A bookstore with 18 copies of a book sold 5/6 of the books
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The width of the rectangle is unit
Step-by-step explanation:
The given is:
- A rectangles width is 4 less than its area
- Its length is 19 units
We need to find the width of the rectangle
Assume that the width of the rectangle is x units
∵ The area of the rectangle = length × width
∵ The width of the rectangle = x units
∵ The length of the rectangle = 19 units
∴ The area of the square = 19 × x = 19 x units²
∵ The width of the rectangle is 4 less than its area
- That means subtract 4 from the area to find the width
∴ x = 19 x - 4
- Subtract 19 x from both sides
∴ -18 x = -4
- Divide both sides by -18
∴ x =
- Reduce the fraction by dividing up and down by -2
∴ x =
The width of the rectangle is unit
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The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point
- a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
- k is the value of y when x = h
∵ y = x² + 16x - 7
∵ y = ax² + bx + c
∴ a = 1 , b = 16 , c = -7
∵
∴
∴ h = -8
To find k substitute y by k and x by -8 in the equation above
∵ k is the value of y when x = h
∵ h = -8
∴ k = (-8)² + 16(-8) - 7 = -71
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -71
∴ y = (1)(x - (-8))² + (-71)
∴ y = (x + 8)² - 71
∵ (h , k) are the coordinates of the vertex point
∵ h = -8 and k = -71
∴ The vertex is (-8 , -71)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
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