Which point represents the quotient of 3-1?

A
B
C
D

#1) A

#2) B

#3) C

#5) A

#7) D

#10) D

#11) D

#14) A

#15) D

#16) A

#19) D

Explanation

#1)  If the data set is linear, the slope will be constant throughout the entire data set.  For data set A, the slope between the first two points is:

m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2

Between the second two points,

m=(4-1)/(5-3) = 3/2

Between the third pairs of points,

m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set.  The set is also increasing; as x increases, y increases as well.

#2)  Substituting 4 for y and 1 for x,

y = (x+1)²

4 = (1+1)² = 2²

9 = (1+2)² = 3²

16 = (1+3)² = 4²

This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t.  Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term.  If the common difference is 2, this means that 2 was added each time.  This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:

m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have

3=(d-5)/(4-2)

3=(d-5)/2

Multiply both sides by 2:

3*2 = ((d-5)/2)*2

6 = d-5

Add 5 to both sides:

6+5 = d-5+5

11 = d

#11) Using point slope form,

y-y₁ = m(x-x₁)

y-1 = 3(x--2)

y-1 = 3(x+2)

Using the distributive property,

y-1 = 3*x + 3*2

y-1 = 3x + 6

Add 1 to both sides:

y-1+1 = 3x+6+1

y=3x+7

#14) If two lines are parallel, they have the same slope.  The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped).  The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2.  The only one with this slope is D.

#16)  The two equations are not the same, so there are not infinitely many solutions.  The variables do not both cancel, so there is at least one solution.  This only leaves one solution as the answer.

#19)  Using 1 for 7 and 4 for x, we check each equation.  The only one that comes out correct is D.

Step-by-step explanation:

21

step-by-step explanation:

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: