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3 years ago

Lines k and l are parallel and the measure of angle ABC is 22 degrees. Find the measure of the other angles.

Mathematics

2 answers:

pychu [463]3 years ago

7 0

Answer:

22°

Step-by-step explanation:

Alternate interior angles are equal to each other

Ne4ueva [31]3 years ago

5 0

Answer:

Option B, 22

Step-by-step explanation:

Alternate interior angles are same

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Which is the approximate solution to the system y = 0.5x + 3.5 and y = − 2/3 x + 1/3 shown on the graph? (–2.7, 2.1) (–2.1, 2.7)

AlekseyPX

Answer:

The approximate solution to the system is $(-2.7, 2.1)$ .

Step-by-step explanation:

To solve the system of equations $\begin{bmatrix}y=0.5x+3.5\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$ you must:

$\mathrm{Rationalize\:equations}\\\\\begin{bmatrix}y=\left(\frac{1}{2}\right)x+\left(\frac{7}{2}\right)\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}$

$\mathrm{Subsititute\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\begin{bmatrix}-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\\\\-\frac{2}{3}x=\frac{19}{6}+\frac{1}{2}x\\\\-\frac{7}{6}x=\frac{19}{6}\\\\6\left(-\frac{7}{6}x\right)=\frac{19\cdot \:6}{6}\\\\-7x=19\\\\x=-\frac{19}{7}\approx-2.7$

$\mathrm{For\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\mathrm{Subsititute\:}x=-\frac{19}{7}\\\\y=-\frac{2}{3}\left(-\frac{19}{7}\right)+\frac{1}{3}\\\\y=\frac{15}{7}\approx 2.1$

The approximate solutions to the system of equations are:

$x=-2.7 ,\:y=2.1$

5 0

3 years ago

Read 2 more answers

Consider the two data sets below:

alina1380 [7]

Answer:

Option c) The data sets will have the same values of their interquartile range.

Explanation:

1. The values are in order: they are in increasing oder, from lowest to highest value.

2. Calculate the interquartile range.

Interquartile range, IQR, is the third quartile, Q3, less the first quartile Q1:

IQR = Q3 - Q1

To find the first and the third quartile, first find the median:

Data Set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59

[19, 25, 35, 38], 41, [49, 50, 52, 59]

↑

median = 41

Data Set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99

[19, 25, 35, 38] , 41, [49, 50, 52, 99]

↑

median = 41

Now find the median of each subset: the values below the median and the values above the median.

Data set 1: First quartile

[19, 25, 35, 38],

↑

Q1 = [25 + 35] / 2 = 30

Third quartile

[49, 50, 52, 59]

↑

Q3 = [50 + 52] / 2 = 51

IQR = Q3 - Q1 = 51 - 30 = 21

Data set 2: First quartile

[19, 25, 35, 38]

↑

Q1 = [25 + 35] / 2= 30

Third quartile

[49, 50, 52, 99]

↑

Q3 = [52 + 50]/2 = 51

IQR = 51 - 30 = 21

Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)

This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.

An outlier will change the range because the range is the maximum value less the minimum value.

5 0

3 years ago

Sorry, the last one wasn’t showing the picture. Is this a function or not? Also tell me how you got the answer. TwT ty

kap26 [50]

Answer:

yes this is a function

Step-by-step explanation:

simple method to find if something is a function

if you can draw a vertical line at any point on the graph and get two intersections, it is not a function

7 0

3 years ago

Ben writes the number 74,443. The value of the digit 4 in the hundreds place is 10 times the value of the digit 4 is what place

Minchanka [31]

Place Value Going to Left of Decimal:

Decimal
Ones
Tens
Hundreds
Thousands
Ten-Thousands

The middle 4 in 74,443 is in the hundreds place. The 4 next to the 3 is in the tens place.

The 4 in the tens place is worth 40. 40 * 10 would equal the 400 in the hundreds place.

ANSWER: tens place

Hope this helps! :)

6 0

3 years ago

Need help with this asap!

My name is Ann [436]

Answer:

Step-by-step explanation:

1 ) 2 + 7t [ there are no like terms , so no further simplifying ]

2) 6r + ( - 16 r )

= 6 r - 16 r [ both are like terms ]

= - 10 r

3) (3x + 2 ) + ( 2x - 4 )

= 3x + 2 + 2x - 4

= 3x + 2x - 4 + 2 [ arranging like terms together ]

= 5x - 2

4) (8 n² - 3 n + 6 ) + ( n - 2 )

= 8n² - 3n + 6 + n - 2

= 8n² - 3n + n + 6 - 2 [ bringing like terms together ]

= 8n² - 2n + 4

6 0

3 years ago

Read 2 more answers