<u><em>Answers:</em></u>
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle
<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape
Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes
<u>Let's check the choices:</u>
<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
This option is incorrect as dilation changes the lengths of the sides
<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
This option is correct as neither dilation nor rotation alters the measures of the angles
<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image
<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced
<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)
<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position
Hope this helps :)
The commission would be $2095.
Step-by-step explanation:
Given,
Commission on first $1000 = 7%
Amount of commission = 0.07*1000 = $70
Worth of sold items = $14,500
We will subtract $1000 from it.
Balance = 14500-1000 = $13500
Commission on balance = 15% = 0.15
Amount of commission = 0.15*13500
Amount of commission = $2025
Total commission = 70+2025 = $2095
The commission would be $2095.
Keywords: percentage, subtraction
Learn more about subtraction at:
#LearnwithBrainly
Answer:
The nth term of an AP will be 27 -7n.
Step-by-step explanation:
First five terms of the Arthemetic Sequence is given to us , which is 26 , 19 , 12 , 5
Hence here Common Difference can be found by subtracting two consecutive terms . Here which is 19 - 26 = (-7) .
Here first term is 26 .
And the nth term of an AP is given by ,
★ T_n = a + ( n - 1) d
<u>Subst</u><u>ituting</u><u> respective</u><u> values</u><u> </u><u>,</u>
⇒ T_n = a + ( n - 1 )d
⇒ T_n = 26 + (n - 1)(-7)
⇒ T_n = 26 -7n+1
⇒ T_n = 27 - 7n
<h3>
<u>Hence </u><u>the</u><u> </u><u>nth</u><u> </u><u>term</u><u> of</u><u> an</u><u> </u><u>AP</u><u> </u><u>can</u><u> </u><u>be</u><u> </u><u>found </u><u>using </u><u>T_</u><u>n</u><u> </u><u>=</u><u> </u><u>2</u><u>7</u><u> </u><u>-</u><u> </u><u>7</u><u>n</u><u>. </u></h3>
The second part of Rita's race is about 1800 meters at a speed of 150 meters per minute.
<h3>Speed</h3>
let
- distance covered in first Part = d1
- distance covered in second Part = d2
- distance covered in third Part = d3
- speed covered in first Part = s1
- speed covered in second Part = s2
- speed covered in third Part = s3
Distance in second Part:
d₃ = 15 x 300
= 4500 m
d₂ = 2/5 × d₃
= 2/5 x 4500
d₂ = 1800 meters
Speed in second part:
S₂ = 1800 m / 12 min
S₂ = 150 meters per minute
Learn more about distance:
brainly.com/question/4931057
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