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2 years ago

Solve the following: 6(2x+3)-3(x-2)=6

Mathematics

2 answers:

nikklg [1K]2 years ago

5 0

Answer:

12x +18 - 3x + 6 = 6

9x + 24 = 6 / -24 from both sides

9x = - 18 / divide both sides by 9

x = -2

i hope this helps

REY [17]2 years ago

4 0

The value of x is -2

Step-by-step explanation:

Given that

6 (2x + 3) - 3(x - 2) = 6

Expand the bracket

6 (2x + 3) - 3(x - 2) = 6

12x + 18 - 3x + 6 = 6

Collect like terms

12x - 3x = 6 - 6 - 18

9x = -18

Divide through by 9

9x / 9 = -18 / 9

x = -2

Therefore, the value of x is -2

Learn more about inequality here : brainly.com/question/20252161

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3 years ago

Which number is a prime number? 161. 151. 141. 171.

Scorpion4ik [409]

I think the answer is 151.

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3 years ago

When a trend line is drawn on a scatterplot, there are 4 points above the trend line. About how many points should be below the

scoundrel [369]

There is no exact rule for lines of best fit. However, in general, there should be roughly the same amount above as below. So, if we are following this rule, there should be about 4 below as well.

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3 years ago

Read 2 more answers

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

Nicole runs a farm stand that sells bananas and peaches. Each pound of bananas sells for $2 and each pound of peaches sells for

stepan [7]

Answer:

The required system of equations is:

2x + 3.25y = 231.75

x = y + 3

where x is the number of pounds of bananas and y is the number of pounds of peaches

Explanation:

1- Defining the variables:

Assume that the number of pounds of bananas sold is x

Assume that the number of pounds of peaches sold is y

2- Setting the system of equations:

We are given that:

i. Each pound of bananas sells for $2

Money gained from selling x pounds of bananas is 2x

ii. Each pound of peach sells for $3.23

Money gained from selling y pounds of peaches is 3.25y

iii. Nicole made $231.75 in total. This means that:

2x + 3.25y = 231.75 .................> equation I

iv. Nicole sold 3 more pounds of bananas than pounds of peaches. This

means that:

pounds of bananas = pounds of peaches + 3

x = y + 3 ..................> equation II

3- Solving the equations (if required):

In equation II, we have: x = y + 3

Substitute with equation II in equation I and solve for y as follows:

2x + 3.25y = 231.75

2(y+3) + 3.25y = 231.75

2y + 6 + 3.25y = 231.75

5.25y = 231.75 - 6

5.25y = 225.75

y = 43

Substitute with y in equation II to get x:

x = y + 3

x = 43 + 3 = 46

Based on the above:

Number of pounds of bananas = x = 46 pounds

Number of pounds of peaches = y = 43 pounds

Hope this helps :)

4 0

3 years ago