B.
Let's simply look at each conjecture and determine if it's true or false.
A. 2n– 1 is odd if n is positive: Since n is an integer, 2n will
always be even. And an even number minus 1 is always odd. Doesn't matter
if n is positive or not. So this conjecture is true.
B. 2n– 1 is always even: Once again, 2n will always be even. So 2n-1 will always be odd. This conjecture is false.
C. 2n– 1 is odd if n is even: 2n is always even, so 2n-1 will always
be odd, regardless of what n is. So this conjecture is true.
D. 2n– 1 is always odd: 2n will always be even. So 2n-1 will always be odd. Once again, this conjecture is true.
Of the 4 conjectures above, only conjecture B is false. So the answer is B.
Special cases of the sum and difference formulas for sine and cosine yields what is known as the double‐angle identities and the half‐angle identities.
All sides are the same, hence, all three angles are the same, and each one of them is 60 degrees. Due to that:
7x + 4 = 60
7x = 56
x = 56/7 = 8
8y + 12 = 60
8y = 48
y = 48/8 = 6
Answer:
y = -2x + 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
The slope of the line, m, is -2 because the line shows a negative trend and moves right 1 unit every time a point moves down 2 units.
The y-intercept, b, is 5 because the line crosses that number once on the y-axis.
You can substitute what y is into the second equation, so:
3x + 4(2x + 1) = 26
3x + 8x + 4 = 26
11x + 4 = 26
- 4
11x = 22
÷ 11
x = 2
y = (2 × 2) + 1
y = 5 + 1
y = 5
So you get x as 2 and y as 5, I hope this helps!
