Solve the inequality 2r^2-13x+15<0
2 answers:
Answer:
<u>Step-by-step explanation:</u>
First, factor the inequality and solve for x to find the zeros.
Then, choose test points on the outside of those values and between them.
Plug them in to determine which one(s) yield a negative (< 0).
2x² - 13x + 15 < 0
(2x - 3)(x - 5) < 0
2x - 3 = 0 and x - 5 = 0
x = 3/2 and x = 5
I choose the left test point of 0 (2(0) - 3) × (0 - 5) > 0 (+)
I choose the between test point of 2 (2(2) - 3) × (2 - 5) < 0 (-)
I choose the right test point of 6 (2(6) - 3) × (6 - 5) > 0 (+)
<u />
<u>Illustration of Graph:</u>
+ --- +
←----|----------o----------------|---------------o--------------|----→
0 3/2 2 5 6
Since the "between" test point is the only one that yielded a negative, then the solution is the values between 3/2 and 5.
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The length of the smaller leg is 3.79
<h3>How to determine the length of the smaller leg?</h3>Represent the smaller leg with x.
So, we have:
-- Pythagoras theorem
This gives
2x^2 = 144/5
Divide by 2
x^2 = 72/5
This gives
x^2 = 14.4
Take the square root
x = 3.79
Hence, the length of the smaller leg is 3.79
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Answer:
The line equation is given as: 3 y = 2 x - 9
Step-by-step explanation:
Here, Y intercept is at point ( 0.-3)
So, at x = 0, y = -3
or, C = -3
Also, the point on the equation line is (x,y) = (-9,-9)
Now, by <u>SLOPE INTERCEPT FORM</u> of a line equation,we get:
y = m x + C : m = slope of line ......... (1)
So, substituting the values of C and (x,y) , we get:
-9 = m (-9) + (-3)
or, -9 + 3 = - 9 m
or, m = -6/-9 = 2/3
or, m = 2/3
Now, substitute the value of m back in to the line equation (1)
Hence, the line equation is given as: 3 y = 2 x - 9.