Solve the system of equations: y = 2x + 1 y = x2 + 2x – 8
A. (0, 1) and (2, 5)
B. (–4, 0) and (2, 0)
C. (–3, –5) and (3, 7)
D. (–3, 5) and (3, 2)

Correct answer is option C.(-3,-5) and (3,7)

Step-by-step explanation:

Let us take the value of y from equation y=2x+1 and plugin to the equation y=x2+2x-8

so

2x+1=x2+2x-8

taking constants on left hand side and literals on the right hand side

1+8=x2+2x-2x

9=x2

this implies that value of x=+3,-3

now plug in the value of x in the equation y=2x+1

when x=+3

y=2*3+1 = 7

so (3,7)

when x=-3

y=2*(-3)+1 = -5

so (3,-5)

hence the answer is (-3,-5) and (3,7)

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;

the correct answer is 1.7