Did somebody say you're supposed to draw the graph of the equation ?
Is that the assignment ?
OK. Just like every other equation you need to graph, get it in the
standard form, where 'y' is all alone on one side, and everything else
is on the other side. When you do that, you'll be able to spot the slope
and y-intercept of the line, or get some points, or whatever you want.
4y + 12 = 0
Subtract 12 from each side: 4y = -12
Divide each side by 4: y = -3
There's the equation you can handle.
The y-intercept is -3, and the slope is zero.
Would you like some points ? OK. Pick a couple of values for 'x',
and calculate the value of 'y' for each one:
The first value I picked for 'x': x = 72
The equation is y=-3, so when x=72, y=-3. The point is (72, -3)
The second value I picked for 'x' is: x = 1
The equation is y=-3, so when x=1, y=-3. The second point is (1, -3).
The third value I picked for 'x' is 4 billion.
The equation is y=-3, so when x=4 billion, y=-3. The third point is (1, -3).
Do you see what's going on here ? Your original equation didn't even
have 'x' in it, so we could tell right away that when the graph is drawn,
the value of 'y' at every point can't depend on 'x'.
When we simplified the equation and got it in standard form, we found that
the slope of the graph is zero. That means the graph doesn't rise or fall ...
it's just a horizontal line. Sure enough, the height of points on the line
doesn't depend on 'x'. The value of 'y' at every point on the line is -3 .
Answer: graph A (see picture attached)This question is about understanding how a piecewise function works and the intervals in which it is defined. Indeed, all the graphs are similar, the only difference is the extremities (full or empty dots).
We know:
20 $/h = regular wage
x = number of hours worked
5 $/h = extra wage
We can say that Jack's regular wage can be defined by the function:
y₁ = 20 · x
if 5 < x < 8
(later we will consider if the extremities of the interval are included or not)
We can also say that Jack's wage if he works overtime, can be defined by the function:
y₂ = 5 · (x - 8) + 160
if 8 < x < 14
where:
(x - 8) takes into account that the first 8 hours worked are paid with the regular wage,
160 is the regular wage earned in 8 hours.
We now need to understand what happens in the extremities of the intervals:
- Jack can work only 5 hours (not less), therefore 5 is included;
- Jack can work 14 hours (not more), therefore 14 is included;
- if Jack works exactly 8 hours, he gets paid according to the regular wage; this means that 8 is included in the first interval and excluded in the second one.
Hence, we need to look for the graph representing the intervals:
5 ≤ x ≤ 88 < x ≤ 14Remembering that an included extremity is represented by a full dot, while an excluded extremity is represented by an empty dot,
the correct graph is option A).
Answer:
B. 5/6
Answer explained:
Prime numbers include 2, 3, and 5 and all numbers after 3 are 4, 5, 6 so 5 out of 6 or 5/6
Answer:
Step-by-step explanation:
To find the value of x, using Pythagorean theorem.
x² = 6² + 4²
= 36 + 16
= 52
= 2*2*13
x = √2*2*13
x = 2√13
Step-by-step explanation:
Decrease in price = $50 - $20 = $30.
Percent of decrease = ($30/$50) * 100% = 60%. (A)