A. The
y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the
given table,
y - intercept
= 8
Since at
time zero the displacement is 8 ft, this means that the horse was already
outside the barn initially.
B. The
average rate of change of the function represents the slope of the linear
equation (m). This can be calculated using the formula:
average rate
of change = m = (y2 – y1) / (x2 – x1)
m = (158 –
58) / (3 – 1)
m = 50
<span>C. Since we have determine the y-intercept and
the slope, we can formulate the linear equation:</span>
y = m x + b
y = 50 x + 8
The domain
is the value of x. When y = 508, x is equivalent to
508 = 50 x +
8
<span>x = 10 hrs</span>
Answer:
210
Step-by-step explanation:
5 is a prime number, 6 = 2·3 and 7 is a prime number. Since those number do not have common factors, the least common multiple will be their product:5·6·7 = 210 . Given fractions are already in order from least to greatest.
<span>Y=-2x+1, y=-2/3x+5
X= -3 and Y =7</span>
A plane cuts horizontally across a rectangular pyramid will always be a rectangle. (Answer B)
Answer:
Step-by-step explanation:
If we have a linear function and we multiply the input of the function, we aren't really <em>changing</em> the values of the function, we're changing the rate at which those values are reached.
E.g. if you look at the attached picture, we have 
and 
, which is just 
. The value when the red line is x = 1 is half that of the value of the blue line when x = 1.
The values of the f(2x) line are reaching the values of f(x) twice as fast, meaning it has a slope of twice as much. However, it still grows through the same intercept.
If you're interested in the calculus behind this, look up the chain rule of derivatives.
However, when you start changing the output of the function, you're changing the entire equation. It's not the same line anymore.
