Answer:
Area = 81; Side Length = 3
Step-by-step explanation:
The area of a square is the side lenght squared, and 9² is 81.
The side lengh can be found by taking the square root of the area. √9 = 3
Answer:
hope this helps. Happy Holidays
Answer:
98 cats and 19 dogs
Step-by-step explanation:
cat = c
dog = d
The animal shelter currently has a total of 117 animals
c + d = 117
c = 117 - d
the number of cats is 3 more than 5 times the number of dogs
c = 3 + 5d
subtitute c
117 - d = 3 + 5d
117 - 3 = 5d + d
114 = 6d
6d = 114
d = 114/6 = 19
so, the cat is 117-19 = 98
Answer:
Question 6: -8
Question 7: C
Step-by-step explanation:
Question 6:
The reason question 6 is -8 is because of the distance in between each number, e.g -7 and -15. This is not to be confused with + 8 each time that would make the sequence 9, 18, 27.
Question 7:
The way we solve this question is using the nth term rule, whatever is before the n is the times tables we follow. So if it is 2n the sequence would be 2, 4, 6, 8 etc. However when we add something like the -2 we do the 2 times tables but this time we -2 for each one. Example: 2 - 2 = 0 so the first number of the sequence is 0, Example 2: 4-2 = 2 so the second number of the sequence is 2.
There are 2 possibilities for where A can be: one where C is 30° (and A is 60°) and another where C is 60° (and A is 30°). Since it's not specified, we can find both.
30°:
drawing the triangle on a graph, you can see that point C is 4 units above point B, so we know that one side of the triangle is 4. Once we find the other "leg" of the triangle (the one that's parallel to the x-axis), we can just add that value to B to find the x coordinate of A.
If angle C is 30°, using the side ratios of a 30-60-90 triangle, that side is "a√3", and the side we're looking for is a. So, to find a, we just divide 4 by √3. In that case, point A is 4/(√3) units to the right of -2√3. We can rationalize 4/(√3) like this:
(4√3)/3
and then add that to 2√3:
(4√3)/3 + -2√3
(4√3)/3 + (-6√3)/3 = (-2√3)/3
We know that the x-coordinate of A is (-2√3)/3, and the y-coordinate is -1 because B is a right angle and we're just moving horizontally. So, if C is 30° and A is 60°, point A is at ((-2√3)/3, -1).
60°:
in this case, the leg we know is "a" and the leg we're looking for is "a√3". So, we can multiply 4 by √3 to get the distance from B:
4 x √3 = 4√3
4√3 + -2√3 = 2√3
So the x-coordinate of A here is 2√3, and the y-coordinate is still -1: (2√3, -1).
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