Albert wants to show that tan(theta)sin(theta)+cos(theta)=sec(theta). He writes the following proof:tan(theta)sin(theta)+cos(theta)=sec(theta)sin(theta)/cos(theta) sin(theta)+cos(theta)=sec(theta)sin^2(theta)/cos(theta)+cos(theta)=sec(theta)What is the next step in this proof?A.) He should write tan(theta)=sin(theta)/cos(theta) to find a common denominator.B.) He should write cos(theta)=cos^2(theta)/cos(theta) to find a common denominator.C.) He should write cos(theta)=1-sin(theta) to convert all the terms to sine.D.) He should write sin(theta)=1-cos(theta) to convert all the terms to cosine.

Question
solved
general 11 months ago 6464

Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.

Question
solved
general 11 months ago 1370

A researcher randomly surveyed two separate age groups to determine the number of hours teens spend on the Internet each week. The results are shown in this table. 13- to 14-year-olds 12 8 7 8 9 6 7 7 9 10 15- to 16-year-olds 15 6 21 12 13 12 8 9 7 10 Based on these results, which conclusions can you draw about these two groups of teens? Select each correct answer. A. On average, 15- to 16-year-olds spend a few hours more on the Internet each week compared to 13- to 14-year-olds. B. On average, 15- to 16-year-olds spend a few hours less on the Internet each week compared to 13- to 14-year-olds. C. On average, the two groups of teens spend about the same amount of time each week on the Internet. D. The amount of time that 15- to 16-year-olds spend on the Internet each week is more variable than the amount time 13- to 14-year-olds spend. E. The amount of time 15- to 16-year-olds spend on the Internet each week is less variable than the amount time 13- to 14-year-olds spend. F. The amount of time that the two groups spend on the Internet each week varies by about the same amount.

Question
solved
general 11 months ago 5770

Albert wants to show that tan(theta)sin(theta)+cos(theta)=sec(theta). He writes the following proof: tan(theta)sin(theta)+cos(theta)=sec(theta) sin(theta)/cos(theta) sin(theta)+cos(theta)=sec(theta) sin^2(theta)/cos(theta)+cos(theta)=sec(theta) What is the next step in this proof? A.) He should write tan(theta)=sin(theta)/cos(theta) to find a common denominator. B.) He should write cos(theta)=cos^2(theta)/cos(theta) to find a common denominator. C.) He should write cos(theta)=1-sin(theta) to convert all the terms to sine. D.) He should write sin(theta)=1-cos(theta) to convert all the terms to cosine.

Question
solved
general 11 months ago 5355