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
liberstina [14]
3 years ago
5

For what value(s) of k is the linear system consistent? (Enter your answers as a comma-separated list.)

Mathematics
2 answers:
Leokris [45]3 years ago
8 0

Answer:

k\neq -\frac{27}{2}

Step-by-step explanation:

We have been given a system of equations as 6x_1-9x_2 = 8\\\\9x_1+kx_2 =-1. We are asked to find the value of k such that the given system is consistent.

Let us consider two equations as:

a_1x+b_1y = c_1\\\\a_2x+b_2y =c_2

For a system to be consistent the ratio of coefficient of x terms and y terms should not be equal that is:

\frac{a_1}{a_2}\neq \frac{b_1}{b_2}

Upon substituting our given values, we will get:

\frac{6}{9}\neq \frac{-9}{k}

6k\neq -81

\frac{6k}{6}\neq -\frac{81}{6}

k\neq -\frac{27}{2}

Since the given system will be consistent for all value except -\frac{27}{2}, therefore, we can choose any values for k such as -2 or 2.

AleksAgata [21]3 years ago
4 0

Answer:

Step-by-step explanation:

Given

6x_1-9x_2=8

9x_1+kx_2=-1

The given system is AX=B can be represented by

\begin{bmatrix}6 &-9 \\ 9 & k\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}8\\ -1\end{bmatrix}

The given system is consistent when determinant of A is not equal to zero

|A|

|A|=6k-(-81)=6k+81

k\neq \frac{-27}{2}

i.e. system is consistent for all value of k except k=\frac{-27}{2}

R-\frac{-27}{2}

                 

You might be interested in
If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m
Korvikt [17]

Answer:

The final integration in the given limits will be 89.876

6 0
3 years ago
Michelle drew a scale drawing of a swimming pool she used the scale 14 millimeters 5 meters in the drawing the pool is 42 millim
Lera25 [3.4K]

EXPLANATION

Let's see the facts:

The scale is---> 14 milimeters ----> 5 meters

Width = 42 milimeters

Applying the unitary method, the actual width of the pool is:

Actual_{}width=42\text{ mm}\cdot\frac{5m}{14\text{ mm}}=15m

The width of the pool is 15m

6 0
1 year ago
chantal volunteered to bring 1 gallon of freshly squeezed orange juice to a picnic.the local grocery store sells 4-pound bags of
pochemuha
(128 oz) * (2 oranges)/(5 oz) * (1 bag)/(11.5 oranges) * $3.49/bag ≈ $15.54

Note that we have assumed 11.5 oranges per bag, and that partial bags are available.

If Chantal must buy whole bags of oranges, 5 bags will be needed and the cost will be $17.45.
6 0
3 years ago
Adam is hired at a salary of $50000 per year but will earn an annual increase of 2.5% per year. Brock is hired at the same time
nadezda [96]
A=50000(1.025^t), B=50000+3000t

A(10)=$64004.23, B(10)=$80000

So Brock will be earning $15995.77 more than Adam in the tenth year.
4 0
3 years ago
In​ 2000, 49 %49% of the residents in a large city regularly used newspapers for getting news and this has decreased at an avera
kogti [31]

Answer:

  P(x) = -1.1x +49

Step-by-step explanation:

You are given the percentage in 2000 (for x=0) as 49, and told that its rate of change is -1.1 percent per year. So, with a slope of -1.1 and an intercept of 49, the slope-intercept form of the linear equation becomes ...

  P(x) = -1.1x +49

_____

The slope-intercept form for slope m and y-intercept b is ...

  y = mx + b

7 0
3 years ago
Other questions:
  • Question 2 (20 points)
    15·2 answers
  • Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 2; B: the numbers add to 5
    6·1 answer
  • True or False: The null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on
    7·1 answer
  • PLEASE HELP WILL GIVE GOOD RATINGS AND 15 POINTS!! I will give BRAINLIEST
    11·1 answer
  • Factor each expression completely.<br> a. X^2- X-72
    9·1 answer
  • PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!<br><br> What is the value of x?
    11·2 answers
  • 60°<br> Х<br> Х<br> X =<br> degrees.
    11·2 answers
  • Find the value of y. help pls
    14·1 answer
  • Help???????????????? Giving brainiest to right answer
    13·1 answer
  • Put in ascending order <br><br>1.2, 0.2 ,1.22, 0.12, 0.002<br>​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!