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Oksanka [162]
2 years ago
15

$abcd$ is a square. how many squares have two or more vertices in the set $\{a, b, c, d\}$?

Mathematics
2 answers:
marshall27 [118]2 years ago
7 0
There are 4 squares having a side corresponding to a side of square abcd.

There are 4 squares having a side corresponding to the diagonals of square abcd.

And then the original square

Therefore, there are 4 + 4 + 1 = 9 squares <span>having two or more vertices in the set {a, b, c, d}.</span>
Vadim26 [7]2 years ago
7 0

Answer:

13

Step-by-step explanation:

There are (4 choose 2) = 6 ways to choose two points P and Q from the set of four points {A, B, C, D}. Two squares can be formed with P and Q as adjacent vertices (one on each side of PQ), and one square can be formed with P and Q as opposite vertices. This gives us 6 x 3 = 18 squares total.

However, we must subtract repeats. We see that the original square ABCD is counted 6 times, so the number of actual squares is 18 - 5 = 13.

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The situation will be represented by linear equation, this is given by:
y=ax+b
where:
a=slope=rate
b=y-intercept
from our situation:

a=-1/20
b=5 ft
thus the equation modeling the situation will be:
y=-1/20x+5

Answer: y=-1/20x+5
3 0
2 years ago
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3.274 x 10^3 as an ordinary number
Alborosie

Answer:

327.4

Step-by-step explanation:

All you have to do to simplify a number written in scientific notation is to move the decimal place to the left (if the number is negative) and to the right (if the number is positive).

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2 years ago
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A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can
Lady_Fox [76]

Answer:

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

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In the real world, length and width only make sense when they are positive. For that to be the case, the width must be greater than 2. There is nothing in the description that restricts the values to integers.

8 0
2 years ago
Randolph is creating parallelogram WXYZ so that XY has an equation of y = 2 over 3x −5. Segment WZ must pass through the point (
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Step-by-step explanation:

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2 years ago
Solve the system using elimanation: 5x + 4y = 12. 3x -3y = 18
Scorpion4ik [409]
If you would like to solve the system of equations 5x + 4y = 12 and 3x - 3y = 18 using elimination, you can do this using the following steps:

<span>5x + 4y = 12    /*3
3x - 3y = 18    /*4
_____________
15x + 12y = 36
12x - 12y = 72
_____________
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
x = 4

</span><span>3x - 3y = 18
</span>3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
3y = -6
y = -6/3
y = -2

(x, y) = (4, -2)

The correct result would be: x = 4 and y = -2.
4 0
2 years ago
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