Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
_____
A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
_____
<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
The Perimeter = the distance around the frame. Therefore P=w+w+l+l
or P= 2w+2l
We are given l=15 1/4 and P= 50 2/4
Therefore 50 2/4 = 2w + 2(15 1/4)
50 2/4 = 2w + 30 2/4
Solve for w:
50 2/4 - 30 2/4 = 2w + 30 2/4 - 30 2/4
20 = 2w
20/2 = 2w/2
10 = w
In this problem, the dependent variable is the time or the year while the independent variable is the percent increase of donations. We try to plot these data through the years (percent increase vs year) in MS Excel and then obtain the trendline equation. Attached is the graph drawn from the data provided. According to the software, the equation applicable to this data is y = 5.2x - 10129 in which R² = 1. This means the relationship between the two variables is linear and perfect. The slope is positive which means that as the year goes on, the percent increase in donations also increases.
Answer:
The linear model of her monthly earnings is; Y =1200 +0.03*X. The amount earned is 1350; choice A
Step-by-step explanation:
Let Y denote her monthly earnings and X her total sales. The linear model can thus be formulated as; Y =1200 +0.03*X. We are then to find the value of Y given X =5000. We simply substitute X =5000 into the linear model which yields; Y =1350
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
<span>Instead of k, k+1, k+2, you should use k, k+2, k+4 with the constraint that k is even (i.e. if you return an odd integer for k, or a non-integer, then return no solution).
</span><span>k + (k+2) + (k+4) = 4k
</span><span>3k + 6 = 4k
k = 6
</span><span>Indeed, 6+8+10 = 4*6.</span>