Which system of equations is inconsistent? a) 2x+8y=6 5x+20y=2 b) 5x+4y=-14 3x+6y=6 c) x+2y=3 4x+6y=5 d) 3x-2y=3 6x-4y=4

Option A and D

Step-by-step explanation:

we know that

A system of equations is inconsistent, when the system has no solutions (because the lines are parallel) and the system is consistent when has at least one solution

Verify each case

case A) we have

2x+8y=6 > equation A

5x+20y=2 > equation B

Multiply the equation A by 2.5 both sides

2.5*(2x+8y)=6*2.5

5x+20y=15 > equation C

Compare equation B and equation C

5x+20y=2 > equation B

5x+20y=15 > equation C

the lines are parallel with different y-intercept

therefore

The system has no solution, hence the system is inconsistent

case B) we have

5x+4y=-14 > equation A

3x+6y=6 > equation B

Multiply equation A by 1.5 both sides

1.5*(5x+4y)=-14*1.5

7.5x+6y=-21 > equation C

Compare equation B and equation C

3x+6y=6 > equation B

7.5x+6y=-21 > equation C

The lines are different (their slopes are not equal)

therefore

The system has only one solution, hence the system is consistent

case C) we have

x+2y=3 > equation A

4x+6y=5 > equation B

Multiply by 3 equation A both sides

3*(x+2y)=3*3

3x+6y=9 > equation C

Compare equation B and equation C

4x+6y=5 > equation B

3x+6y=9 > equation C

The lines are different (their slopes are not equal)

therefore

The system has only one solution, hence the system is consistent

case D) we have

3x-2y=3 > equation A

6x-4y=4 > equation B

Multiply equation A by 2 both sides

2*(3x-2y)=3 *2

6x-4y=6 > equation C

Compare equation B and equation C

6x-4y=4 > equation B

6x-4y=6 > equation C

the lines are parallel with different y-intercept

therefore

The system has no solution, hence the system is inconsistent

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

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: