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We know that (-3,5) is the location of one of the endpoints.... and we know the midpoint is at (2,-6)... .now.. what's the distance between those two guys?
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 5}})\quad % (c,d) &({{ 2}}\quad ,&{{ -6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[2-(-3)]^2+[-6-5]^2}\implies d=\sqrt{(2+3)^2+(-6-5)^2} \\\\\\ d=\sqrt{5^2+(-11)^2}\implies d=\sqrt{25+121}\implies d=\sqrt{146}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-3%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%26%28%7B%7B%202%7D%7D%5Cquad%20%2C%26%7B%7B%20-6%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%5B2-%28-3%29%5D%5E2%2B%5B-6-5%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%282%2B3%29%5E2%2B%28-6-5%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B5%5E2%2B%28-11%29%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B25%2B121%7D%5Cimplies%20d%3D%5Csqrt%7B146%7D)
so, the distance "d" from the midpoint to that endpoint is that much. And the distance from the midpoint to the other endpoint is the same "d" distance, because the midpoint is half-way in between both endpoints.
so, the length of AB is twice that distance, or
Answer:
2, 3, 7
Step-by-step explanation:
Since you know your multiplication tables, you know that ...
42 = 6 × 7
and
6 = 2 × 3
The numbers 2, 3, and 7 are prime numbers (not further divisible). This list is in order least to greatest, so is the combination of the lock.
To get a certain percentage as a decimal, all you have to do is divide this percentage by 100.
Applying this on the given question, we will find that:
3.58% = (3.58) / (100) = 0.0358
Comparing the calculated value to the given choices, we will find that the correct choice is:
<span>c) 0.0358</span>
<span>Simplifying
3a + -2b = 5a + 6b
Solving
3a + -2b = 5a + 6b
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-5a' to each side of the equation.
3a + -5a + -2b = 5a + -5a + 6b
Combine like terms: 3a + -5a = -2a
-2a + -2b = 5a + -5a + 6b
Combine like terms: 5a + -5a = 0
-2a + -2b = 0 + 6b
-2a + -2b = 6b
Add '2b' to each side of the equation.
-2a + -2b + 2b = 6b + 2b
Combine like terms: -2b + 2b = 0
-2a + 0 = 6b + 2b
-2a = 6b + 2b
Combine like terms: 6b + 2b = 8b
-2a = 8b
Divide each side by '-2'.
a = -4b
Simplifying
a = -4b</span>
