Answer:
No, it is D.
Step-by-step explanation:
<em>It can not be A or C, because length can not be negative</em>
Because the y is the same, you only have to <em>count the distance of the x-axises</em>.
4 - (-3) is 7 units, which is D.
Question #1, refers to the graph that appears on the left:
The graph is comprised of 4 segments.
All of the segments are linear.
Segment 'B' is the only one that's rising.
Question #2, also refers to the graph that appears on the left:
As discussed in the answer to Question #1,
interval-B is a segment that's linear and rising.
Question #3:
Keisha runs to Natasha's house, stays there for 15 minutes,
then ... with Natasha ... runs the rest of the way to swim practice.
If the story is graphed, the graph has 3 segments. Since the slope
of each segment is Keisha's speed during that interval:
-- the middle segment will have no slope, while she sits motionless
at Natasha's house;
-- the 1st and 3rd segments will have positive slopes, while Keisha
is running.
Choice A). Terrible choice. It says that at time=0, when Keisha begins
running, she is 5 blocks from home. Then it says that the line decreases,
as if she runs from there toward her house. Not a good choice.
Choice B). Somewhat better, but doesn't fit the story. This graph
says that she starts from her house, runs at 3 different speeds
until she is 9 blocks away, then immediately turns around and
spends the next hour running back home. Also not a good choice.
Choice C). This is it. If I had not read the story and just saw this graph,
I could see that Keisha started at her house, ran 5 blocks away from in
0.25 hour, stayed at that -place for the next 0.25 hour, then ran to some
place that was 9 blocks from her house in another 0.25 hour, and finally,
stayed there for the next hour. That's all the information that appears on
this graph, but it certainly matches the story, and additionally tells us
how long she stayed at swim practice.
Choice D). Now that we know we have a good graph in choice-C,
this one is not only wildly wrong, but it's funny too.
This graph says that at time zero, Keisha is 5 blocks away from her
house, and she stays right there for 0.3 hour. She moves 1 block
from there in the next 0.2 hour, then stays at THAT place for the next
0.3 hour, and finally proceeds steadily to 9 blocks from her house
over the next 0.95 hour.
Question #4. Refers to the graph on the right side.
This graph is comprised of 5 linear segments. The slope of
each segment is the rate at which the level of water in the tub
is changing. A rising line says that the water level is rising.
A falling line says that the water level is falling. If the water
level isn't changing, then the slope of the line is zero ... it's
a horizontal segment.
Before we even look at the story, let's look at the graph:
Segment A: the tub is empty at time zero, then rises slowly
for about 8 minutes;
Segment B: suddenly at 8 minutes, the level rises by 50%
(from level 20 to level 30) in 2 minutes or less;
Segment C: for the next 15 minutes, the level doesn't change;
Segment D: the water drops quickly to level-20 in 2 minutes or less;
Segment E: in about 8 minutes, the water level drops slowly to zero.
If somebody told us that this was the graph of a girl taking a bath,
we could just about read the story from the graph:
A: filling the tub from the faucets ... takes 8 minutes;
B: the person slowly and carefully getting into the tub, making the level rise
C: the person in the tub;
D: the person slowly and carefully getting out of the tub;
E: the tub emptying in 8 minutes.
Now I'm ready to look at the choices.
OK. I see that the question is only asking about segment-C.
K ran water to fill the tub ... No. The level isn't changing.
K emptied the tub ... No. The level isn't changing.
K got into the tub ... No. The level isn't changing.
K soaked in the bathtub ... Yes ! The level isn't changing.
A 120 watt light-bulb is a 0.120 kilowatt light bulb.
In one hour, it uses 0.120 kilowatt-hour of energy.
If electrical energy costs $0.20 per kilowatt hour, then that light bulb costs
(0.120 kilowatt-hour / hour) x (0.20 dollar / kilowatt-hour) =
(0.120 x $0.20 / hour) =
$0.024 / hour = <span>2.4¢ per hour </span>
The function is
.
To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:
f(1)=1-11+36-36, not 0
f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).
Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).
We can also try some other factors of 36. Indeed we can check that
f(3)=27-99+108-36=135-135=0,
and
f(6)=216-396+216-36=0.
Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.
This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).
Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6.
The y-intercept is f(0), which is -36.
Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly,
we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.
Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity,
and it goes to minus infinity as x goes to - infinity.
Converting 25 degrees to radians:
180° = π radians.
1° = π/180 radians.
25° = (π/180 radians) * 25
= (25/180) * π radians.
Leaving the answer in terms of π, 25/180 = 5/36
= (25/180) * π radians = (5/36)π radians or ≈ 0.1389π radians.
Therefore 25° = (5/36)π radians or ≈ 0.1389π radians
I hope this explains it.
I think why you did not get it was because you did not leave your answer in terms of π or as a multiple of π, so as a multiple of π our answer is:
= (5/36)π radians or ≈ 0.1389π radians
