Answer:
x-intercept: 
y-intercept: 
Step-by-step explanation:
To find the x-intercept, substitute in 
for 
and solve for 
.
Simplify 2(0): 
Subtract 0 - 3 = -3: 
Subtract 7 from both sides: 
Simplify: 
Divide both sides by -4 
To find the y-intercept, substitute in for and solve for .
Switch sides: 
Simplify -4(0): 
Add 3 to both sides: 
Simplify: 
Divide both sides by 2: 
-- He must have at least one of each color in the case, so the first 3 of the 5 marbles in the case are blue-green-black.
Now the rest of the collection consists of
4 blue
4 green
2 black
and there's space for 2 more marbles in the case.
So the question really asks: "In how many ways can 2 marbles
be selected from 4 blue ones, 4 green ones, and 2 black ones ?"
-- Well, there are 10 marbles all together.
So the first one chosen can be any one of the 10,
and for each of those,
the second one can be any one of the remaining 9 .
Total number of ways to pick 2 out of the 10 = (10 x 9) = 90 ways.
-- BUT ... there are not nearly that many different combinations
to wind up with in the case.
The first of the two picks can be any one of the 3 colors,
and for each of those,
the second pick can also be any one of the 3 colors.
So there are actually only 9 distinguishable ways (ways that
you can tell apart) to pick the last two marbles.
The method of factorization is used to find the roots of a given polynomial. Roots are the solutions of the function. Graphically, these roots are where the curve passes the x-axis. The first step to do is to find the common factor of the equation. That would be x. So you place it outside of the parenthesis.
x³-4x²+45x = x(x² - 4x + 45)
If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.
The final answer is x(x² - 4x + 45).
Answer:
Week 1: 10 Minutes
Week 10: 77.5 Minutes or 1 hour and 17.5 Minutes
Week n: 10 + 7.5n
Step-by-step explanation:
Every week, Greg adds another 7.5 minutes to his workout time. Week 1 starts off with 10 minutes and continuously adds 7.5 minutes until he gets to week three, which 10 + 7.5(2) = 25 minutes.
Answer:
Complementary angles
Step-by-step explanation:
The sum of the 2 angles = 27° + 63° = 90°
This is the definition of Complementary angles
