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Gnesinka [82]
3 years ago
15

Supposed that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in the tank. When ca

rrying 14 gallons of fuel the airplane weighs 2177 pounds when carrying 42 gallons of fuel it weighs 2331 pounds. How much does the airplane weigh if it is carrying 48 gallons of fuel?
Mathematics
1 answer:
polet [3.4K]3 years ago
8 0

Answer:2885

Step-by-step explanation:

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Someone help me out please
uysha [10]

1 step (B): raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2,\\   (x+3)-2\sqrt{x+3}\cdot \sqrt{2x-1}+(2x-1)=4,\\ 3x+2-2\sqrt{x+3}\cdot \sqrt{2x-1}=4.

2 step (A): simplify to obtain the final radical term on one side of the equation.

-2\sqrt{x+3}\cdot \sqrt{2x-1}=4-3x-2,\\ -2\sqrt{x+3}\cdot \sqrt{2x-1}=2-3x,\\ 2\sqrt{x+3}\cdot \sqrt{2x-1}=3x-2.

3 step (F): raise both sides of the equation to the power of 2 again.

(2\sqrt{x+3}\cdot \sqrt{2x-1})^2=(3x-2)^2,\\ 4(x+3)(2x-1)=(3x-2)^2.

4 step (E): simplify to get a quadratic equation.

4(2x^2-x+6x-3)=(3x)^2-2\cdot 3x\cdot 2+2^2,\\ 8x^2+20x-12=9x^2-12x+4,\\ x^2-32x+16=0.

5 step (D): use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 16=1024-64=960, \\ \sqrt{D} =8\sqrt{5} ,\\ x_{1,2}=\dfrac{32\pm 8\sqrt{5}}{2} =16\pm 4\sqrt{5}.

6 step (C): apply the zero product rule.

x^2-32x+16=(x-16-4\sqrt{5}) (x-16+4\sqrt{5}) ,\\ (x-16-4\sqrt{5}) (x-16+4\sqrt{5}) =0,\\ x_1=16+4\sqrt{5} ,x_2=16-4\sqrt{5}.

Additional 7 step: check these solutions, substituting into the initial equation.

3 0
3 years ago
A and B are partners sharing profit and loss in the ratio of 3:2. A new partner C is admitted and 1/4 share off profit is given.
Gre4nikov [31]

Answer:

Correct option is: 9:6:5

Step-by-step explanation:

I'm not sure but hope it helps.

6 0
3 years ago
6/30=3/15 true or false
Dennis_Churaev [7]

Answer: True

Step-by-step explanation: This is because they are equivalent fractions

Hope this helps and have a nice day

4 0
3 years ago
Read 2 more answers
There are 7 red candies in a pack, 9 blue candies in a pack, and 12 pink candies in a pack. If your wonderful math teacher wants
pentagon [3]
Given:
7 red candies
9 blue candies
12 pink candies

Condition:
Number of bags that has equal number of candies.

We can do 7 bags with 1 colored candy each. There will be an excess of 2 blue candies and 5 pink candies.

We can do 4 bags with 1 red candy, 2 blue candies, 3 pink candies. There will be an excess of 3 red candies and 1 blue candy.

We can do 3 bags with 2 red candies, 3 blue candies, 4 pink candies. There will be an excess of 1 red candy.
5 0
3 years ago
How does writing equivalent equations help you solve a system of equations?
Alexus [3.1K]
Writing equivalent equations help you solve system of equations because it sets it up for being broken down part by part.

3 0
3 years ago
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