Answer:
The exponential equation is y = -2×(1/2)^x
Step-by-step explanation:
Ok we have a couple things to note here:
1) The horizontal asymptote of the function is the x axis (always nice)
2) At x=0, y=-2 (i.e, this function will be multiplied by -2 bc the exponent part will transform into one at x=0)
3) Then we need to ascertain the base of the exponential. Based on the facts that at x=1, y=-1 and the "a-value" is -2, we can set up an equation to find b:
y=a×b^x----> -1 = (-2)(b) ------> b=1/2
Therefore, the exponential equation is y = -2×(1/2)^x
Test:
At x = 0, y= -2
At x = -1, y = (-2)*(1/2)^-1 = (-2)*2 = -4
At x=2, y = (-2)*(1/2)^2= (-2)*(1/4) = -1/2
Thus we can be quite certain that this is correct
To answer this you must know the rule for the slopes of perpendicular lines. the rule is that if 2 lines are perpendicular to each other, then their slopes are opposite reciprocal.
the word opposite means that if the slope of one is positive, then the other is negative. And vice versa.
the word reciprocal means that you divide 1 by whatever the slope is. So the reciprocal of x is 1/x.
so let's say we have a slope of -2 and what to find a line perpendicular. We need to find the opposite reciprocal. the opposite of -2 is 2. And the reciprocal of 2 is 1/2. So perpendicular line would have slope of 1/2
now to answer yours.
We know that y = mx + b, where m = slope and b = y intercept.
so:
y - 3 = 4 (x + 2)
y = 4x + 11
so m = 4. the slope is 4.
the opposite of 4 is - 4 and the reciprocal of - 4 is - 1/4. So that is out new slope of perpendicular line.
We know that given a point we can use:
(y - y1) = m (x - x1), where (x1, y1) is the given point
We are given point (- 5, 7) and we know m = - 1/4. so:
y - (7) = - 1/4(x - (- 5))
y - 7 = - 1/4(x + 5)
y - 7 =- 1/4x - 5/4
y = - 1/4x + 23/4
this should be equAtion. We can check by seeing if slopes are opposite reciprocal and by plugging in point.
- 1/4 is opposite reciprocal of 4.
plug in point
7 = - 1/4 (- 5) + 23/4
7 = 5/4 + 23/4
7 = 7
this is correct
The first one simplifies to 81a^4b
Sorry, I cannot solve the second one without placement of parentheses on the exponents
3/8 pencils do not have erasers at the end.
Hope this helps and please give brainliest!
Answer:
1) -6
2) 6
3) -6i
Step-by-step explanation:
tbese are your answer flw me
