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3 years ago

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Mr. Smith donated $378 to 2 charities. Charity A received 5 times as much as Charity B. How much did Charity B received from Mr

Smith?

1 answer:

MariettaO [177]3 years ago

5 0

Answer:

$63

Step-by-step explanation:

let x represent Charity B then Charity A = 5x

Sum the two and equate to 378, that is

x + 5x = 378

6x = 378 ( divide both sides by 6 )

x = 63

Thus Charity B received $63

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Write an equation to represent each situation.

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Answer:

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Step-by-step explanation:

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3 years ago

What is the solution to the system of equation <br><br> -2x+6y=-38<br> 3x-4y=32

Alla [95]

Answer:

x= 4

y= -5

Step-by-step explanation:

-2x+6y=-38 equation 1

3x-4y=32 equation 2

using equation 1 we have:

-2x+6y=-38

6y +38 = 2x

3y + 19 = x equation 3

using equation 3 in equation 2 we have:

3(3y + 19) - 4y = 32

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so we have:

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3 years ago

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Given g(x)=-2x+1 solve for x when g (x)=5

nevsk [136]

Answer:

x = -2

Step-by-step explanation:

g(x) = 5

-2x + 1 = 5

-2x = 5 - 1

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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.

<u>If the discriminant is zero</u>, the equation will have only one solution and it will be real
<u>If the discriminant is greater than zero</u>, then the equation will have two solutions and they both will be real.
<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.

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3 years ago

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densk [106]

Answer:

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Step-by-step explanation:

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