Line L is mapped onto line m by a dilation centered at the origin with a scale factor of 2/5. Line m is represented by y=2x+10 a
2 answers:
Dilating a line changes the size of the line.
The true statement is <em>(c) Line L passes through the origin</em>
The scale of dilation is given as:
The scale represents the slope of line L.
The equation of line M is:
From the above equation, the slope of line M is:
The two lines do not have the same slope.
<em>This means that, the lines are not parallel and they are not the same line.</em>
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For the two lines to be perpendicular, then the relationship between their slopes is:
The above is false, because:
Hence, the true statement is <em>(c) Line L passes through the origin</em>
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Read more about dilations at:
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Answer:
Area = 230 cm
Step-by-step explanation:
We can split this shape into different parts: a rectangle and a triangle (I attached an image below as a visual aid).
The area of a rectangle is given as:
and the area of a triangle is given as:
Let's first solve for the area of the rectangle. The width of the rectangle is 20cm, and the height of the rectangle is 7cm. So, the area is 7 × 20 = 140cm.
Now, let's solve for the area of the triangle. The base of the triangle is 20 cm, and the height of the rectangle is 16 - 7 = 9cm. So, the area is = 90cm.
We add the two values together to get the combined area of the shape. 140 + 90 = 230 cm.
<h3>Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.