7/10;1/3;5/6 ayuda es de matemáticas
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Answer:
see below for drawings and description
Step-by-step explanation:
For geometry problems involving translation, rotation, and reflection—transformations that change location, but not size ("rigid" transformations)—it might be helpful for you to trace the image onto tracing paper or clear plastic so that you can manipulate it in the desired way. Eventually, you'll be able to do this mentally, without the aid of a physical object to play with.
For the images attached here, I copied the triangle onto a piece of clear plastic so I could move it to the desired positions. The result was photographed for your pleasure.
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a. Translation means the image is moved without changing its orientation or dimensions. You are asked to copy the triangle so that the upper left vertex is moved to what is now point E. See the first attachment.
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b. Reflection means the points are copied to the same distance on the other side of the point or line of reflection. Just as an object held to a mirror has its reflection also at the mirror, any points on the line of reflection do not move. Reflection flips the image over. See the second attachment.
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c. Rotation about point D means point D stays where it is. The angle of rotation is the same as the angle at D, so the line DE gets rotated until it aligns with the line DF. The rest of the triangle maintains its shape. See the third attachment.
a. Find the graph of their common region in the attachment
b. The area of the common region of the graphs is 8 units²
<h3>a. How to sketch the region common to the graphs?</h3>Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.
- The graph of x ≥ 2 is the region right of the line x = 2.
- The graph of y ≥ 0 is the region above the line y = 0 or x-axis.
- To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.
So, the graph of x + y ≤ 6 is the region below the line y = - x + 6
From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)
Find the graph of their common region in the attachment
<h3>b. The area of the common region</h3>From the graph, we see that the common region is a right angled triangle with
- height = 4 units and
- base = 4 units
So, its area = 1/2 × height × base
= 1/2 × 4 units × 4 units
= 1/2 × 16 units²
= 8 units²
So, the area of the common region of the graphs is 8 units²
Learn more about region common to graphs here:
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Answer:
The probability that the sum of the dice is 3, is 3/16.
Step-by-step explanation:
It is given that two four-sided dice are rolled.
Total number of sides of each dice = 4
Possible values for each dice = 1,2,3,4
If two four-sided dice are rolled, then the total possible outcomes are
Total number of possible outcomes = 16
The sum of the dice is 3.
Total number of favorable outcomes = 3
The probability that the sum of the dice is 3.
Therefore the probability that the sum of the dice is 3, is 3/16.
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
