Answer:
No
Step-by-step explanation:
Explanation 1)A vertical line can be represented by the equation x=a, where a can be any number. If you think about it, there is no y in the function, this making it not a function.
Explanation 2) For a line to be a function it has to pass the vertical line test, so you will draw a vertical line through the function and if it touches more than one point then it is not a function. In this case if you draw a vertical line through a vertical line there are an infinite number of places where the lines intercept, so it is not a function.
Answer:
- False
- True
-- False
-- True
-- True
Step-by-step explanation:
The points are
,
,
,
and
---- missing from the question
Given
![y = 1\frac{1}{2}x](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7Dx)
Required
Determine if each of the points would be on ![y = 1\frac{1}{2}x](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7Dx)
To do this, we simply substitute the value of x and of each point in
.
(a)
In this case;
and ![y = 1](https://tex.z-dn.net/?f=y%20%3D%201)
becomes
![y = 1\frac{1}{2} * 1\frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7D%20%2A%201%5Cfrac%7B1%7D%7B2%7D)
![y = \frac{3}{2} * \frac{3}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%2A%20%5Cfrac%7B3%7D%7B2%7D)
![y = \frac{9}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B9%7D%7B4%7D)
![y = 2\frac{1}{4}](https://tex.z-dn.net/?f=y%20%3D%202%5Cfrac%7B1%7D%7B4%7D)
<em>The point </em>
<em> won't be on the graph because the corresponding value of y for </em>
<em> is </em>
<em></em>
(b) ![(4,6)](https://tex.z-dn.net/?f=%284%2C6%29)
In this case;
![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
![y = 6](https://tex.z-dn.net/?f=y%20%3D%206)
becomes
![y = 1\frac{1}{2} * 4](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7D%20%2A%204)
![y = \frac{3}{2} * 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%2A%204)
![y = \frac{3* 4}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%2A%204%7D%7B2%7D)
![y = \frac{12}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B12%7D%7B2%7D)
![y = 6](https://tex.z-dn.net/?f=y%20%3D%206)
<em>The point </em>
<em> would be on the graph because the corresponding value of y for </em>
is ![y = 6](https://tex.z-dn.net/?f=y%20%3D%206)
(c) ![(18,12)](https://tex.z-dn.net/?f=%2818%2C12%29)
In this case:
![x = 18;y = 12](https://tex.z-dn.net/?f=x%20%3D%2018%3By%20%3D%2012)
becomes
![y = 1\frac{1}{2} * 18](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7D%20%2A%2018)
![y = \frac{3}{2} * 18](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%2A%2018)
![y = \frac{3* 18}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%2A%2018%7D%7B2%7D)
![y = \frac{54}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B54%7D%7B2%7D)
![y = 27](https://tex.z-dn.net/?f=y%20%3D%2027)
<em>The point </em>
<em> wouldn't be on the graph because the corresponding value of y for </em>
<em> is </em>
<em></em>
(d) ![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)
In this case;
![x =0; y = 0](https://tex.z-dn.net/?f=x%20%3D0%3B%20y%20%3D%200)
becomes
![y = 1\frac{1}{2} * 0](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7D%20%2A%200)
![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
<em>The point </em>
<em> would be on the graph because the corresponding value of y for </em>
is ![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
(e)
In this case:
; ![y = 3\frac{3}{4}](https://tex.z-dn.net/?f=y%20%3D%203%5Cfrac%7B3%7D%7B4%7D)
becomes
![y = 1\frac{1}{2} * 2\frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%201%5Cfrac%7B1%7D%7B2%7D%20%2A%202%5Cfrac%7B1%7D%7B2%7D)
![y = \frac{3}{2} * \frac{5}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%2A%20%5Cfrac%7B5%7D%7B2%7D)
![y = \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B15%7D%7B4%7D)
![y = 3\frac{3}{4}](https://tex.z-dn.net/?f=y%20%3D%203%5Cfrac%7B3%7D%7B4%7D)
<em>The point </em>
<em> would be on the graph because the corresponding value of y for </em>
is ![y = 3\frac{3}{4}](https://tex.z-dn.net/?f=y%20%3D%203%5Cfrac%7B3%7D%7B4%7D)
Answer:
see explanation
Step-by-step explanation:
Given that the the difference of cubes is
a³ - b³ = (a - b)(a² + ab + b²)
Given
64
- 27 ← a difference of cubes
with a = 4x² and b = 3, thus
= (4x²)³ - 3³
= (4x² - 3)(16
+ 12x² + 9) ← in factored form
There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n
=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14![C_{12}](https://tex.z-dn.net/?f=C_%7B12%7D)
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
Learn more about combinations at brainly.com/question/11732255
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