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Ede4ka [16]
3 years ago
9

How can you tell that a system of linear equations will have infinitely many solutions without computation?

Mathematics
1 answer:
Contact [7]3 years ago
3 0

If you can manipulate the two equations so that they have exactly the same coefficients (e. g., 3x + 4y = 8 and 2x + 4y = 8), then you conclude that the two lines coincide (overlap), and that there are thus infinitely many solutions.

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Need Help
grigory [225]
<h3>Answer:  Approximately 191 bees</h3>

================================================

Work Shown:

One way to express exponential form is to use

y = a*b^x

where 'a' is the initial value and 'b' is linked to the growth rate.

Since we're told 34 bees are there initially, we know a = 34.

Then after 4 days, we have 48 bees. So we can say,

y = a*b^x

y = 34*b^x

48 = 34*b^4

48/34 = b^4

24/17 = b^4

b^4 = 24/17

b = (24/17)^(1/4)

b = 1.090035

Which is approximate.

The function updates to

y = a*b^x

y = 34*(1.090035)^x

------------------------

As a way to check to see if we have the right function, plug in x = 0 and we find:

y = 34*(1.090035)^x

y = 34*(1.090035)^0

y = 34*(1)

y = 34

So there are 34 bees on day 0, ie the starting day.

Plug in x = 4

y = 34*(1.090035)^x

y = 34*(1.090035)^4

y = 34*1.4117629

y = 47.9999386

Due to rounding error we don't land on 48 exactly, but we can round to this value.

We see that after 4 days, there are 48 bees.

So we confirmed the correct exponential function.

------------------------

At this point we can find out how many bees there are expected to be after 20 days.

Plug in x = 20 to get

y = 34*(1.090035)^x

y = 34*(1.090035)^20

y = 190.672374978452

Round to the nearest whole number to get 191.

There are expected to be roughly 191 bees on day 20.

4 0
3 years ago
A bag of m&amp;m's has 4 red, 7 green, 8 blue, and 6 yellow m&amp;m's. what is the probability of randomly pickinga blue or gree
bogdanovich [222]

Step-by-step explanation:

a probability is always desired cases over total possible cases.

the bag has 4 + 7 + 8 + 6 = 25.

so, when we pick a random M&M we have total 25 possible outcomes.

the desired cases are to pick a green or a blue M&M.

that means these are 7+8 = 15 cases.

the probability to pick one or of the desired cases is

15/25 = 3/5 = 0.6

3 0
2 years ago
Write the equation of a line in slope-intercept form if m=-3 and b=7. help please.
pychu [463]
Slope-intercept form is y = mx + b. all you have to do for this question is plug your given information in:

m = -3
b = 7

y = mx + b
y = -3x + 7
3 0
3 years ago
Which of the following values are in the range of the function graph below? Check all that apply.
Gelneren [198K]

Answer:

hey there,

Step-by-step explanation:

make sure you add your image. we don't know what to answer

3 0
4 years ago
HELP PLEASE IM IN A TIMED TESTTTT !!!
mixas84 [53]

Answer:

Step-by-step explanation:

2. 9a +4c=43

a+c=7

The total tickets for adults and children = 7 (a+c =7)       7 people in all

price for adult = $9  (9a)   Price per child =$4 (4c)

total price =$ 43

  9a +7c = 43

3 0
3 years ago
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