Regroup to express the number differently.
1 answer:
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Answer:
x = 0,
Step-by-step explanation:
Factorise f(x) and equate to zero for x- intercepts
f(x) = - 5x(9x² - 12x + 4) = 0 ( common factor of - 5x )
To factor the quadratic consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is
product = 9 × 4 = 36 , sum = - 12
The factors are - 6 and - 6
Use these factors to split the middle term
9x² - 6x - 6x + 4 = 0 ( factor the first/second and third/fourth terms )
3x(3x - 2) - 2(3x - 2) ( factor out (3x - 2) )
(3x - 2)(3x - 2), hence
f(x) = - 5x(3x - 2)(3x - 2) = 0
equate each factor to zero and solve for x
- 5x = 0 ⇒ x = 0
(3x - 2)² = 0 ⇒ x = of multiplicity 2, indicating turning point
x - intercepts are x = 0,
Answer:
y = -0.85 + 0.09x; $49.82
Step-by-step explanation:
1. Calculate Σx, Σy, Σxy, and Σx²
The calculation is tedious but not difficult.
2. Calculate the coefficients in the regression equation
To two decimal places, the regression equation is
y = -0.85 + 0.09x
3. Prediction
If x = 563,
y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85 + 50.67 = $49.82
(If we don't round the regression equation to two decimal places, the predicted value is $50.56.)
Answer:
Option (1)
Step-by-step explanation:
Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)
Since ABCD is a square,
Perimeter of a square = 4 × (length of a side)
= 4 × (AB)
Formula to calculate the distance between two points and
is,
d =
Therefore, distance between two points A(-2, 1) and B(2, 7) will be,
AB =
AB =
AB =
AB =
Now area of square ABCD = 4 ×
= unit
Therefore, option (1) will be the answer.