A line has this equation: y=-3x+7
1 answer:
Given:
The equation of line is .
A line is parallel to given equation and passes through the point (-4,-8).
To find:
The equation of parallel line.
Solution:
The equation of a line is
On comparing this equation with , we get
So, slope of given line is -3.
We know that, slopes of parallel lines are equal. It means, the slope of the parallel line is also -3.
The parallel line passes through (-4,-8) and having slope -3. So, the equation of line is
Therefore, the equation of parallel line is .
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Answer: y = -3(x + )² +
,
,
<u>Step-by-step explanation:</u>
First, you need to complete the square:
y = -3x² - 5x + 1
<u> -1 </u> <u> -1 </u>
y - 1 = -3x² - 5x
y - 1 = -3(x² +
y - 1 + -3() = -3(x² +
+
)
↑ ↓ ↑
=
y - 1 - = -3(x +
)²
y - -
= -3(x +
)²
y - = -3(x +
)²
y = -3(x + )² +
Now, it is in the form of y = a(x - h)² + k <em>where (h, k) is the vertex</em>
Vertex = ,
Answer:
132 mm^2
Step-by-step explanation:
The line added to the figure in the attachment shows it can be divided into two figures whose area is easily calculated.
1. A parallelogram of base length 20 mm and height 4 mm:
A = bh = (20 mm)(4 mm) = 80 mm^2
2. A trapezoid with bases 32 mm and 20 mm, and height 2 mm:
A = (1/2)(b1 +b2)h = (1/2)(32 mm +20 mm)(2 mm) = 52 mm^2
The total area of the figure is then ...
80 mm^2 +52 mm^2 = 132 mm^2
