1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Advocard [28]
3 years ago
12

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z

= 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2
Mathematics
1 answer:
Luden [163]3 years ago
5 0

Answer:

a) If a=20 the system has no solutions.

b) If a≠20 the system has exactly one solution.

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}1&2&-3&4\\3&-1&5&2\\4&1&a-14&a+2\end{array}\right].

Using rows operations we obtain the echelon form of the matrix, ie,

\left[\begin{array}{cccc}1&2&-3&4\\0&-7&-4&-10\\0&0&a-20&a+4\end{array}\right]

Since the echelon form of the matrix does not have free variables then the problem has exactly one solution or has no solutions.

a) If a=20 the system has no solutions because in the last equation solving for x3 it has that 0=24. Then the system is inconsistent.

b) If a≠20, the the system has exactly one solution that is obtained solving the system of the echelon form matrix.

You might be interested in
20 POINTS!!
Finger [1]

Answer:

Since we have two congruent sides with one congruent angle in between the answer is SAS.

6 0
3 years ago
Please help check my answers I beg you!!!!!!!
Alchen [17]
1. the answes for the graph ones is the 3rd and 4th graph because both graphs are 1 line and a line is infinite

2. (-3,5) x=(-) y=(+)that means that it must to the left and up part of graph, therefor it is the 4th graph

1. it would be the 4th graph that you didn't show because none of the included answers are correct
7 0
3 years ago
Work out 2.6 cos 12° rounded to 2 d.p.
AlexFokin [52]

Answer:

2.54. Calculate the approximate value:2.6 *

Step-by-step explanation:

8 0
2 years ago
A small company’s net income for the first six months of the year was $76,500 and for the last six months it was $100,000. What
mr Goodwill [35]

Answer:153/200

Step-by-step explanation:

8 0
3 years ago
I'm really not sure how to go about solving this algebraic equation, please help! .513 = (2x)^2 / (.05-x)
LiRa [457]
Let's set it up like this:
0.513=\frac{\left(2x\right)^2}{\left(0.05-x\right)}
Multiply both sides by 0.05-x
0.513\left(0.05-x\right)=\frac{\left(2x\right)^2}{0.05-x}\left(0.05-x\right)
0.513\left(0.05-x\right)=4x^2
We are then going to use the distributive property. Since we also know that the opposite of an number that is squared is the square root, we can also apply that. We would be left with something like this:
x=-\frac{0.513+\sqrt{0.673569}}{8},\:x=\frac{\sqrt{0.673569}-0.513}{8}
The variable x can be both positive or negative.
We have found successfully our answer.

Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish<span />
4 0
3 years ago
Other questions:
  • Can some one tell me if it’s a, b, c, or d. Thank you
    7·2 answers
  • How many hours is 10:30 am to 2:30 pm?
    6·1 answer
  • What is the solution set for. <br> |X+3| = 5?
    10·2 answers
  • Four times the sum of f and g is identical to six times g
    14·2 answers
  • Suppose Ellie makes a lamb stew in a 13-quart pot. If the diameter of the bottom of the pot is 14 inches, how big is the circumf
    13·1 answer
  • So I'm calculating the areas of squares and rectangles.
    10·1 answer
  • What is the formula to find the volume in a rectangular ​
    5·1 answer
  • Basic geometry Episode 8
    6·1 answer
  • Pls help me it is only one questionnnn:)
    5·2 answers
  • Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartF
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!