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BigorU [14]
3 years ago
14

You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board wi

th T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

You might be interested in
Which is the simplified form of the expression 3(7/5x+4) - 2(3/2 - 5/4x)?
Kruka [31]

Answer:

B. \frac{67}{10} x + 9

Step-by-step explanation:

Simplify the expression. Remember to go by the order of operations, or PEMDAS.

1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

3(\frac{7}{5} x + 4) -2 (\frac{3}{2} -\frac{5}{4} x)

\frac{21}{5}x + 12  - \frac{6}{2} + \frac{10}{4} x

\frac{21}{5} x + 12 - 3 + \frac{10}{4} x

2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

\frac{21}{5} x + 9 + \frac{10}{4}x \\\frac{84}{20}x + \frac{50}{20}x + 9 \\\frac{134}{20}x + 9 \\\frac{67}{10}x + 9

Thus, the answer is \frac{67}{10} x + 9.

8 0
3 years ago
How many distinguishable ways can you arrange the letters in the word "MISSISSIPPI"?
Ipatiy [6.2K]
34,650 is the answer, I think
3 0
3 years ago
Read 2 more answers
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Ivahew [28]
Check the picture below.

\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D

\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D

7 0
3 years ago
Guys pls help me im failing my grade and i really need help plsssss and dont do it for the points
Nataliya [291]

Answer:

simplified:  \frac{3}{5}

unsimplified:  \frac{12}{20}

Step-by-step explanation:

Since the fractions have the same denominator, all we have to do is subtract the numbers in the numerator:

15 - 3 = 12

The difference of the two fractions is \frac{12}{20}. To simplify this answer, divide both the numerator and the denominator by 4:

12/4 = 3

20/4 = 5

The difference in simplified form is \frac{3}{5}.

I hope this helps. :)

6 0
3 years ago
NEED HELP ASAP!!! 20 POINTS, 5 STAR REVIEW AND BRAINLIEST TO WHOEVER IS FIRST!
lesya [120]

Answer:

#1 is 30 degrees

#2 is obtuse

#3 is "No rhombuses are rectangles"

#4 is D

#5 is A

Step-by-step explanation:

For #1, we have an angle vertical to 120 degrees which includes a right angle, so we make an equation:

90+x=120

x=30

So angle x is 30 degrees aka. Option A

For #2, obtuse angles have the sum of the square of the side lengths that are less than the square of the hypotenuse. In this case, 6^2+4^2<9^2 or 50<81

For #3, rhombuses have two pairs of congruent sides but no right angles while rectangles have two pairs of congruent sides but they also have right angles.

For #4, they are similar because one of the triangles is dialated by a scale factor of 1.5.

For #5, just think of turning the triangle on its other side, aka. option A

4 0
3 years ago
Read 2 more answers
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