A group of 50 people were asked their gender and if they liked cats. The data from the survey are shown in the Venn diagram. Det
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Answer:
Triangles represented by option B are similar triangles.
Step-by-step explanation:
Please find the attachment.
We have been given 4 group of triangles and we are asked to find which group contains similar triangles.
A. We can see from our diagram that triangles provided in option A are not similar.
The first triangle is an isosceles right triangle as it has 2 angles each having measure 45 degrees. By angle sum property the measure of 3rd angle will be:
The second triangle is an equilateral triangle as all the sides equal to 7 units, so all angles will be equal to 60 degrees.
The 3rd triangle is an isosceles triangle as it has 2 angles each having measure 53 degrees. By angle sum property the measure of 3rd angle will be:
We can see that none of the triangles have same angle measures, therefore, option A is not a correct choice.
B. The triangles provided in option B are similar triangles as each triangle have one right angle and they are sharing the same vertex.
Let us assume that the common vertex has x degrees angle, then by angle sum property the measure of 3rd angle in each triangle will be degrees. Therefore, the triangles provided in option B are similar triangles by AAA similarity theorem.
C. The triangles provided in option C are not similar triangles as we are not told that the given lines are parallel or not. In addition the bottom figure is a quadrilateral as it has 4 angles, Therefore, the given triangles are not similar triangles.
D. We can see that our given triangles have vertical angles, so their measure will be 32 degrees. Since the given side lengths are different, therefore, this group of triangles is not similar.
<h3>Answer: (a - 1)(2a² + a + 2)</h3>
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Explanation:
Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2
Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.
If we tried say a = -1, then,
2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6
The result is not zero, so a = -1 is not an actual root.
But if we tried say a = 1, then,
2a³-a²+a-2 = 2(1)³-1²+1-2 = 0
We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.
Since a = 1 is a root, this makes (a-1) to be a factor.
From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.
Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.