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3 years ago

If a system of two inequalities has a solution, then their two half planes intersect , true or false ?

Mathematics

1 answer:

Nana76 [90]3 years ago

7 0

Answer: The answer is true.

Step-by-step explanation: The given statement is

'If a system of two inequalities has a solution, then their two half planes intersect'.

We are to check whether the statement is true or false.

Let a system of two inequalities be

$x+y\geq 3,\\\\2x+5y\leq 10.$

These inequalities has a solution, for example, x = 2, y = 1.

Plotting these inequalities on a graph paper (please see the attached graph), we see that the two half planes intersect, which is represented by the double shaded region in the graph.

Thus, the given statement is TRUE.

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Solve for e.<br> 9e+4=-5e+14+13e9e+4=−5e+14+13e<br> e=

Kitty [74]

Answer:

e = 10

Step-by-step explanation:

9e+4=-5e+14+13e

Combine like terms

9e+4=14+8e

Subtract 8e from both sides

9e-8e+4=8e-8e +14

e +4 = 14

Subtract 4 from each side

e+4-4 = 14-4

e = 10

5 0

3 years ago

How do you use the metric system?

baherus [9]

Answer:

The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.

8 0

3 years ago

In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponen

Mashcka [7]

Answer:

a) P' = P

$P(t) = 24e^{0.693t}$ where t is step of 6 months

b) 7.7 years

c)1064.67 rabbits/year

Step-by-step explanation:

The differential equation describing the population growth is

$\frac{dP}{dt} = P$

Where t is the range of 6 months, or half of a year.

P(t) would have the form of

$P(t) = P_0e^{kt}$

where $P_0 = 24$ is the initial population

After 6 month (t = 1), the population is doubled to 48

$P(1) = 24e^k = 48$

$e^k = 2$

$k = ln(2) = 0.693$

Therefore $P(t) = 24e^{0.693t}$

where t is step of 6 months

b. We can solve for t to get how long it takes to get to a population of 1,000,000:

$24e^{0.693t} = 1000000$

$e^{0.693t} = 1000000 / 24 = 41667$

$0.693t = ln(41667) = 10.64$

$t = 10.64 / 0.693 = 15.35$

So it would take 15.35 * 0.5 = 7.7 years to reach 1000000

c. $P' = P_0ke^{kt}$

We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48

$24e^{0.5k) = 48$

$0.5k = ln2 = 0.693$

$k = 1.386$

Therefore, $P' = 1.386*24e^{1.386t}$

At the mid of the 3rd year, where t = 2.5, we can calculate P'

$P' = 1.386*24e^{1.386*2.5} = 1064.67$ rabbits/year

4 0

3 years ago

Brainliest Answer!!!

AleksandrR [38]

Its fairly straightforward. Since the bottom equation only has one unknown,x, because y=1.3, you can plug y in and solve for x. Once you find the value of x, you then have the value for two variables, x and y, and again have one unknown coefficient a. To solve for the coefficient you just plug in your y value (1.3) and your x value (which can be rounded to 0.42). Using a little bit of algebra, you can then solve for a which should be a=2.108. I am not sure if your teacher wants you to solve it this way but you could also use the elimination method or substitution method that you would of learned when discussing system of equations. But no matter which way you do it, the math follows the rules. Hope this helps. I’d suggest you solve it yourself to double check my work.

To verify my credibility,
I am a Mechanical Engineering major w/ minor in mathematics

7 0

3 years ago

An elephant drinks about 4368 milliliters per day. Use dimensional analysis to show how many liters per hour this is.

viktelen [127]

Answer:

182 milliliters per hour

Step-by-step explanation:

4368/24=182

6 0

3 years ago