Answer:
option 2
4/7
Step-by-step explanation:
Multiply 4/3x3/7 = 12/21
now simplify 12/21 = 4/7
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:2/3
Step-by-step explanation:
Simplifying
(9m + -6) * 7 = 0
Reorder the terms:
(-6 + 9m) * 7 = 0
Reorder the terms for easier multiplication:
7(-6 + 9m) = 0
(-6 * 7 + 9m * 7) = 0
(-42 + 63m) = 0
Solving
-42 + 63m = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '42' to each side of the equation.
-42 + 42 + 63m = 0 + 42
Combine like terms: -42 + 42 = 0
0 + 63m = 0 + 42
63m = 0 + 42
Combine like terms: 0 + 42 = 42
63m = 42
Divide each side by '63'.
m = 0.6666666667
Simplifying
m = 0.6666666667=2/3 when simplified
Oliver is the runner in 1st place 16 meters ahead of Nick, who is the runner in the last place.
