MATHEMATICS HIGH SCHOOL

Given the equation 4x + 2y = 9, which equation below would cause an inconsistent-independent system?A:6x + 12y = 13
B: 2x + y = -6
C:x - 2y = 7
D:8x - 4y = -5

Answers

Answer 1
Answer: Inconsistent-independent system means that there are no solutions.
Graphically the lines of those equations will never cross - the lines are parallel.

So when the two lines are parallel?
When they have the same A factors.

So when you have an equation 4x+2y=9 we need to rewrite it to
y= -2x+9/2
So the A factor is -2 (it is the number with x) and the B factor is 9/2

So all we need to do now is to find an equation with the same A factor.

Lets rewrite equations in answers:
A: 6x+12y=13 -> y=-1/2x+13/12 A=-1/2 - so it is not an equation we are looking for
B: 2x+y=-6 -> y=-2x-6 A=-2 - this is an equation we were looking for.
C: x-2y=7 -> y=1/2x-7/2 A=1/2 - so it is also not a good answer

The answer is B: the equation 2x+y=-6 will cause the inconsistent-independent system with the given equation.

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The table below shows data from a survey about the amount of time, in hours, high school students spent reading and the amount of time spent watching videos each week (without reading): Reading Video
3 1
3 2
4 3
5 4
6 6
7 7
10 8
12 8
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30 15

Which response best describes outliers in these data sets?
A, Reading has a suspected outlier in the 30-hour value.
B. Reading has a suspected outlier in the 30-hour value, and video has a possible outlier in the 15-hour value.
C. Neither data set has suspected outliers.
D. The range of data is too small to identify outliers.

Answers

Reading: 3, 3, 4, 5, 6, 7, 10, 12, 14, 30
Video:      1, 2, 3, 4, 6, 7,   8,   8,   9, 15

                         Reading               Video
Minimum          3                               1
1st quartile       4                               3
Median             6.5                            6.5
3rd quartile      12                             8
Maximum         30                           15
IQR                    8                               5
Outliers             30                           no outliers

A, Reading has a suspected outlier in the 30-hour value. 

Answer:

The correct option is: A,B

Step-by-step explanation:

" An outlier is a odd value which on removing from the data leads to the less mean as calculated mean on including that value ".

There are total 10 data points.

  • The table for reading is given as:

3    3    4    5    6     7    10    12    14    30

The mean of this data is given by:

(3+3+4+5+6+7+10+12+14+30)/(10)=(94)/(10)=9.4

Also the mean after omitting the odd value i.e. 30 we get:

(3+3+4+5+6+7+10+12+14)/(9)=(64)/(9)=7.11

Hence, there is a change in its mean;

Hence the outlier for reading is 30.

  • The table for Video is given by:

1     2     3    4    6    7      8    8     9    15

The possible maximum value here is 15 so we will check whether it is an outlier or not.

The mean of this data is given by:

(1+2+3+4+6+7+8+8+9+15)/(10)=(63)/(10)=6.3

Also the mean after omitting the odd value i.e. 15 we get:

(1+2+3+4+6+7+8+8+9)/(9)=(48)/(9)=5.33

Hence, there is a change in its mean hence 15 is an outlier.

Hence option A and B are true.

The three lengths of four triangles are given. Which triangle is a right triangle?

Answers

A 3-4-5 right triangle is a triangle whose side lengths are in the ratio of 3:4:5. In other words, a 3-4-5 triangle has the ratio of the sides in whole numbers called Pythagorean Triples.

What is the equation of -1/2 that passes through the point (6,-6) Options are ..1) y= 1/2x-3
2) y= -1/2x+3
3) y= -1/2x-3
4) y= -2x-3

Please explain why the answer is what it is.

Answers

formula of the line is
 y = mx + c
we know y, m and x, find c

-6 = - (1)/(2)(6) + c
-6 = -3 + c
-6 + 3 = -3 + 3 + c
-3 = c

y = - (1)/(2) x - 3

Answer is the third one.

Find an equivalent function to f(x) = 5(3)3x. f(x) = 125x(27)x
f(x) = 152x
f(x) = 5(27)x
f(x) = 135x

Answers

If you would like to find an equivalent function to f(x) = 5(3)^(3x), you can do this using the following steps:

f(x) = 5(3)^(3x) = 5(3^(3x)) = 5(27)^x = 5(27)x

The correct result would be f(x) = 5(27)x.

Answer:

The correct result would be f(x) = 5(27)x.

Step-by-step explanation:

Name the correct property of (-5)(-3)=(-3)(-5)

Answers