Answer:
y = 4(x+6)(x-2)
Step-by-step explanation:
y = 4x² + 16x - 48, factor out the 4
y = 4(x² + 4x - 12), find factors of 12
Factors of 12:
1*12, 2*6, 3*4; find a pair that sums to 4x or 4
6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4
y = 4(x+6)(x-2)
The Formula of the relation is M = 8AT.
The mass of the metal sheet is 960 g.
The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).
Proportionality:
Removing the proportionality sign,
Where:
- K = constant of proportionality.
make K the subject of the equation:
- K = M/KT.................... Equation 1
From the question,
Given:
- M = 200 g
- A = 250 cm²
- T = 1 mm = 0.1 cm
Susbtitute into equation 1
- K = 200/(250×0.1)
- K = 8 g/cm³
Formula:
- M = 8AT................. equation 2
Hence the formula of the relation is M = 8AT
If,
- A = 400 cm²
- T = 3 mm = 0.3
Substitute these values into equation 2
Hence, the mass of the metal sheet is 960 g
Learn more about joint variation here: brainly.com/question/26047253
Answer:
A) y = (x + 3)² + 4
B) y = (x - 3)² + 2
C) y = (x - 1)² - 5
Step-by-step explanation:
2 units UP means that the vertex will be shifted from (-3 , 2) to (-3, (2 + 2) or (-3, 4)
As the y = (x + 3)² will still be zero at x = -3, we just need to change the "+ 2" to
"+ 4" to shift the curve upward by 2
y = (x + 3)² + 4
When we want to shift the curve to the right, we want the vertex to move from (-3, 2) to (3, 2)
This means that the term in parenthesis must be zero with our desired x value
(3 + C)² = 0
3 + C = 0
C = -3
y = (x - 3)² + 2
4 units right and 7 units down mean that the vertex is desired at (1, -5)
(1 + C)² = 0
C = -1
y = (x - 1)² - 5
I assume you're looking for the number:
0.5n + 9 = 21
- 9
0.5n = 12
÷ 0.5
n = 24
So the beginning number is 24, hope this helps!