The piece-wise linear functions can be written as follows:
.
.
.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:
.
For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:
.
For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:
m = (-3 - (-5))(3 - 2) = 2.
The rule is:
y = 2x + b.
When x = 2, y = -5, hence:
-5 = 2(2) + b
b = -9.
Hence:
.
More can be learned about linear functions at brainly.com/question/24808124
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X = 4.33333333333
y = 5.33333333333
z = 6.33333333333
If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.
<h3>What is a cylinder?</h3>
A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a height of 4 meters and a radius of 1.5 meters.
Then the approximate radius of a sphere that has the same surface area as the cylinder.
We know that the Surface area of the cylinder will be is given as
Surface area = 2πrh
Surface area = 2 x π x 1.5 x 4
Surface area = 12π square meters
Then we have
Surface area of sphere = surface area of cylinder
4πr² = 12π
r² = 3
r = 1.7 meters
More about the cylinder link is given below.
brainly.com/question/3692256
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Answer:
y - 7 = -2(x - 4)
Step-by-step explanation:
We are asked to write the equation of a line in point slope form
Step 1 : find slope
We are given the slope to be -2
Slope m = -2
Step 2: substitute m into point slope form
y - y_1 = m( x - x_1)
y - y_1 = -2 ( x - x _1)
Step 3: substitute the point into the equation
y - y_1 = -2( x - x _1)
( 4 , 7)
x_1 = 4
y_1 = 7
y - 7 = -2( x - 4)
We don't need to open the bracket because we are asked to write the equation in a point slope form
5 5/9
5 * 5/9
25/9
The correct answer is 25/9, as shown above.
