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
A postal carrier can deliver to 130 house in a 2.5- hour period At this rate how many hours will it take to deliver to 312 house
mylen [45]

Answer:6 hours


Step-by-step explanation:

312/130=2.4

2.4*2.5=6

5 0
3 years ago
Which rule yields the dilation of the figure STUV centered at the origin?
Stels [109]

The length of ST is 10 units, the length of S't" is 2 units.


This means the dilated figure was decreased by a factor of 5.

Because it is smaller it would be a scale factor of 1/5 ( 0.2 as a decimal).

5 0
3 years ago
Read 2 more answers
1. Write an algebra equation for each purchase. I (Mickey) bought an ice cream treat and a bottle of water for $10. Pam purchase
Ne4ueva [31]

x+y=10

x+2y=14
x is common in both so u have to subtract the second one from 1st
x-x + y-2y = 10-14
-y = -4
y=4
which means bottle of water (y) = 4
and then substitute 4 in equation (x+y=10 or x+2y=10)
x + 4 = 10
x=6
5 0
3 years ago
The number of buses needed for school field trip depends on the total number of people going one field trip require seven buses
joja [24]
217+35=252
252/7=36
36 people per bus
4 0
3 years ago
Apple would like to estimate the web browsing battery life of the iPad. The following data represents the battery life, in hours
umka21 [38]

Answer:

12.5 hours

Step-by-step explanation:

The data which represents the battery life, in hours, experienced by six users is given below:

10 14 14 16 13 8

To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.

Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5

The point estimate for the web browsing battery life of the iPad is: 12.5 hours

8 0
3 years ago
Other questions:
  • Solve the equation x+12+2x=20+3x−8.
    13·1 answer
  • Factor out -1/4 out of -1/2x-5/4y
    8·1 answer
  • Estimate the difference 625-248
    8·1 answer
  • Jude is placing boxes on a shelf that holds no more than 80 lb. He has x small boxes that weigh 5 lb each and y large boxes that
    12·1 answer
  • Carlos spent 45% of his savings on a bike. The bike cost $126. How much did Carlos have after buying his bike
    15·2 answers
  • IXL: will give Brainlest and thanks!!!
    12·1 answer
  • Find the surface area and volume oF a cylinder <br> 2 cm radius <br> 18 cm height
    5·1 answer
  • What is 25% of 50? Is it,<br> A- 200<br> B- 10<br> C- 25<br> D- 12.5
    15·2 answers
  • If x = 10 find the value of<br>2x + 9​
    5·2 answers
  • The book store is having a sale on bookmarks. Each bookmark is on sale for $0.84. Each student in Ms. Duke's class decides to bu
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!