(x + 2)² - 10 = 0 (assuming it's equal to zero)
Expand the binomial: (x + y)² = x² + 2xy + y²
Thus, x² + 4x + 4 - 10 = 0
x² + 4x - 6 = 0
(by quadratic formula)
, since we're taking the positive solution.
Answer:
242
Step-by-step explanation:
Here, we want to calculate t15 + t25
Mathematically, nth term is
a + (n-1)d
here, a = 26 and d = 31-26 = 5
t15 = 26 + (15-1)5
t15 = 26 + 70
t15 = 96
t25 = 26 + (25-1)5
t25 = 26 + 120
t25 = 146
t15 + t25 = 96 + 146 = 242
Answer:
x = 4
y = 3
Step-by-step explanation:
2x - 3(x - 1) = -1
2x - 3x + 3 = -1
-x + 3 = -1
- 3 - 3
(-1) -x = -4 (-1)
x = 4
y = 4 - 1
y = 3
Answer:
A. & D.
Step-by-step explanation:
A. 8x + x = 9x
B. 9x + x = 10x
C. 10 - x = 10 - x (not like terms)
D. 5x + x + 3x = 9x
E. 7x + x + 2x = 10x
The general form for a sine function is
y = A*sin(B(x-C)) + D
where,
- |A| = amplitude
- B = 2pi/T, with T being the period, so T = 2pi/B
- C = phase shift
- D = midline
Put another way,
- A affects how vertically tall the sine graph is
- B tells when the graph will repeat itself, or how long one cycle is
- C determines the left and right shift of the graph
- D determines the up and down shift of the graph
For example,
y = 3sin(2(x-5)) + 10
has
- A = 3, so the amplitude is |A| = |3| = 3, meaning the original parent function has been vertically stretched by a factor of 3.
- B = 2 which leads to T = 2pi/B = 2pi/2 = pi as the period. The period is half as much as the parent function's period of 2pi radians, so the graph is horizontally compressed by a factor of 2.
- C = 5 is the phase shift telling us to move the parent function 5 units to the right
- D = 10 tells us to move the parent function 10 units up
The same basic idea applies to cosine graphs as well because cosine is a cofunction of sine.
