Answer:
The solution is:
Step-by-step explanation:
The first step to solve this equation is placing everything with the exponential to one side of the equality, and everything without the exponential to the other side. So
To find x, we have to apply log to both sides of the equality.
We also have that:
So
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum
can be written as:
,
<span>
from the binomial expansion formula: </span>
.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>
.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression
, which is equivalent to
, takes it smallest value.
Substituting, we would find
=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
Answer:
27.05 miles per gallon
Step-by-step explanation:
384.1 miles = 14.2 gallons
x = 1 gallon
14.2x = 384.1
x = 384.1/14.2
= 27.0492958
≈ 27.05 miles per gallon
Answer:
36.46 inches
Step-by-step explanation:
The tangent of the angle is the ratio of the height to the base length:
Tan = Opposite/Adjacent
tan(25°) = (17 in)/(base)
base = (17 in)/tan(25°) ≈ 36.46 in
The base of the ramp is about 36.46 inches long.
Additive inverses are numbers that add up to zero, such as 1 and -1. Z is the additive inverse of -1/9, so z is 1.9.
1.9 + -1.9 =0.
Drag the -1.9 icon to just one mark to the right of -2 on the number line, since each dash equals 0.1. Drag z to just one mark to the left of 2 on the number line.The sum will be zero, so drag the sum icon to 0 on the number line.
