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3 years ago

If 4m + n = 7 and n =3, then 4m +3 = 7 what is the property ?

Mathematics

1 answer:

mr Goodwill [35]3 years ago

8 0

Answer:

M equals 1

Step-by-step explanation:

4 x 1 + 3 = 7

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Find the median of this set of data 34 36 30 37 40 30 42 a 37 b 35 c 36 d 30

shusha [124]

Answer:

Step-by-step explanation:

The median is the value that separates the higher half from the bottom half of the data sample (middle value).

We have

34, 36, 30, 37, 40, 30, 42

Write from the smallest to the largest number

30, 30, 34, 36, 37, 40, 42

3 0

3 years ago

Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

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 = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

3 years ago

How to do the problem

trapecia [35]

Step-by-step explanation:

$g(0.5) = 2 \\ \\ h(x) = g(x).f(x) \\ \therefore \: h(2) = g(2).f(2) \\ \therefore \: h(2) = 5 \times 2\\ \therefore \: h(2) = 10\\ \\ \\ j(x) = g(x) - f(x) \\ \therefore \: j(4) = g(4) - f(4) \\ \therefore \: j(4) = 9 - 8\\ \therefore \: j(4) = 1\\ \\ \\$