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Drupady [299]
2 years ago
11

What is the area of the figure? 118 in 48 in 128 in 108 in

Mathematics
1 answer:
Talja [164]2 years ago
5 0

Answer:

108 In

Step-by-step explanation:

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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
The sum of two numbers is 148. The larger number is two less than three times the smaller. What are the two numbers?
Lyrx [107]
Let
x--------->  the larger number
y---------> the smaller number

we know that
x+y=148------> equation 1
x=3y-2------> equation 2

substitute 2 in 1
[3y-2]+y=148--------> 4y=150---------> y=150/4------> y=37.5
x=3y-2----> x=3*37.5-2-----> x=110.5

the answer is
the larger number is 110.5
the smaller number is 37.5
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3 years ago
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Sandra throws an object into the air with an initial vertical velocity of 38 feet per second, from a platform that is 30 feet ab
Blababa [14]
<span>To solve it, use the quadratic formula with (½)(-32.174 ft/s²) = a, 38 ft/s = b, and 30 ft = c. There are two answers; the only positive answer is t = 2.986 s </span>
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HELP ME AS FAST AS POSSIBLE PLEASE HELP What does this answer equal PLEASE HELP PLEASE
hichkok12 [17]
The answer for the blank space is 21.8
5 0
2 years ago
On a scale drawing, the scale factor is 1/12. A plum tree is 7 inches tall on the scale drawing. What is the actual height of th
Sedbober [7]
B. 84

The scale factor is 1/12 which means to get back to the actual height, you would multiply 7x12
7 0
2 years ago
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