All categories

3 years ago

What is the solution to the following system? x+y+z=6 x-y+z=8 x+y-z=0

Mathematics

2 answers:

Ghella [55]3 years ago

4 0

I don't really know if this is correct but I think it is x+y+z=14

Gnoma [55]3 years ago

3 0

Subtract the second equation from the first equation :

The xs and zs would cancel. On the left side, y–(-y)=2y. On the right side, 6–8=-2

We're left with 2y=-2
Divide both sides by 2:
Y=-1

Subtract the third equation from the second equation. The xs would cancel again. -y–y=-2y and z–(-z)=2z. So on the left side we have -2y+2z and on the right side, 8-0=8.

We get -2y+2z=8.
Plug in -1 for y:
-2(-1)+2z=8
2+2z=8
Subtract 2 from both sides:
2z=6
Divide both sides by 2:
Z=3

Plug in -1 for y and 3 for z into the first equation:
X+(-1)+3=6

Solve for x:
X+2=6
Subtract 2 from both sides:
X=4

Hope this helps! :)

You might be interested in

If the function f(x) = -1/2x - 7 were graphed, which of the following would be true?

Fittoniya [83]

ANSWER

D. As the x-values increase, the y-values would decrease

EXPLANATION

The given function is
$y = - \frac{1}{2} x - 7$

The slope of this function is
$m = - \frac{1}{2}$

Since the slope is negative, there is a negative or an inverse relationship between x and y.

As the values of x increases, the values of y decreases.

Also, as the values of x decreases, the values of y increases.

The first option is not true because as x is becoming bigger and bigger negatively, y will become positive.

For instance, when
$x = - 40$
$y = - \frac{1}{2} ( - 40) - 7$

This implies that,

$y = 20 - 7 = 13$

Options B is obviously not true because the function has a negative relationship between x and y.

Option C is also false because, x can be positive since it is the independent variable.

See graph

Therefore, the correct answer is option D.

5 0

3 years ago

In early 2012, the Pew Internet and American Life Project asked a random sample of U.S. adults, "Do you ever ... use Twitter or

8090 [49]

Answer:

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0

3 years ago

Which of the following describes the function −x3 + 5?

algol13

Answer:

The correct choice is C

Step-by-step explanation:

The given function is:

$-x^3+5$

The degree of this function is odd so the function will rise at one end and fall on the other end.

Since the coefficient of the leading term is negative, the graph of the function will rise at the left and fall on the right.

The correct answer is option C.

4 0

3 years ago

1. Describe a situation that could be modeled by x≤50

Dimas [21]

There are many ways to answer. The x represents some number. We don't know what the number is, but we know that it must be less than or equal to 50. Put another way, the number can be anything you want as long as it doesn't go past 50. We say that 50 is the so called "ceiling" more or less.

Some examples:

* An elevator can only hold 50 people at maximum. Therefore, x can be any number smaller than 50 or 50 itself. Having 51 or over will be too much.

* You can only work 50 hours for one stretch of some 2 week period. If x is the number of hours you work, then x must be 50 or less as written by $x \le 50$ . So x could be x = 37 as it's less than 50, but x = 62 is not possible.

* For some small ride at a theme park, the seats are designed such that only people 50 inches or less can ride on them. If x is the height of a person in inches, then $x \le 50$ means something like x = 37 is possible but x = 62 is too high.

8 0

3 years ago

How many liters is 250,000 cm3?

eimsori [14]

Once cubic centimeter = 1 milleter

1 mL = 1000 L

250,000 ÷ 1000 = 250

There are 250 liters in 250,000 cubic centimeters.

3 0

3 years ago

Read 2 more answers