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katrin [286]
3 years ago
15

X+5 divided by 3 is less than or equal to 2

Mathematics
1 answer:
hichkok12 [17]3 years ago
5 0
\frac{x+5}{3}  \leq 2
times both sides by 3
x+5≤6
minus 5 both sides
x≤1
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Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!​
Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

\frac{3}{x + 4}  - \frac{1}{x + 3}  = \frac{x + 9}{(x^2 + 7x + 12)}

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

\frac{3*(x + 4)}{x + 4}  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

3  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x + 3)

3*(x + 3)  - \frac{(x + 4)*(x+3)}{x + 3}  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

3*(x + 3)  - (x + 4)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

(2*x + 5)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x^2 + 7*x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = (x + 9)*(x + 4)*(x+3)

Now we need to solve this:

we will get

2*x^3 + 19*x^2 + 59*x + 60 =  (x^2 + 13*x + 3)*(x + 3)

2*x^3 + 19*x^2 + 59*x + 60 =  x^3 + 16*x^2 + 42*x + 9

Then we get:

2*x^3 + 19*x^2 + 59*x + 60 - (  x^3 + 16*x^2 + 42*x + 9) = 0

x^3 + 3x^2 + 17*x + 51 = 0

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0
2 years ago
Use the figure below to find the lateral surface area. Help needed ASAP. (WILL MARK BRAINLIEST)
o-na [289]

Answer:

60 is your answer

Step-by-step explanation:

Good Luck!!!   :D

Can i have brainliest?

4 0
2 years ago
184500 $ are to be divided between 2 people. One person has 80% of what the other person has. How much does each one receive in
Annette [7]

Given:

$184500 are to be divided between 2 people.

One person has 80% of what the other person has.

To find:

The amount each one receive in $.

Solution:

Let $x be the amount received by first person. Then,

Amount received by the second person = 80% of x

                                                                   = 0.80x

Total amount = Amount received by first person + by second person

                      =x+0.80x

                      =1.80x

Total amount is 184500. So,

1.80x=184500

x=\dfrac{184500}{1.80}

x=102500

So, the amount received by the first person is $102,500.

0.80x=0.80\times 102500

0.80x=82000

So, the amount received by the second person is $82,000.

6 0
3 years ago
Given cos t = 1/2 tan 0 find sin (t) and sec (t)
777dan777 [17]

Answer:

Sin(t) =  \frac{\sqrt{3} }{2} } and sec(t) =2

Step-by-step explanation:

The secant function is the reciprocal function of the cosine function. Therefore, given that sec(t) = \frac{1}{cos(t)} then, if  cos(t) = \frac{1}{2} then  sec(t) =2.

On the other hand, if cos (t) = 1/2 ⇒ t = ±\frac{\pi}{3}

Then, the sin(\frac{\pi}{3}) = \frac{\sqrt{3} }{2} }

3 0
2 years ago
The length of a rectangle is 3 more inches than the width. Find the length and width of the rectangle is the perimeter of the re
n200080 [17]

Part A:

Let the width of the rectangle be = x inches

As given, the length of a rectangle is 3 more inches than the width so let the length of the rectangle be = x+3 inches

Perimeter is given as = 54 inches

Perimeter = 2(l+b)

Equation becomes:

2(x+3+x)=54

2(2x+3)=54

Part B:

Solving the equation we get

4x+6=54

4x=54-6

4x=48

x=12

Hence, the width of the rectangle is 12 inches

Length = x+3 = 12+3 = 15 inches

Hence, length of the rectangle is 15 inches.


5 0
3 years ago
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