Solve the absolute value equation by graphing. <br><br>|x + 6| = |1-2x|<br>

How many solutions does the system have ? 20x - 5y = 5 4x - y = 1

Aleks04 [339]

Answer:

Infinite solutions.

Step-by-step explanation:

Just plug your equation into desmos graphing calculator and it will graph it for you. If it is infinite the two lines will lay on top of one another. If there is only one solution it will be where the two lines intersect. If there are no solutions the two lines will be parallel.

3 0

3 years ago

Read 2 more answers

A physicist must make sure that the temperature of a metal dies not get colder than -80°C. The physicist changes the metals temp

NeTakaya

The answer is negative 84 because there are to ne

6 0

3 years ago

A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose t

marshall27 [118]

Answer:

n=269 residents should be sample required to be sure that a 90% confidence interval for the proportion who favor the construction will have a margin of error no greater than 0.05

Step-by-step explanation:

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimates proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.64})^2}=268.96$

And rounded up we have that n=269

4 0

3 years ago

Ten times the sum of half a number and 6 is 8

kari74 [83]

Times means multiplication
sum means addition
is means the equal sign
lets call our number 'n'

That as an expression would be

$10(\frac{1}{2}n + 6) = 8$

6 0

4 years ago

Write an equation for each problem. The square of a number is 8 more than twice the number.

avanturin [10]

Answer:

The equation is equal to

$x^{2}=2x+8$

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represented the problem is equal to

$x^{2}=2x+8$

$x^{2}-2x-8=0$

Solve the quadratic equation by graphing

The solution are x=-2 and x=4

see the attached figure

therefore

The number can be -2 or 4

3 0

4 years ago

Solve the absolute value equation by graphing. |x + 6| = |1-2x|​

Solve the absolute value equation by graphing. |x + 6| = |1-2x|