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stira [4]
3 years ago
5

Show a full solution to the inequality [(x+2)/(x-4)]

Mathematics
1 answer:
Papessa [141]3 years ago
3 0
Your sign chart is a bit off. The first two rows are correct. However keep in mind that you factored out a negative (when you factored -2x+14) so you need to negate the signs of the f(x) row.

Another thing to keep in mind: x = 4 is not allowed as its the vertical asymptote. However, x = 7 is valid. So you'll have an open circle at x = 4 and a close circle at x = 7

The answer in interval notation is (-infinity, 4) U [7, infinity)
which translates to this disjoint set of inequalities: x < 4 or x >= 7
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Sara has 24 sweets
Tresset [83]
<h2>Hello!</h2>

The answer is:

The expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

<h2>Why?</h2>

To write the expressions for the number of sweets that Sara and Tim have now, we need to follow the next steps:

Sara starts with 24 sweets and Tim starts with 24 sweets

Sara=24 Sweets\\Tim=24 Sweets

Then, Sara gives Tim x Sweets

Sara=(24-x)Sweets\\Tim=(24+x)Sweets

Then. Sara eats 7 of her Sweets

Sara=(24-x-7) Sweets\\Sara=(17-x )Sweets\\Tim=(24+x) Sweets

Then, Tim eats half of his sweets

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

So, the expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x) Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

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8 0
3 years ago
Which expressions are equivalent to 2(b+3c)?
Rina8888 [55]

Answer:

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step-by-step explanation:

we have

2(b+3c)

Distribute the number 2

2(b+3c)=2b+2(3c)=2b+6c

Verify each case

case A) 3(b+2c)

distribute the number 3

3(b+2c)=3b+3(2c)=3b+6c

3b+6c \neq 2b+6c

therefore

Choice A is not equivalent to the given expression

case B) (b+3c)+(b+3c)

Combine like terms

b+3c)+(b+3c)=(b+b)=(3c+3c)=2b+6c

2b+6c= 2b+6c

therefore

Choice B is equivalent to the given expression

case C) 2(b)+2(3c)

Multiply both terns by 2

2(b)+2(3c)=2b+6c

2b+6c= 2b+6c

therefore

Choice C is equivalent to the given expression

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