Answer:
a) b = 8, c = 13
b) The equation of graph B is y = -x² + 3
Step-by-step explanation:
* Let us talk about the transformation
- If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then the new function g(x) = f(x + h)
In the given question
∵ y = x² - 3
∵ The graph is translated 4 units to the left
→ That means substitute x by x + 4 as 4th rule above
∴ y = (x + 4)² - 3
→ Solve the bracket to put it in the form of y = ax² + bx + c
∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)
∴ (x + 4)² = x² + 4x + 4x + 16
→ Add the like terms
∴ (x + 4)² = x² + 8x + 16
→ Substitute it in the y above
∴ y = x² + 8x + 16 - 3
→ Add the like terms
∴ y = x² + 8x + 13
∴ b = 8 and c = 13
a) b = 8, c = 13
∵ The graph A is reflected in the x-axis
→ That means y will change to -y as 1st rule above
∴ -y = (x² - 3)
→ Multiply both sides by -1 to make y positive
∴ y = -(x² - 3)
→ Multiply the bracket by the negative sign
∴ y = -x² + 3
b) The equation of graph B is y = -x² + 3
Answer:
Did the question get cut off?
a = -(1/5)
b = 1
c = 0
Step-by-step explanation:
y = x/5 may be rewritten as y = (1/5)x
y = (1/5)x
y - (1/5)x = 0
- (1/5)x + y + 0 = 0
ax + by + c = 0
a = -(1/5)
b = 1
c = 0
Answer:
7x+1
Step-by-step explanation:
Let's simplify step-by-step.
4x−5+3x+6
=4x+−5+3x+6
Combine Like Terms:
=4x+−5+3x+6
=(4x+3x)+(−5+6)
=7x+1
Hope this helps!
Answer:
25 wooden boards
Step-by-step explanation:
Given that:
Width of wooden board = 6 inches
Number of boards required to build a fence of 150 inches long if there are no gaps :
The lenght of fence / width of wooden board
= 150 inches / 6 inches
= 25 wooden boards
2x + y = 1
2x - 2x + y = 1 - 2x
y = 1 - 2x
y = -2x + 1
4x + 2y = -1
4x + 2(-2x + 1) = -1
4x + 2(-2x) + 2(1) = -1
4x - 4x + 2 = -1
2 ≠ -1
The solution of the problem can't be a solution because they are both parallel lines, which means they have no solution.
