sides form fractions which are equal (due to the nature of the similar polygons)
3/x = 15/60
3*60 = x*15 ... cross multiply
180 = 15x
15x = 180
x = 180/15 .... divide both sides by 15
x = 12
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Another way you can see this is note how the jump from 15 to 60 is "times 4", so the jump from 3 to x must also be "times 4" to keep the same proportion
3 ---> x = 3*4 = 12
Or you could set up the proportion
60/15 = x/3
4 = x/3
x/3 = 4
x = 3*4
x = 12
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<h3>Final Answer: 12</h3>
