Hector and Evelyn are solving the following problem. Find x,y, and z in this 45-45-90 triangle.

Mathematics

1 answer:

Murljashka [212]3 years ago

8 0

Answer: A. They are both incorrect

Step-by-step explanation:

x=3√2

y=6

z=3√2

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45-45-90=1:1:√2

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solve for x

x is the side accordingly to 90 in the smaller triangle, so it should be the [45] side times √2

3×√2=3√2

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solve for y

y is the side accordingly to 90, so it should be the [45] side times √2

3√2×√2=6

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solve for z

z is the side accordingly to 45 in the bigger triangle, x is also accordingly to 45 in the bigger triangle

z=x

z=3√2

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if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the

Marta_Voda [28]

There are 6 letters, each different
Before MOTHER, words from E , H will come
Words from E = 5! (there are 5 letters to arrange)
Words from H = 5!( there are 5 letters to arrange)

Now words starting by M will come.
First ME will have = 4! (as 4 letters will be arranged)
Then MH = 4!
Now words with MO<span>
</span><span>First words starting with MOE... =3!
And words starting with MOH... =3!
the words starting with MOR... =3!

Now, words starting from MOT will come
words starting with MOTE.. = 2!
then after words starting from MOTH will come and first word will MOTHER

so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3!
= 120 +120 + 48 + 18
= 306
so, rank of MOTHER = 307</span>

7 0

4 years ago

Refer to the photo :D

OlgaM077 [116]

well, we know the ceiling is 6+2/3 high, and Eduardo has 4+1/2 yards only, how much more does he need, well, is simply their difference, let's firstly convert the mixed fractions to improper fractions and then subtract.

$\stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} ~\hfill \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{20}{3}-\cfrac{9}{2}\implies \stackrel{using ~~\stackrel{LCD}{6}}{\cfrac{(2\cdot 20)-(3\cdot 9)}{6}}\implies \cfrac{40-27}{6}\implies \cfrac{13}{6}\implies\blacktriangleright 2\frac{1}{6} \blacktriangleleft$