Answer: a is the # of elements in A but NOT B, that is A ONLY
b is the # of elements in B but NOT A, that is B only
N is the # of elements in the INTERSECTION of A and B
a + N = 99
b + N = 25
a + b + N = 123
Subtracting the first two equations: a - b = 74
Subtracting the last two equations: -a = -98
a = 98
So then a - b = 74 and a = 98
98 - b = 74
-b = -24
b = 24
a = 98, b = 24 and a + b + N = 123
98 + 24 + N = 123
122 + N = 123
N = 1
98 are in A only
24 are in B only , which is the answer to the question
1 is in both A and B
Step-by-step explanation:
Answer:
b part is the answer
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The given polynomial is f(x) = x² - 2x - 6
Rewrite the function by completing the square.
f(x) = [x² - 2x] - 6
= [(x-1)² - 1] - 6
= (x-1)² - 7
In vertex form,
f(x) = (x-1)² - 7
The vertex is located at (1, -7).
Because the leading coefficient is +1, the curve opens upward.
Answer: f(x) = (x - 1)² - 7
Answer: y = -6x -10
Step-by-step explanation:
The equation is y = mx + b
1. m is the slope so you can replace m with -6.
2. You are given a point, so you can replace variables x and y with the point. The equation should now look like this:
y = -6x + b
-4 = -6(-1) + b
3. Then multiply -6 and -1 to get 6. Now you are left with -4 = 6 + b
4. To solve for b you must get it alone. Right now B isn't alone because a 6 is being added to b. To get b alone you need to subtract 6. Now your equation should look like this: -4 - 6 = B
5. Get a calculator or use mental math and you will get B = -10.
6. Then plug b and m into y = mx + b, and you should get y = -6x - 10
