For each diagram, describe a translation, rotation, or reflection that takes line ℓ to line ℓ′. Then plot and label A′ and B′, t
he images of A and B.
1 answer:
Answer:
- translate down 3
- reflect across the horizontal line through A
Step-by-step explanation:
1. There are many transformations that will map a line to a parallel line. Translation either horizontally or vertically will do it. Reflection across a line halfway between them will do it, as will rotation 180° about any point on that midline.
In the first attachment, we have elected to translate the line down 3 units.
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2. Again, there are many transformations that could be used. Easiest is one that has point A as an invariant point, such as rotation CW or CCW about A, or reflection horizontally or vertically across a line through A.
Any center of rotation on a horizontal or vertical line through A can also be used for a rotation that maps one line to the other.
In the second attachment, we have elected to reflect the line across a horizontal line through A.
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Answer:
a.
Step-by-step explanation:
The given equation is;
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.
The corresponding function is
The solution to is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(3,0) and (6,0).
Therefore the real solutions are:
The sum of the equation is = 5494000.
<h3>What does summation mean in math?</h3>The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
<h3>Briefing:</h3>Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
<h3>Calculation according to the statement:</h3>simplifying them we get:
Split the summation into smaller summations that fit the summation rules.
The formula for the summation of a polynomial with degree 2
is:
Substitute the values into the formula and make sure to multiply by the front term.
we get: 5373400
Evaluating same as above :
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
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