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
kolbaska11 [484]
3 years ago
14

Determine which system below will produce infinitely many solutions.

Mathematics
1 answer:
DaniilM [7]3 years ago
4 0
<span>A.  −6x + 3y = 18 4x − 3y = 6
B   2x + 4y = 24 6x + 12y = 36
C.  3x − y = 14 −9x + 3y = −42
D.  5x + 2y = 13 −x + 4y = −6

For infinitely many solutions,  we are looking for linearly dependent equations, which means that one equation is an exact multiple or sub-multiple of the other.
Example: 
</span>2x + 4y = 24
6x + 12y = 36
<span>is a system that does NOT have a solution, because 6/2=3 for x, 12/4=3 for y, but 36/24=1.5.  The two lines have the same slope (therefore parallel), but they have different y-intercepts.  So the two lines will never meet, and therefore no solution.


or another example:
</span>  3x  -y = 14
  -9x + 3y = -42
We see that -9/3=-3, 3/-1=-3, -42/3=-14, this system has coefficients all in the same ratio, meaning that the lines are coincident (and linearly dependent), therefore infinitely many solutions.

Still another example:
−6x + 3y = 18
4x − 3y = 6
we see that 18/6=3, 3/(-3)=-1 , since the ratios are different, the two equations are not linearly dependent, and therefore the system has unique solution.

Last example:
5x + 2y = 13
−x + 4y = −6
Check the ratio of the coefficients:
-1/5=-1/5
4/2=2  ..... we can stop here and conclude that there is a unique solution because the equations are not in the same ratio. (unique means that there is exactly one solution)

You might be interested in
1140 was rounded to the nearest ten.<br>What is the upper bound?<br>​
zloy xaker [14]

Answer:

1145

Step-by-step explanation:

  • <em>The upper bound is the smallest value that would round up to the next estimated value</em>.

Since the number was rounded to nearest ten, the upper bound is:

  • 1145

which rounds up to 1150 which is the next estimated value greater than 1140

8 0
3 years ago
Read 2 more answers
A 1,000 mL solution of acetic acid contains 26 mL of pure acetic acid. Find the percent concentration of this solution.
Mrac [35]

Given:

Total solution : 1000mL

Pure acetic acid = 26mL

To find:

The percent concentration of given solution.

Solution:

We know that,

\text{Percent concentration}=\dfrac{\text{Pure acetic acid}}{\text{Total solution}}\times 100

Putting the given values, we get

\text{Percent concentration}=\dfrac{26}{1000}\times 100

\text{Percent concentration}=\dfrac{26}{10}

\text{Percent concentration}=2.6

Therefore, the percent concentration of this solution is 2.6%.

6 0
3 years ago
The length of the side sqaure A is 50% OF THE LENGTH OF THE SIDE SQUARE b
UNO [17]

Let's say the side length of square A is x, which means the side length of square B is 2x.

Then, the area of square A can be written as , and the area of square B can be written as .

There's no diagram here with shaded region, so I'll just find the area of square A as a percentage of the area of square B:

= 1/4 = 25%

So, the answer is 25% (note this is the answer to the question: "express the area of square A as a percentage of the area of square B; there is no diagram showing me where the shaded area is, so I cannot answer the original question

4 0
2 years ago
A company makes wax candles in the shape of a cylinder. Each candle has a diameter of 8 inches and a height of 3 inches. How muc
Sveta_85 [38]

Answer:

18,086.4 cubic units

Step-by-step explanation:

The volume of one such cylinder can be computed by multiplying the height by pi by the radius squared: 3×3.14×4²=150.72.

If you want to make 120 candles, multiply that number by 120: 150.72×120=18086.4.

3 0
3 years ago
Question 4 of 25
Gnoma [55]

Answer:

Step-by-step explanation:

We are looking for P(58 < x < 64). We need to find the percentage to the left of the z-scores for each of these numbers. To find the z scores, use the formula:

z=\frac{x_i-\bar{x}}{\sigma}

z=\frac{58-62}{4} which gives us a z-score of -1. The percentage of numbers to the left of a z-score of -1 is .1586553

Now for the other z-score:

z=\frac{64-64}{4} which gives us a z-score of .5. The percentage of numbers to the left of a z-score of .5 is .69146246

The lower percentage subtracted from the higher gives the area in question:

.69146246 - .1586553 = .53280716, or as a percentage, 53.3%, choice A.

7 0
3 years ago
Other questions:
  • How do I work out "The beam from a lighthouse reaches a distance of 8 kilometers and spreads to an angle of 35 degrees. Calculat
    11·1 answer
  • 3^2 • 3^-8 • 3^0<br> i need help with this asap
    7·2 answers
  • The same sequence may be defined in three ways: 1) f(x) = 6x + 5 for x = {1, 2, 3, ...}, 2) a1 = 11 and an + 1 = an + 6 for n =
    15·2 answers
  • Give the number of significant figures in this number: 40.00
    14·2 answers
  • 5. What are the zeros of the graph below?<br> A -2 and 0<br> B-1 and 0<br> C 0 and 2
    6·1 answer
  • You have a shuffled deck of three cards: 2, 3, 4. You draw one card. Let C_i denote the event that the card i is picked. Let E d
    7·1 answer
  • Twenty-six is what percent of 40?
    15·1 answer
  • A student is trying to calculate his semester average. He knows that his test average is an 80, his quiz average is a 72, homewo
    8·1 answer
  • If Sheila can type 531 words in 3 minutes, how many words does she type in 1 minute?
    13·1 answer
  • Help me! I'll give brainliest.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!