45. which research method would be the best to study the effect of sugar on the freezing point of milk?\na…
45. which research method would be the best to study the effect of sugar on the freezing point of milk?\na. a census\nb. an experiment\nc. a sample survey\nd. an observational study\n46. neil is asked to solve the following system of equations using elimination.\n2x - y = 2\\3x + y = 13\nwhat is the solution to this system of equations? type your answer in the boxes below.\nx = \n y = \n47. which of these equations has two solutions?\na. \\sqrt{x}+5 = 0\nb. x = \\sqrt{2 - x}\nc. x = \\sqrt{5x - 4}\nd. x - 5 = 4\\sqrt{x}\n48. a smoothie shop offers two sizes of smoothies. a small smoothie costs $4, and a large smoothie costs $6. on a particular day, the shop sold 50 smoothies and collected $236. which of the following systems of equations can be used to determine the number of small smoothies, x, and the number of large smoothies, y, sold?\nx + y = 236\\4x + 6y = 50\nx + y = 236\\6x + 4y = 50\nx + y = 50\\4x + 6y = 236\nx + y = 50\\6x + 4y = 236
Answer
45.
Brief Explanations:
An experiment can manipulate the amount of sugar to observe its effect on the freezing - point of milk, controlling other variables. A census is for collecting data on an entire population, a sample survey is for gathering opinions or data from a sample, and an observational study just observes without manipulation.
Answer:
B. An experiment
46.
Explanation:
Step1: Add the two equations
Adding (2x - y=2) and (3x + y = 13) eliminates (y). ((2x - y)+(3x + y)=2 + 13), which simplifies to (5x=15).
Step2: Solve for (x)
Dividing both sides of (5x = 15) by 5 gives (x = 3).
Step3: Substitute (x = 3) into the first equation
Substitute (x = 3) into (2x - y=2), we get (2\times3 - y=2), which is (6 - y=2).
Step4: Solve for (y)
Subtract 6 from both sides: (-y=2 - 6=-4), so (y = 4).
Answer:
(x = 3) (y = 4)
47.
Explanation:
Step1: Analyze option A
For (\sqrt{x}+5 = 0), we have (\sqrt{x}=-5). Since the square - root of a non - negative number (x\geq0) is non - negative, there are no real solutions.
Step2: Analyze option B
Square both sides of (x=\sqrt{2 - x}), we get (x^{2}=2 - x), or (x^{2}+x - 2=0). Factoring gives ((x + 2)(x - 1)=0), so (x=-2) or (x = 1). But when (x=-2), the left - hand side is (-2) and the right - hand side is (\sqrt{2-(-2)} = 2), so (x=-2) is an extraneous solution, and there is 1 solution ((x = 1)).
Step3: Analyze option C
Square both sides of (x=\sqrt{5x - 4}), we get (x^{2}=5x - 4), or (x^{2}-5x + 4=0). Factoring gives ((x - 1)(x - 4)=0), so (x = 1) or (x = 4). Both values satisfy the original equation, so there are 2 solutions.
Step4: Analyze option D
Let (t=\sqrt{x}(t\geq0)), then the equation (x - 5=4\sqrt{x}) becomes (t^{2}-4t - 5=0). Factoring gives ((t - 5)(t+1)=0), so (t = 5) or (t=-1). Since (t\geq0), (t=-1) is extraneous, and when (t = 5), (x = 25), so there is 1 solution.
Answer:
C. (x=\sqrt{5x - 4})
48.
Explanation:
The total number of smoothies sold is the sum of small and large smoothies, so (x + y=50). The total money collected is the sum of the money from small smoothies ((4x)) and large smoothies ((6y)), so (4x + 6y=236).
Answer:
(x + y=50\4x+6y=236)