How can you solve the equation 4−x = 2x + 3 graphically?

Mathematics

2 answers:

pychu [463]3 years ago

7 0

Answer:

x = 1/3

Step-by-step explanation:

Hello,

we can draw the two lines defined by

y = 4 - x

y = 2x + 3

And search for the intersection point as below

This is the point A (1/3, 11/3)

Do not hesitate if you have any question

Thanks

Dafna1 [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Graph the two lines separately but on the same graph paper, and then from the completed graph read off the coordinates of the point of intersection.

y = 4 - x has a y-intercept of 4 and a slope of -1. Plot the point (0, 4) and then draw a line with slope -1 through it.

y = 2x + 3 has a y-intercept of 3 and a slope of 2. Plot (0, 3) and then draw a line with slope +2 through it.

As a check, solve for x and y algebraically:

4 - x = 2x + 3 becomes 1 - x = 2x, or 3x = 1. Then x = 1/3.

Use y = 4 - x to find the y value when x = 1/3:

y = 4 - 1/3 = 11/3

Thus, the solution is (1/3, 11/3)

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A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

attashe74 [19]

Answer:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

$X= 36$ represent the families owned at least one DVD player

$n= 85$ represent the total number of families

$\hat p=\frac{36}{85}= 0.424$ represent the estimated proportion of families owned at least one DVD player

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 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by: