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RideAnS [48]
3 years ago
8

1. Jayden spent $46.20 on 12 gallons of gasoline. What was the price per gallon? 2. Jayla buys 1.2 pounds of bananas. The banana

s cost $1.29 per pound. To the nearest cent, how much does Jayla pay for the bananas? 3. Billy ate 1/4 of a pizza, and Wi ate 1/3 of the same pizza. How much of the Pizza did they eat in all?
Mathematics
1 answer:
dolphi86 [110]3 years ago
8 0

Answer:

1. $3.85 per gallon

2. $1.59

3. 7/12

Step-by-step explanation:

1. Jayden spent $46.20 on 12 gallons of gasoline. The price per gallon can be gotten by dividing the total price paid by the total number of gallons bought:

46.20 / 12 = $3.85 per gallon

The price per gallon is $3.85

2. Jayla buys 1.2 pounds of bananas and they cost $1.29 per pound. The total amount paid for the bananas is:

1.2 * 1.29 = $1.59

3. Billy ate 1/4 of a pizza, and Wi ate 1/3 of the same pizza. The total fraction of the pizza ate is:

1/4 + 1/3 = 7/12

They ate 7/12 of the pizza

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Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2
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1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

<u>1. 2x^2 - 7x + 3</u>

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

  • a = 2
  • b = -7
  • c = 3

we can use the quadratic formula: x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}

Substitute the a, b, and c values into the quadratic formula: x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}

Now simplify using the laws of pemdas: x=\frac{7\pm\sqrt{(49)-(24)} }{4}

Simplify even further: x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}

Now split this equation into two equations to solve for x: x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

\boxed {x=3,\frac{1}{2} }

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

  • x - 3 = 0
  • 2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

<u>2. 3x^2 + 7x + 2</u>

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Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

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3x = -1

Divide both sides by 3.

x = -1/3

<u>Second factor:</u> x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

\boxed {x = -\frac{1}{3} , -2}

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