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Dimas [21]
3 years ago
6

Square ABCD and square EFGH share a common center on a coordinate plane. is parallel to diagonal . Across how many lines of refl

ection can the combined figure reflect onto itself?.

Mathematics
2 answers:
Oduvanchick [21]3 years ago
7 0
Square ABCD and square EFGH will reflect onto themselves across 8 lines of reflection
Ludmilka [50]3 years ago
6 0

Answer:

<h2>4 lines of reflection.</h2>

Step-by-step explanation:

The complete problem states:

<em>Square ABCD and square EFGH share a common center on a coordinate plane. EH is parallel to diagonal AC. Across how many lines of reflection can the combined figure reflect onto itself?</em>

<em />

Basically, all diagonals work as lines of reflection of the figure, because we have squares which are complete symmetrical, and their diagonals always divide them in halves, creating a reflection.

So, the first two lines of reflection are the diagonals of the big square AC and BD. Due to square EFGH share a common center and EH is parallel to diagonal AC, bigger diagonals divide its side equally, creating reflections.

Also, based on the parallelism given, the diagonals of the small square will divide in half the sides of the big square, if we prolong them. So, there we have two more lines that create reflections.

In sum, there are 4 lines of the figure combined that reflect onto itself.

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A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the are
Katarina [22]

Answer: Area = 6m²

              Smaller number = 16

              Hours = 9.6 h

Step-by-step explanation:

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the area remains the same. Find the area of the rectangle.

1) w = x m                                2) w = x + 1 m

     l = x + 5  m                               l = x + 5 - 2 = x + 3 m

A₁ = A₂

A = w*l

A₁ = x(x+5) = x² + 5x

A₂ = (x+1)(x+2) = x² + x + 2x + 2 = x² + 3x + 2

A₁ = A₂

x² + 5x = x² + 3x + 2

5x - 3x = 2

2x = 2

x = 1

A₁ = x(x+5) = 1.6 = 6 m²

The ratio of two numbers is 2:5. If the larger number is 40, what is the smaller number.

<u> 2 </u> = <u> x </u>

5     40

5x = 80

x = 80/5 = 16

Sixteen construction workers can finish cementing a floor of a building in 3 hours. On a certain day, only 5 construction workers are available for the job. How long will it take the 5 construction workers to do the cementing job?

workers                      hours

    16                              3

     5                               x

↑                                          ↓              inversely proportional

<u> 5 </u> = <u> 3 </u>

16      x

5x = 16*3

5x = 48

x = 48/5

x = 9.6 h

 

6 0
3 years ago
Expanded form: (4a+4b)^3
TiliK225 [7]

Step-by-step explanation:

use the formula: (a+b)³ = a³+3a²b+3ab²+b³

and place the corresponding values.

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3 years ago
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stellarik [79]
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8 0
2 years ago
Find the exact length of the third side.<br> 41<br> 9 <br> what’s the other side
vazorg [7]

Step-by-step explanation:

{d}^{2}  =  {a}^{2}  +  {b}^{2}  \\ 41 = 9 +  {b}^{2}  \\  {b}^{2}  = 41 - 9 \\  {b}^{2}  = 32 \\ b =  \sqrt{32}  \\ b = 5.66 \:

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2 years ago
Sally is completely unprepared for a three-question multiple-choice pop quiz, so she randomly guesses the answer to each questio
timurjin [86]
There are 3 questions and 4 choices.
So she has 1/4 of a chance of getting each question right.
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8 0
3 years ago
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