Answer:
Part A - 
Part B - 
Step-by-step explanation:
Hey!To solve this problem, we need to set up two equations and use the system of equations to solve.
Let x be the first number.
Let y be the second number.
(x + y) ÷ 2 = 34
x = 3y
Now, we can use substitution to solve.
(3y + y) ÷ 2 = 34
4y ÷ 2 = 34
2y = 34
y = 17
Now, you plug the value of y in the equation to solve for x.
x = 3*17
x = 51
hope this helps!!
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
You are most likely to pick up a red because the quantity is more and a blue marble can be anywhere
Answer:
x=4
Step-by-step explanation:
4x - 3 = 2x + 5
4x - 2x = 5 + 3
2x = 8
x = 8/2
x = 4
