Using the points (0,14) and (10,0), the gradient of the line is (14-0)/(0-5) which simplifies to -7/5.
From these points, we can also see that when the x value is zero, the y value is 14. Therefore the y-intercept is 14.
We can then put this into the equation of a straight line, y=mx+c:
y = (-7/5)x + 14
Answer:
"all real numbers"
Step-by-step explanation:
This is an exponential function. The domain of the basic exponential function 3^x is "all real numbers." This domain also applies to f(x) = 3^x - 2.
Answer:
Good
Step-by-step explanation:
How has been your day?
Answer:
The first table.
Step-by-step explanation:
A slope of 0 means that as x increases, y stays the same. In the first table, all of our y-values are 2; this means that y stays constant.
To prove it, we use our formula for slope:
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The slope of the line between the first two points is
(2-2)/(-3--1) = 0/-2 = 0
The slope of the line between the second pair of points is
(2-2)/(-1-1) = 0/-2 = 0
The slope of the line between the next pair of points is
(2-2)/(1-3) = 0/-2 = 0
Since the slope between each pair of points is 0, the slope of the entire line is 0.
Answer:
see explanation
Step-by-step explanation:
To find the zeros let p(x) = 0 , that is
(x² - 1)(x² - 5x + 6) = 0
Factorise each factor
x² - 1 ← is a difference of squares and factors as (x - 1)(x + 1)
x² - 5x + 6 = (x - 2)(x - 3), thus
(x - 1)(x + 1)(x - 2)(x - 3) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x + 1 = 0 ⇒ x = - 1
x - 2 = 0 ⇒ x = 2
x - 3 = 0 ⇒ x = 3
The zeros are x = ± 1, x = 2, x = 3