Answer:
Step-by-step explanation:
Our inequality is |125-u| ≤ 30. Let's separate this into two. Assuming that (125-u) is positive, we have 125-u ≤ 30, and if we assume that it's negative, we'd have -(125-u)≤30, or u-125≤30.
Therefore, we now have two inequalities to solve for:
125-u ≤ 30
u-125≤30
For the first one, we can subtract 125 and add u to both sides, resulting in
0 ≤ u-95, or 95≤u. Therefore, that is our first inequality.
The second one can be figured out by adding 125 to both sides, so u ≤ 155.
Remember that we took these two inequalities from an absolute value -- as a result, they BOTH must be true in order for the original inequality to be true. Therefore,
u ≥ 95
and
u ≤ 155
combine to be
95 ≤ u ≤ 155, or the 4th option
Answer:
times
21.12
28
I will pay 11.20 and get back .20 for the half(.5) of a drink box I can't buy
Step-by-step explanation:
Answer:
a. y = -1/2x - 2
Step-by-step explanation:
The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.
__
<h3>slope</h3>
The x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...
m = rise/run = -2/4 = -1/2
In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.
__
<h3>equation</h3>
The slope-intercept equation is ...
y = mx +b . . . . . . . slope m, y-intercept b
We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...
y = -1/2x -2 . . . . . matches choice A
_____
<em>Additional comment</em>
When answering multiple-choice questions, you only need to do enough work to tell which answers are <em>not</em> viable.
When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.
Fractions are just unsimplified numbers. For example 5/8 is just 5 divided by 8 so 0.625. To find the percent from that you move the decimal two places to the right making it 62.5%. Hope this helps!
Answer:
The answer is "
"
Step-by-step explanation:
Given:

Find critical points:

differentiate the value with respect of x:
critical points
![\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3](https://tex.z-dn.net/?f=%5Cto%20%28x-e%29%5E2%20e%5E%7B%28e-x%29%7D%20%5Be%2B3-x%5D%3D0%5C%5C%5C%5C%5Cto%20e%5E%7B%28e-x%29%7D%5Cneq%200%20%5C%5C%5C%5C%5Cto%20%28x-e%29%5E2%3D0%5C%5C%5C%5C%20%5Cto%20%5Be%2B3-x%5D%3D0%5C%5C%5C%5C%5Cto%20x%3De%5C%5C%5C%5C%5Cto%20x%3De%2B3%5C%5C%5C%5C%5Cto%20x%3D%20e%2Ce%2B3)
So,
The critical points of 