20/01/2020 04:43 PM
If y is a function of x, then the equation would be written as a "y =" equation, not an "x = " equation. This example is one where x is a function of y.
Given : The number of granola bars = 6
The number of pieces of dried fruit = 10
If the snack bags should be identical without any food left over, then the greatest number of snack bags Emily can make is the greatest common factor (GCF) of 6 and 10.
Since , factors of 6 = 1, 2, 3, 6
Factors of 10 = 1, 2, 5, 10
Hence, the greatest common factor of 6 and 10 = 2
Thus, the greatest number of snack bags Emily can make = 2.
Equation of ellipse is of form where are the x-intercepts and are the y-intercepts . If then it is a horizontal ellipse and if then it is a vertical ellipse .
For horizontal axis ,
Here, are known as the vertices of ellipse and are the co-vertices of ellipse .
Horizontal axis is known as the major axis and vertical axis is known as the minor axis .
Here, x-intercepts are , take a = 5
y-intercepts are , take b = 3
As , it is a horizontal ellipse .
On putting a = 5 and b = 3 , we get equation as
x = - 5, x = - 1
To find the x- intercepts let f(x) = 0, that is
x² + 6x + 5 = 0 ← in standard form
Consider the factors of the constant term (+ 5) which sum to give the coefficient of the x- term ( + 6)
The factors are + 5 and + 1, since
5 × 1 = 5 and 5 + 1 = + 6, hence
(x + 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 )
x + 1 = 0 ⇒ x = - 1 ⇒ (- 1, 0)
Either or , depending on whether is larger than .
The two roots (might necessarily be distinct or real) of the quadratic equation
, where , , and are constants and are
The difference between the two will be either:
For this question,
A - the sum of the numbers is 5
The slope-intercept form of an equation of a line:
m - slope
b - y-intercept → (0, b).
The formula of a slope:
We have the points A(0, -4) → b = -4 and B(6, 2).
Calculate the slope:
Put the value of m and of b to the equation:
add 4 to both sides
x^2 - x - 12 = (x + 3)(x - 4)
p = 3, q = -4
The Cartesian equation is
This implies that
Let us evaluate the exponents to get:
Factor the RHS to get:
Divide through by r²
Apply the double angle identity
The polar equation then becomes: