Answer: green shirts = 6
Blue shirts = 11
Yellow shirts = 4
Red shirts = 7
Step-by-step explanation:
Red shirts = 7
Let green shirts be x.
There are 5 more blue shirts than green shirts. This means:
Blue shirts = x + 5
There are 2 fewer yellow shirts than green shirts. This means:
Yellow shirts = x - 2
There are 28 shirts in total
Red + blue + yellow + green = 28
7 + (x + 5) + (x - 2) + x = 28
7 + x + 5 + x - 2 + x = 28
10 + 3x = 28
3x = 28 - 10
3x = 18
x = 18/3
x = 6
There are 6 green shirts
Blue shirts = x + 5 = 6 + 5 = 11
Yellow shirts = x - 2 = 6 - 2 = 4
Red shirts = 7
40 % out of 80 for red
20% out of 80 for blue
The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
