Which statement completes step 6 of the proof?


Coordinate plane with line f at y equals 3 times x plus 1 and line g at y equals negative one third times x plus 1. Triangle JKL is at J negative 1 comma negative 2, K 0 comma 1, and L 0 comma negative 2. Triangle J prime K L prime is at J prime negative 3 comma 2, K 0 comma 1, and L prime negative 3 comma 1.



Step 1 segment KL is parallel to the y-axis, and segment JL is parallel to the x-axis.

Step 2 ΔJKL was rotated 90° clockwise to create ΔJ'KL'. Point K did not change position, so it remains point K. Therefore, ΔJKL ≅ ΔJ'KL'.

Step 3 segment K L prime is perpendicular to the y-axis, and segment J prime L prime is perpendicular to the x-axis.

Step 4 segment JK lies on line f and has a slope of 3.

Step 5 segment J prime K lies on line g and has a slope of negative one third.

Step 6 ?

A. The product of the slopes of segment JK and segment J prime K is −1; therefore, lines f and g are perpendicular.

B. The slopes of segment JK and segment J prime K are congruent; therefore, lines f and g are parallel.

C. The product of the slopes of segment KL and segment K L prime is −1; therefore, lines f and g are perpendicular.

D. The slopes of segment KL and segment K L prime are congruent; therefore, lines f and g are parallel.

the answear us true im preety sure

Answer: 252

Step-by-step explanation:

You just multiply 84 by two and then ad another 84.

The scale factor is 4.

Important information:

From the given figure it is clear that:

DG = 2

D'G' = 8

The scale factor is:

[tex]k=\dfrac{D'G'}{DG}[/tex]

[tex]k=\dfrac{8}{2}[/tex]

[tex]k=4[/tex]

Therefore, the scale factor is 4.

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Answer: 1/6

Step-by-step explanation: To find the probability of rolling a six,

let's use our ratio for the probability of an event.

number of favorable outcomes / total number of outcomes

Since only one side of a die has a six on on it, the number of favorable

outcomes for rolling a six is 1 and since there are six sides to a die and it's

equally likely that the die will landy on any of these sides, the total number

of outcomes is 6.

So the probability of rolling a six is 1/6.

Answer:

-0.86

Step-by-step explanation:

Answer:

x = 90 degrees

y = 28 degrees

Step-by-step explanation:

x: all the angles in the middle are 90

y: 180 - 90 - 62 = 28

Answer:

[tex] (45 - 5) \div 5 + {6}^{2} \\ 40 \div 5 + {6}^{2} \\ 8 + {6}^{2} \\ 8 + 36 \\ 44 \: answer [/tex]

Answer:

faster then the other one

Answer: B 1/3

Step-by-step explanation:

For every 3x it travels 1 y so you will get 1/3 as your answer.

At 50y the line is at 10x.  By the time it is at 60 y it is at 40x.  This was a change in y by 10 and change in x by 30.  There fore the answer is 10/30 or 1/3.

Answer:

1/3

Step-by-step explanation:

(10,50),(40,60)

When you find the slope of the two points, you'll get 1/3

Answer:

x = 5.4

Step-by-step explanation:

3/x = 4/7.2

cross-multiply:

4x = 21.6

x = 5.4

Answer:

5.6

Step-by-step explanation:

First five prime numbers are 2, 3, 5, 7 and 11. The mean or the average formula is = Sum/number of items = (2 + 3 + 5 + 7 +11)/5 = 5.6

Solution :

Number      Values (X)       [tex]$\sum (X_i - \bar X)^2$[/tex]

    1               121.5            193494.4144

   2               138.9            178489.3504

   3                155.7    164576.2624

   4           172            151616.7844    

   5               172.9            150916.7104

  6              196.5             133137.4144

   7              202.3            128938.4464

  8              202.7            128651.3424

  9              334.5            51474.5344

  10               504            3292.4644

   11              563.7              5.3824

   12       574.1              161.7984

   13                935           139591.9044

  14              952.6        153053.0884

   15     3194.3           6932267.726

Total             8420.7         8509667.624

Mean [tex]$\bar X = \sum \frac{X_i}{n}$[/tex]

              [tex]$=\frac{8420.7}{15}$[/tex]

              = 561.38

Median :

[tex]$Q_2 = \left(\frac{1}{2}n+\frac{1}{2}\right)^{th}$[/tex]value

     [tex]$ = \left(\frac{1}{2}\times 15+\frac{1}{2}\right)^{th}$[/tex]value

    = 202.7

Percentile = [tex]$\left(\frac{P}{100} \times n + \frac{1}{2}\right)^{th}$[/tex]  value

                 = [tex]$\left(\frac{50}{100} \times 15 + \frac{1}{2}\right)^{th}$[/tex] value

                 = 202.7

Percentile = [tex]$\left(\frac{P}{100} \times n + \frac{1}{2}\right)^{th}$[/tex]  value

                 = [tex]$\left(\frac{40}{100} \times 15 + \frac{1}{2}\right)^{th}$[/tex] value

                 = 198.82

Percentile = [tex]$\left(\frac{P}{100} \times n + \frac{1}{2}\right)^{th}$[/tex]  value

                 = [tex]$\left(\frac{90}{100} \times 15 + \frac{1}{2}\right)^{th}$[/tex] value

                 = 1849.28

[tex]$Q_1 = \left(\frac{1}{4}n+\frac{1}{4}\right)^{th}$[/tex]value

     [tex]$ = \left(\frac{1}{4}\times 15+\frac{1}{4}\right)^{th}$[/tex]value

    = 172

[tex]$Q_3 = \left(\frac{3}{4}n+\frac{3}{4}\right)^{th}$[/tex]value

     [tex]$ = \left(\frac{3}{4}\times 15+\frac{3}{4}\right)^{th}$[/tex]value

    = 574.1

Therefore, the range = highest value - lowest value

                                  = 3194.3 - 121.5

                                  = 3072.8

Now the interquartile range = [tex]$Q_3-Q_1$[/tex]

                                              = 574.1 - 172

                                             = 402.1

Answer:

6

Step-by-step explanation:

I just learned about this yesterday. The line inside of the box is the median. The left side of the box, on the number 2, is the lower quartile. The dot on the line to the left, outside of the box, is above the smallest value. The right side of the box is the upper quartile. The line outside of the box on the right is the highest value. Hope this helps!

Answer:

B & D

Step-by-step explanation:

-3 (0.15 - 0.2 + 0.25p) = - 3 * 0.15 - (-3) * 0.2 + (-3) * 0.25p

-0.45 + 0.6 - 0.75p = 0.15 - 0.75p = -3 (-0.05 + 0.25p}

Answer:

1. Mean = 55.8

Median = 23

Mode = None

2. Mean = 2.1

Median = 1.4

Mode 0.5

3. Mean = 4.5

Median = 4.5

Mode = 1,4, 5, 8

4. Mean 68

Median 58

Mode = 0

Step-by-step explanation:

Mean = 17 + 25 + 23 + 200 + 14 / 5 = 279/5 = 55.8

Median= Because its odd you put them in order 17, 14, 23, 25, 200 = 23 because it is the middle number. Mode = None

2. Mean = 0.5 + 1.4 + 3.0 + 7.0 + 0.5 +1.8 + 0.5 = 14.7 = 14.7/7 = 2.1

Median = because it is odd you put them in order 0.5, 0.5, 0.5, 1.4, 1.8, 3.0, 7.0 = 1.4 The mode is 0.5 because it repeats three times

3. Mean = 1 + 8 + 5 + 4 + 1 + 8 + 5 + 4 = 36/8 =4.5

Median = Because its even you divide by the two middle numbers = 1, 1, 4,4, 5, 5 , 8 , 8 = 4+5 = 9/2 = 4.5 Mode = 1, 4, 5, and 8 are the numbers that are repeated most often.

Mean = 0+78+99+58+65+0+47+38+227 = 68 Median, Because there is an odd number you get the odd number from the middle. 0, 0, 38, 47, 58, 65, 78, 99, 227 = 58 Mode = 0 because it repeats more often.

Sorry I kept commenting I'm new to this platform!

Answer:

259.80 dollars was deposited from his last pay check and he will have saved 6235.20 dollars in total

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

It's decreasing by 7

The relation is the descending the series by 7 and the next term is 33.

We have to determine, find the pattern and what numbers come next

We have given that, 61, 54, 47, 40.

What is the series?

A series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other.

61-54=7

54-47=7

47-40=7

So the next term is

40-7=33

Therefore the relation is the descending the series by 7 and the next term is 33.

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Answer:

think its 4 and 6

Step-by-step explanation:

Please open each section so i can answer

Answer:

Step-by-step explanation:

Answer:

500 grams

Step-by-step explanation:

2.5 kg = 5 loaves

1 loaf = 2.5/5 = 0.5 kg

0.5 kg = 500 grams

Answer:

12

Step-by-step explanation:

For these problems you should use the pythagorean theorem: a^2+b^2=c^2

In this case, 13=c and 5=a

so:

5^2+x^2=13^2

25+x^2=169

subtract 25 from both sides

x^2=144

√144=12

missing side=12

Answer:

the answer is 17

Step-by-step explanation:

2w-10=24

10+24=34

34/2=17

so w=17

Answer:

w=17

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

The final temperature was -18 °F if it decreased by 5 degrees.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The temperature was -13 °F and then dropped 5 degrees.

As per the question, we have data as follows:

The initial temperature = -13 °F

The changed temperature = -5 °F (negative sign indicates temp dropped)

Final temperature = initial temperature + changed temperature

Final temperature = -13 °F + (-5 °F)

Final temperature = -13 °F - 5 °F

Apply the addition operation, and we get

Final temperature = -18 °F

Therefore, the final temperature was -18 °F.

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#SPJ2

Answer:

The length of Louis's basement is 85 feet.

Step-by-step explanation:

The area of the basement, A = 4,335 square feet

The width of the basement is  3/5 its length.

Let length be l.

Width = (3/5)l

The area of the basement is given by :

[tex]A=l\times b\\\\4,335 =l\times \dfrac{3}{5}l\\\\4,335 =\dfrac{3}{5}l^2\\\\l^2=\dfrac{4,335 \times 5}{3}\\\\l=\sqrt{\dfrac{4335\times5}{3}}\\\\l=85\ ft[/tex]

So, the length of Louis's basement is 85 feet.

Answer: 8x62 i found this so here is why this is correct hope it helps!

( I am a middle schooler btw)

Step-by-step explanation: 8 x 60 = 480 + 2 =482 so 8 x 62 is correct

Answer:

point b

Step-by-step explanation

piont b can go to piont e

Answer:

B

Step-by-step explanation:

Go through each point and see which ones works:

Answer:

-107

Step-by-step explanation:

x4-5^3+ 3^2-2x + 7

2x−109/x−1

1   2   −109

    2

second step

1   2                    -109

                    1 * 2 = 2

    2 (-109) + 2 = -107

Coefficients are 2, and -107

Therefore the quotient is 2 and the remainder is -107

Answer:

True

Step-by-step explanation:

Answer:

[tex] \frac{1}{ 2\sqrt{7} } [/tex]

Step-by-step explanation:

[tex] \lim_{x\to 0} \frac{ \sqrt{x + 7} - \sqrt{7} }{x} \\ \\ = \lim_{x\to 0} \frac{( \sqrt{x + 7} - \sqrt{7}) }{x} \times \frac{( \sqrt{x + 7} + \sqrt{7}) }{( \sqrt{x + 7} + \sqrt{7}) } \\ \\ = \lim_{x\to 0} \frac{( \sqrt{x + 7} )^{2} - (\sqrt{7})^{2} }{x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{( {x + 7} - {7}) }{x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{ {\cancel x}}{\cancel x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{ {1}}{\sqrt{x + 7} + \sqrt{7}} \\ \\ = \frac{1}{ \sqrt{0 + 7} + \sqrt{7} } \\ \\ = \frac{1}{ \sqrt{7} + \sqrt{7} } \\ \\ = \frac{1}{ 2\sqrt{7} } [/tex]