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3 years ago

Solve and show steps -2x+y=-7 and -2x-4y=-12

Mathematics

1 answer:

WITCHER [35]3 years ago

6 0

Answer:

(x, y) = (4, 1)

Step-by-step explanation:

The coefficients of x are the same, so we can cancel the x-terms by subtracting one equation from the other. We want to do this so the resulting y-coefficient will be positive. That means we want to subtract the second equation from the first:

(-2x +y) -(-2x -4y) = (-7) -(-12)

5y = 5 . . . . . . . . simplify

y = 1 . . . . . . . . divide by 5

-2x +1 = -7 . . . . . substitute for y in the first equation

-2x = -8 . . . . . subtract 1

x = 4 . . . . . . divide by -2

The solution is (x, y) = (4, 1).

_____

A graphing calculator easily verifies the solution.

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Find an for the arithmetic series with s16 = -288 And a1 =-21

Maru [420]

If $d$ is the common difference between terms in the sequence $\{a_n\}$ , then

$a_1=-21$
$a_2=a_1+d=-21+d$
$a_3=a_2+d=-21+2d$
...
$a_n=a_{n-1}+d=\cdots=-21+(n-1)d$

You're told that $S_{16}=-288$ (the sum of the first 16 terms in the sequence, presumably). Well, we know that

$S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)$
$S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n$

Recall that

$\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2$

so that we have

$-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25$

So we get

$\begin{cases}a_1=-21\\\\a_n=-21+\dfrac25(n-1)\end{cases}$

8 0

3 years ago

What is it pls help !

Nesterboy [21]

Answer:

I got<u> -8, </u>hope dis helps!

6 0

3 years ago

Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of thei

asambeis [7]

Complete Question

Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.

Answer:

The sample size is $n = 1537 \ gallons$

Step-by-step explanation:

From the question we are told that

The margin of error is $MOE = 0.5$

The confidence level is $C = 95$ %

Given that the confidence level is 95% the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5$ %

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the values is $Z_{\frac{\alpha }{2} } = 1. 96$

The reason we are obtaining critical values of

$\frac{\alpha }{2}$

instead of

$\alpha$

is because

$\alpha$

represents the area under the normal curve where the confidence level interval (

$1-\alpha$

) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$

is just the area of one tail which what we required to calculate the sample size

Now the sample size is mathematically represented as

$n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}$

substituting values

$n = \frac{1.96^2 * 10 ^2}{0.5^2}$

$n = 1537 \ gallons$

7 0

3 years ago

Number closest to 87 square root?

Serga [27]

9 i’m pretty sure bc if u do the square root of 87 and round it to the nearest whole number u get 9

6 0

3 years ago

Which operation between two polynomials will not always result in a polynomial?

Assoli18 [71]

In order to build a polynomial we need one or more terms. A term is a number, variable (denoted by a letter) or any combination of numbers and variables held together by multiplication. The following are examples of terms:

$5, 3x, -5ab c^{2}, \frac{2x^{3}y }{5}, x^{6}$

Now it might look like one of those involves division but it can be thought of as multiplication by (2/5). When we do this the exponents must be positive.

Polynomials are expressions made up of terms held together by addition and subtraction. Again, the exponents must be positive. Since polynomials are made up of the sum or difference of terms, adding or subtracting polynomials just leads to more polynomials. Here are some examples of Polynomials:

$4xy-3 x^{2} +7, \frac{2x}{5}-3abc-5j$

Now let’s consider what happens if we multiply polynomials. As an example we use: $(x+5)(2x-y)=2 x^{2} +10x-xy-5y$

What you might notice is that multiplication will lead us to multiply terms (but multiplying terms gives us more term,as) and also to add or subtract terms but that just gives more polynomials. Therefore multiplication leads to more polynomials.

Finally, we consider division. Here a simple example will do the trick: 2 is a term and x is a term. Let us divide 2 by x. We get: $\frac{\2}{x}=2 x^{-1}$ which is not a polynomial because we have a negative exponent.

Thus, the answer to your question is division. Division of polynomials will not always result in a polynomial.

_______END OF ANSWER___________
is.

5 0

3 years ago