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Westkost [7]
2 years ago
9

One fruit punch has 10% juice and another has 50%. How much of the 10% should be mixed with 30 gal of the 50% to create punch th

at is 25% juice
Mathematics
1 answer:
N76 [4]2 years ago
8 0

Answer:

We combine x ounces of 100% juice

with 40-x of 10% juice

to get 40 ounces of 55% juice

 

x + 0.1(40-x) = .55(40)

x + 4 - 0.1x = 22

0.9x + 4 = 22

.09x = 18

x = 20 ounces of 100% juice

40-x = 20 ounces of 10% juice

 

We combine 20 ounces of each.

 

Step-by-step explanation:

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The answer to this is C

4 0
3 years ago
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Use the discriminant to predict the nature of the solutions to the equation 4x-3x²=10. Then, solve the equation.
AleksandrR [38]

Answer:

Two imaginary solutions:

x₁= \frac{2}{3} -\frac{1}{3} i\sqrt{26}

x₂ = \frac{2}{3} +\frac{1}{3} i\sqrt{26}

Step-by-step explanation:

When we are given a quadratic equation of the form ax² +bx + c = 0, the discriminant is given by the formula b² - 4ac.

The discriminant gives us information on how the solutions of the equations will be.

  1. <u>If the discriminant is zero</u>, the equation will have only one solution and it will be real
  2. <u>If the discriminant is greater than zero</u>, then the equation will have two solutions and they both will be real.
  3. <u>If the discriminant is less than zero,</u> then the equation will have two imaginary solutions (in the complex numbers)

So now we will work with the equation given: 4x - 3x² = 10

First we will order the terms to make it look like a quadratic equation ax²+bx + c = 0

So:

4x - 3x² = 10

-3x² + 4x - 10 = 0 will be our equation

with this information we have that a = -3 b = 4 c = -10

And we will find the discriminant: b^{2} -4ac = 4^{2} -4(-3)(-10) = 16-120=-104

Therefore our discriminant is less than zero and we know<u> that our equation will have two solutions in the complex numbers. </u>

To proceed to solve the equation we will use the general formula

x₁= (-b+√b²-4ac)/2a

so x₁ = \frac{-4+\sqrt{-104} }{2(-3)} \\\frac{-4+\sqrt{-104} }{-6}\\\frac{-4+2\sqrt{-26} }{-6} \\\frac{-4+2i\sqrt{26} }{-6} \\\frac{2}{3} -\frac{1}{3} i\sqrt{26}

The second solution x₂ = (-b-√b²-4ac)/2a

so x₂=\frac{-4-\sqrt{-104} }{2(-3)} \\\frac{-4-\sqrt{-104} }{-6}\\\frac{-4-2\sqrt{-26} }{-6} \\\frac{-4-2i\sqrt{26} }{-6} \\\frac{2}{3} +\frac{1}{3} i\sqrt{26}

These are our two solutions in the imaginary numbers.

7 0
3 years ago
What is the product?<br><br> (6 r minus 1)(negative 8 r minus 3)
just olya [345]

Answer:

The required product is -48r^2-10r+3

Step-by-step explanation:

Consider the provided expression.

(6r-1)(-8r-3)

Open the parentheses.

6r\left(-8r\right)+6r\left(-3\right)+\left(-1\right)\left(-8r\right)+\left(-1\right)\left(-3\right)

-6\cdot \:8rr-6\cdot \:3r+1\cdot \:8r+1\cdot \:3

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Add the like terms.

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Hence, the required product is -48r^2-10r+3

3 0
3 years ago
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Some pls help to give 20 points
madreJ [45]

Answer:

Neon= -10+10= 0 on no change

oxide=-10+8=-2

copper=-27 +29 = 2

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Step-by-step explanation:

Its basically subtraction ( i pretty sure thats right)

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Step-by-step explanation:

3x+1 = 5x-1

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2x= 2

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7 0
3 years ago
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