Answer:
x = 5
Step-by-step explanation:
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
-----------------
Eliminate z
Add the 1st and 2nd eqn
4x + 2y + z = 24
2x - 3y - z = 2
----------------
6x - 1y = 26 eqn A
Multiply the 2nd eqn by 2, then add the 3rd.
4x - 6y -2z = 4
5x + y + 2z = 21
----------------
9x - 5y = 25 eqn B
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Now you have 2 eqns in 2 unknowns, not 3.
Multiply eqn A by 5 and subtract eqn B.
30x - 5y = 130 eqn A times 5
9x - 5y = 25 eqn B
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21x = 105
x = 5
Answer:
102
Step-by-step explanation:
We have the mean (m) 128.5 and the standard deviation (sd) 8.2, we must calculate the value of z for each one and determine whether or not it is an outlier:
z = (x - m) / sd
In the first case x = 148:
z = (148 - 128.5) /8.2
z = 2.37
In the second case x = 102:
z = (102 - 128.5) /8.2
z = -3.23
In the first case x = 152:
z = (152 - 128.5) /8.2
z = 2.86
The value of this is usually between -3 and 3, therefore when x is 102 it goes outside the range of the value of z, which means that this is the outlier.
Answer:
x < -7
Step-by-step explanation:
2(4x + 1) < 3(2x - 3)
Distributive Property:
8x + 8 < 6x - 6
Subtract on Both Sides:
8x + 8 < 6x - 6
- 6x -6x
--------------------
2x + 8 < - 6
-8 -8
---------------
2x < -14
Divide on Both Sides:
2x < -14
--- ---
2 2
x < -7
Answer: 3 * 10 ^3
Step-by-step explanation:
Divide the numbers
3.9 / 1.3
3
Subtract the powers of 10
10^5 / 10^2 = 10 ^ (5-2) = 10^3
The result is 3 * 10 ^3
I'm assuming you're referring to problem 6. You are asked to find the number of x intercepts or roots, which is another term for "zero". I prefer the term root or x intercept as "zero" seems misleading. Anyways, all we do is count the number of times the graph crosses the x axis. This happens 4 times as shown in the attached image below. I have marked these points in red. The graph can directly cross over the x axis, or it can touch the x axis and then bounce back. Either way, it is considered an x intercept.
<h3>Answer: there are 4 x intercepts (or 4 roots)</h3>