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2 years ago

How do you solve linear equations with substitutions?

Mathematics

1 answer:

Nostrana [21]2 years ago

5 0

Answer:

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

Step-by-step explanation:

Solve the following system by substitution.

2x – 3y = –2

4x + y = 24

The idea here is to solve one of the equations for one of the variables, and plug this into the other equation. It does not matter which equation or which variable you pick. There is no right or wrong choice; the answer will be the same, regardless. But — some choices may be better than others.

For instance, in this case, can you see that it would probably be simplest to solve the second equation for "y =", since there is already a y floating around loose in the middle there? I could solve the first equation for either variable, but I'd get fractions, and solving the second equation for x would also give me fractions. It wouldn't be "wrong" to make a different choice, but it would probably be more difficult. Being lazy, I'll solve the second equation for y:

4x + y = 24

y = –4x + 24

Now I'll plug this in ("substitute it") for "y" in the first equation, and solve for x:

2x – 3(–4x + 24) = –2

2x + 12x – 72 = –2

14x = 70

x = 5

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Use the given information to determine if the geometric series converges or

lana66690 [7]

Answer:

c) The series diverges. There is no sum.

Step-by-step explanation:

A geometric series is a series of the form:

$S = \Sigma_{i=0}^{n} a\cdot r^{i}$ , $\forall i \in \mathbb{N}_{O}$

Where:

$a$ - First term of the series, dimensionless.

$r$ - Common ratio, dimensionless.

A geometric series converges only if $|r| < 1$ . As $r > 1$ , the geometric series diverges. Hence, the right answer is C.

8 0

3 years ago

How would i solve. been getting wrong

Lisa [10]

Answer:just find a common denomintor and add them

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

The weight of a package of mints is believed to be normally distributed with mean 21.37 grams and standard deviation 0.4, i.e. X

nasty-shy [4]

Answer:

$P(21$

And using a calculator, excel or the normal standard table we have that:

$P(-1.85$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weigths of a population, and for this case we know the distribution for X is given by:

$X \sim N(21.37,0.4)$