2a+3=s
I used the first letter of the name, or you can use x and y in place of a and s
Answer:
5 2/5
Step-by-step explanation:
(2 1/4) / x = (1 1/2) / (3 3/5)
so
x = (2 1/4) * (3 3/5) / (1 1/2)
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
Points on given line = (-12,-2) and (0,-4) because you can see them on the graph. Then draw a parallel line thru (0,6)
To get from (0,-4) to (0,6) your x stays constant and your y coordinate increased by 10. So your new point will do the same in relation to (-12,-2) the x will stay constant at -12 and your y will increase by 10 to +8.
So the answer is A (-12,8)
You can check this because parallel lines have the same slope so
y2-y1/x2-x1 should be equal for both lines.
Line 1: -4 - (-2) / 0 - (-12) = -2/12 = -1/6
Line 2: 6 - 8 / 0 - (-12) = -2/12 = -1/6
To answer this, you need to know the general form of an absolute value function. the equation for this is f(x<span>) = </span>a|x<span> - </span>h<span>| + </span>k, and in this equation, the vertex is (h, k).
with that information, you can see that your vertex will be (-5, 7). you must take the negative for 5 because the general equation states that your h value is usually subtracted from x. to check your vertex, try plugging it into your general equation:
f(x) = a|x - (-5)| + 7
f(x) = a|x + 5| + 7 ... you see that this matches your given equation. this last part here was just to show why your 5 must be negative; your answer is bolded.
