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3 years ago

1 point

Mathematics

1 answer:

-Dominant- [34]3 years ago

5 0

39
Divide 78 by 2 to get 39 and add in to the number

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mrs. johnson gave a sum of money to her son and daughter in the ratio 5:6. Her daughter received $2400. how muh did Mrs. Johnson

Tresset [83]

To find the total amount Mrs. Johnson gave away, you need to know how much she gave the son. Because the ratio of the money given is 5:6, the amount of money he received has to be 5/6 of the money the daughter received.

So, the son received 5/6 of 2400.
To find this, multiply 5/6 x 2400 to get 2000.

The daughter received 2400 and the son received 2000, so the total amount Mrs. Johnson gave away is 4400 dollars.

4 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

2 years ago

Brainliest explain this to me

shutvik [7]

So... Emily gets payed 12 dollars for every hour she works. with and ADDitional 30 dollars by the end of her day. Therefore you would multiply her hourly income (12) by the amount of hours she works (h). Then, add her 30 dollars to it. (Im feeling nice so the answer should look like this ~ 12h + 30.) Hope it helps you <3!

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3 years ago

What’s the greatest common factor of (280, 168)

Lorico [155]

Answer:

Greatest common factor of 280 and 168 is 56

-NULL

Brainliest will be appreciated thank you!

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2 years ago

What is the value of (−12)3? Question 1 options: 16 −16 18 −18<br>PLZ ANSWER ASAP

Lisa [10]

The value of (-12)3 is -36

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3 years ago