Apair of equations is shown below.

x + y = 2
y = one halfx + 5

if the two equations are graphed, at what point do the lines representing the two equations intersect?

(4, −2)
(−2, 4)
(2, 5)
(5, −2)

solution is (-2,4)

Step-by-step explanation:

LEts graph both equations.

solve for y

Make a table to graph the equation

x                    y=-x+2

0                     y=2

1                      y=1

Graph the points (0,2) and (1,1) . then extend the line that connects two points

x                    y=(1/2)x+5

0                     y=5

2                      y=6

Graph the points (0,5) and (2,6) . then extend the line that connects two points

The graph is attached below

Both lies intersects at (-2,4)

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;