Answer:
36
Step-by-step explanation:
consecutive even numbers are 2,4, 6...
Let the smallest of the 3 numbers be x.
2nd number= x+2
3rd number
=x+2+2
= x+4
sum of the 3 numbers= x +x+2 +x+4
114= 3x+6
3x= 114 -6 (-3 on both sides)
3x= 108 (simplify)
x= 108 ÷3
x= 36
Thus, the smallest number is 36.
Let's check!
36+38+40= 114 ✓
Answer:
119
Step-by-step explanation:
The nearest whole numbers from those listed are
10
3
106
The estimated sum = 119
The actual sum is 118.668
When you are doing a test, being able to estimate is a very powerful skill. 119 is close enough to the actual answer that you know your actual answer is likely correct.
Answer:
See below.
Step-by-step explanation:
f(x) = -25x2 + 30x − 9
This is a parabola which opens downwards.
Part A.
The discriminant b^2 - 4ac = 30^2 - 4*(-25) * -9
= 900 - 900
= 0
This indicates that the graph of the function just touches the x-axis. So there is one root of multiplicity 2.
Factoring:
-25x2 + 30x − 9
= -(25x^2 - 30x + 9)
= -(5x - 3)(5x - 3)
so the roots are x = 3/5 multiplicity 2.
The x -intercept is at (0.6, 0).
Part B.
The y intercept is when x = 0 so here it is
y = -25(0)^2 + 30(0) -9
= -9
The constant at the end of the function (-9) indicates the y-intercept.
The y intercept is at (0, -9).
Part C.
The end behaviour of f(x):
The negative coefficient (-25) of x^2 indicates that the graph increases from negative infinity from the left.
Since it is a parabola that opens downwards ( because of the -25) it decreases to negative infinity on the right.
Answer: Scientific inquiry refers to the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work. Inquiry also refers to the activities of students in which they develop knowledge and understanding of scientific ideas, as well as an understanding of how scientists study the natural world. National Science Education Standards, p. 23.
As pointed out in the National Science Education Standards (National Research Council, 1996), students who use inquiry to learn science engage in many of the same activities and thinking processes as scientists who are seeking to expand human knowledge of the natural world. Yet the activities and thinking processes used by scientists are not always familiar to the educator seeking to introduce inquiry into the classroom. By describing inquiry in both science and in classrooms, this volume explores the many facets of inquiry in science education. Through examples and discussion, it shows how students and teachers can use inquiry to learn how to do science, learn about the nature of science, and learn science content.
A good way to begin this investigation is to compare the methods and thinking process of a practicing scientist with the activities of an inquiry-based science lesson. The stories in this chapter set the stage for many of the themes to follow. The sidebars suggest some important aspects of the investigations of both scientists and students.
INQUIRY IN SCIENCE
A geologist who was mapping coastal deposits in the state of Washington was surprised to discover a forest of dead cedar trees near the shore. A significant portion were still standing, but they clearly had been dead for many years. He found similar
1 yard = 3 feet
2/3 of a yard would be 2 feet
4.5 yards = 13.5 feet
13.5-2 = 11.5 feet
11.5 feet = 3.83 yards
therefore at least 11.5 feet or 3.83 yards must be purchased
