Answer:
d.
Step-by-step explanation:
The goal of course is to solve for x. Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions. We have to get them out of that position. The way we do that is by taking the natural log of both sides. The power rule then says we can move the exponents down in front.
becomes, after following the power rule:
x ln(2) = (x + 1) ln(3). We will distribute on the right side to get
x ln(2) = x ln(3) + 1 ln(3). The goal is to solve for x, so we will get both of them on the same side:
x ln(2) - x ln(3) = ln(3). We can now factor out the common x on the left to get:
x(ln2 - ln3) = ln3. The rule that "undoes" that division is the quotient rule backwards. Before that was a subtraction problem it was a division, so we put it back that way and get:
. We can factor out the ln from the left to simplify a bit:
. Divide both sides by ln(2/3) to get the x all alone:

On your calculator, you will find that this is approximately -2.709
Answer:
a)
is a solution of the linear equation.
b) The rate of change of the equation is 3.
c) The y-intercept of the equation is -2.
d) <em>Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?</em>
Step-by-step explanation:
a) If
is a solution of the linear equation, then
. If
, then the function evaluated at this value is:


Hence,
is a solution of the linear equation.
b) The rate of change of the equation is represented by the slope of the function, which is the constant that multiplies the indepedent variable (
). Hence, the rate of change of the equation is 3.
c) The y-intercept of the equation is the only constant of the equation. Hence, the y-intercept of the equation is -2.
d) A real-world scenario would be the following: <em>Jayne is working in the grocery one day, according to her calculations, renting the lot costs 2 dollars per day and she could earn 3 dollars per hour by selling pastries. How much money does she earn after working 8 hours?</em>
Answer:
so
equals 2x2x2x2x2x2x2x2
Step-by-step explanation:
Its that because when expanding Exponents, you always put the first number of the exponet first. like for example,
, you put the three 2 times and multiply. 3x3
Answer:
1/6
Step-by-step explanation:
LCD = 96
2(32) - 16(3)/ 3(32) = 64 - 48/96
= 16/96
Simplify:
16/ 16 = 1
96/16 = 6
2/3 - 16/32 = 1/6
Sorry if my work might seem confusing. If it is, then try searching "fraction calculator." It really helps :)
Answer:
Distance of foot of ladder from building: <em>37.2 inches
</em>
Distance of top of ladder from building's base: <em>114 inches
</em>
Step-by-step explanation:
Please refer to the figure attached in the answer area.
A right angled triangle
is formed by the ladder with the building where hypotenuse is the length of ladder.
Hypotenuse, <em>AC </em>= <em>10 foot
</em>
Also, we are given that angle made by the base of ladder with the ground is
.
We have to find <em>AB</em> and <em>BC</em>.

Using trigonometric functions:


Distance of foot of ladder from building: <em>37.2 inches
</em>
Distance of top of ladder from building's base: <em>114 inches
</em>