The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.
<h3>Equation</h3>
- Number of boxes renita has unpacked = x
- Number of boxes Vanessa has unpacked = 2x - 3
- Total boxes both unpacked = 15
x + (2x - 3) = 15
x + 2x - 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
Therefore,
Number of boxes renita has unpacked = x
= 6 boxes
Number of boxes Vanessa has unpacked = 2x - 3
= 2(6) - 3
= 12 - 3
= 9 boxes
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The value of k is (A) 20/3.
<h3>
What is a parabola?</h3>
- A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics.
- It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
- A point and a line are two ways to describe a parabola.
To find the value of k:
Where (a, b) is the vertex and c is the constant.
- (a, b) = (-4, k)
- y - k = c (x - (- 4))²
- y - k = c (x + 4)²
So,
- x = 0, y = 12
- 12 - k = 16c
- k = 12 - 16c ...... (1)
Then,
- (-3, 7) = (x, y)
- 7 - k = c (1)²
- k = 7 - c ...... (2)
Now,
- 12 - 16c = 7 - c
- 12 - 7 = 16c - c
- 5 = 15c
- c = 5/15 = 1/3
So, the value of k:
- k = 12 - 16 (1/3) = 12 - 16/3 = 36-16/3 = 20/3
Therefore, the value of k is (A) 20/3.
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The complete question is given below:
The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?
(A) 20/3
(B) 16/5
(C) 14/3
(D) 12/5
Answer:
c. 69
b. 7
Step-by-step explanation:
It's an expression that can be simplified to read
( 0.7 x 0.4 ) ( b³ x b⁹ )
= ( 0.28 ) ( b¹² ) = 0.28 b¹² .
