Answer:
(f - g)(x) = x² - 3x - 70
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = x² - 2x - 63
g(x) = x + 7
(f - g)(x) is f(x) - g(x)
<u>Step 2: Find (f - g)(x)</u>
- Substitute: (f - g)(x) = x² - 2x - 63 - (x + 7)
- Distribute -1: (f - g)(x) = x² - 2x - 63 - x - 7
- Combine like terms (x): (f - g)(x) = x² - 3x - 63 - 7
- Combine like terms (Z): (f - g)(x) = x² - 3x - 70
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:
30 I N
Step-by-step explanation:
Answer:
3) 2.7
Step-by-step explanation:
The distance between two points
and
can be determined by:

Since the points are X(1, 2) and Y(6, 7). The distance between the two points is

the x value for the point located 1/3 the distance from X to Y,

The x value = 
Answer:
Solution given:
Volume of cone=⅓πr²h
Volume of cylinder=πr²h
1.
volume =πr²h=π*(10/2)²*6=<u>471.23mm³</u>
2.
Volume =πr²h=π*8*12.5=<u>314.16in³</u>
3.
volume =⅓πr²h=⅓*π*4²*3=<u>5</u><u>0</u><u>.</u><u>2</u><u>6</u><u>c</u><u>m</u><u>³</u>
4.
Volume =⅓πr²h=⅓*π*(8/2)²*12=<u>2</u><u>0</u><u>1</u><u>.</u><u>0</u><u>6</u><u>i</u><u>n</u><u>³</u>