Determine the number and type of solutions for the following quadratic equations using the discriminant. x^2-6x+5 = -11
x^2= 24x+ 50
4x^2 – 8x + 10 = 0
15x^2 + 2 = 7x^2 +8x

Acompany wants to reduce the dimensions of its logo by one fourth to use on business cards. if the area of the original logo is 4 square inches, what is the area of the logo that will be used on the business cards?

Which number line represents the solution set for the inequality - x 24?

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)