9514 1404 393
Answer:
k = 15
Step-by-step explanation:
Look for the missing factors that make all of the factors of 60k be squares.
60 = 2² × 3 × 5
The factors 3 and 5 each have an odd exponent (1), so those two factors must be part of k.
60k = 2² × 3 × 5 × k
is a perfect square when ...
3 × 5 = k = 15
For k = 15, 60k = 900 = 30²
Answer:
x = 5 and x = -19
Step-by-step explanation:
You're on the right track. It's the "discriminant" that tells you what you want to know here. Before starting, arrange the terms of your quadratic in descending orders of x: 5x^2 + 14x - 19 = 0 (Note that I assumed you meant 14x instead of just 14).
Then the coefficients of this quadratic are a = 5, b = 14 and c = -19.
You are referring to the "quadratic formula." It states this:
-b ± √(b²-4ac)
x = -----------------------
2a
So, we insert the a, b and c values as indicated above:
-14 ± √( 14² - 4[5][-19] ) -14 ± √(196 - 4[5][-19] ) -14 ± √576
x = ----------------------------------- = ---------------------------------- = ----------------------
2(10) 20 20
This comes out to:
x = (-14 + 24) / 2 and x = (-14 - 24) / 2
or:
x = 5 and x = -19
Answer:
The spinner is 4 times more likely to land on black.
There were 72 black spins compared to 18 white spins. This means there were 4 times more black spins than white spins; this means the spinner is not equally likely to land on either co
2(10)+5 = 25. The answer is A
