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:
The correct system of inequalities is:
Step-by-step explanation:
Since Samantha wants to buy at least 5 pieces of clothing, this means that the total of clothing she buys can be 5 or more, then the sum of sweaters and dress pants she have to buy is:
She can't spend more than the gift card, this means that the number of clothing pieces she buys multiplied by its cost must be less or equal to the card's value, so she has to spend:
Therefore the correct system of inequalities is:
Answer:
18°
Step-by-step explanation:
Find the diagram attached
From the diagram, since the opposite side are parallel, the sum of the adjacent angle is 180 degrees
From the diagram, m<RQP + m<QPO = 180
Given
m<RQP = 6x+9
m<QPO = 63
Substitute
6x+9+63 = 180
6x + 72 = 180
6x = 180 - 72
6x = 108
x = 108/6
x = 18 degrees
Hence the value of x is 18°
<span>1.) f(x)=x+1/5 is already in that form
</span>2.) f(x)=3/2x-1/2
