Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
Answer:
Ratio 2:3 I think :)
Step-by-step explanation:
To simplify this, you would have to turn b^-2 into a positive exponent.
To do this, we have to flip b^-2, which would get rid of the negate from the exponent: -2
3a^4 b^-2 c^3 / b^-2
Then we get the answer:
3a^4 c^3
------------
b^-2
I have a picture to clarify!
I hope this helped, let me know if you don't understand! ^.^
D
An acute angle is less than 90 degrees
Answer:
The boat traveling at 24 kph when John goes downstream.
Step-by-step explanation:
We are given the following in the question:
John has a boat that will travel at the rate of 15 kph in still water.
Let x be the speed of the current.
Speed of boat in upstream
Speed of water in downstream
Relation:
We have to find the speed of boat in downstream.
Time to travel upstream for 35 km = Time to travel 140 km downstream
Thus, speed of current is 9 kph.
Speed of boat in downstream = 15 + 9 = 24 kph.
Thus, the boat traveling at 24 kph when John goes downstream.