<h3>
Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>
===========================================================
Explanation:
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
------------
Side notes:
- Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
- Choice 2 is not true. Point B is not on the parabola.
- Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.
Answer:
Step-by-step explanation:
Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilations involve multiplication! Dilation with scale factor 2, multiply by 2
A good place to start is to set 
to y. That would mean we are looking for 
to be an integer. Clearly, 
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since 
is a radical, it only outputs values from ![[0,\infty]](https://tex.z-dn.net/?f=%20%5B0%2C%5Cinfty%5D%20)
, which means y is on the closed interval: ![[0,120]](https://tex.z-dn.net/?f=%20%5B0%2C120%5D%20)
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.
Answer:
Surface Area= 144
Step-by-step explanation:
To find the area of the triangle you would multiply the base times the height and divide it by 2. 9x6/2=27. For one triangle the area is 27. Since there are 4 you would multiply it by 4. 27x4= 108. This will give you 108. Now all you need to do is add the square which is 6x6= 36. 108+36=144.
Answer:
degree 24.7
Radian 0.43
Step-by-step explanation:
