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3 years ago

If you have 20 square pieces of wood, describe ways you could make a rectangle by side by side?

Mathematics

2 answers:

sveticcg [70]3 years ago

5 0

Or you could do 10 going down and 2 going across that would work too lol

sveta [45]3 years ago

4 0

You would do 2 going down and 10 going across for a rectangular shape test it if you want to.

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

3 years ago

Triangle ABC is similar to triangle PQR, as shown below:

natita [175]

Answer:

$\frac{q}{b}=\frac{r}{c}$

Step-by-step explanation:

Consider the options for this question are as follow,

$\frac{q}{c}=\frac{r}{b}$

$\frac{c}{p}=\frac{b}{a}$

$\frac{c}{a}=\frac{q}{r}$

$\frac{q}{b}=\frac{r}{c}$

Here, In triangles ABC and PQR,

AB = c, BC = a, AC = b, PQ = r, QR = p and PR = q,

Since,

$\traingle ABC\sim \triangle PQR$

We know that,

The corresponding sides of similar triangles are in same proportion,

Thus,

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

$\frac{c}{r}=\frac{a}{p}=\frac{b}{q}$

$\frac{r}{c}=\frac{p}{a}=\frac{q}{b}$

$\implies \frac{q}{b}=\frac{r}{c}$

3 0

3 years ago

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According to the number line, which statement MUST be true?

Leno4ka [110]

Answer:

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Give 6 irrational numbers between 2÷5 and 3÷4

soldi70 [24.7K]

Hello,

Let's z=0.1234567891011121314151617181920.....(never end)

2/5=(2/(5z)*z<3241/1000 *z
3/4=(3/(4z))*z>6075/1000*z

So here is 2836 irrational numbers:

3241*z/1000
3242*z/1000
3243*z/1000
...
6073*z/1000
6074*z/1000
6075*z/1000

7 0

3 years ago

Toby skated from his house to the beach at a constant speed of 8 kilometers per hour, and then skated from the beach to the park

german

Answer:

8b+7p=20

p=2b

Step-by-step explanation:

8 0

3 years ago