Type the correct answer in the box use/ for the fraction bar y=x^2-2x-19 y+4x=5 the pair of the points representing the solution set of the system of equation is (-6,29) and

see explanation

Step-by-step explanation:

given the 2 equations

y = x² - 2x - 19 → (1)

y + 4x = 5 → (2)

substitute y = x² - 2x - 19 into (2)

x² - 2x - 19 + 4x = 5 ( subtract 5 from both sides )

x² + 2x - 24 = 0 ← in standard form

(x + 6)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 4 = 0 ⇒ x = 4

substitute each value of x into (1) for corresponding y- coordinate

x = - 6 : y = (- 6)² - 2(- 6) - 19 = 36 + 12 - 19 = 29 ⇒ (- 6, 29)

x = 4 : y = 4² - 2(4) - 19 = 16 - 8 - 19 = - 11 ⇒ (4, - 11)

the solutions are (- 6, 29), (4, - 11)

answer: it's upside down and i can't read it

step-by-step explanation:

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;