Answer:
![100](https://tex.z-dn.net/?f=100)
Step-by-step explanation:
<u>Step 1: Make an expression</u>
<u />![200 * 0.29 = x](https://tex.z-dn.net/?f=200%20%2A%200.29%20%3D%20x)
![58 = x](https://tex.z-dn.net/?f=58%20%3D%20x)
<u>Step 2: Round</u>
<u />![58](https://tex.z-dn.net/?f=58)
![100](https://tex.z-dn.net/?f=100)
Answer: ![100](https://tex.z-dn.net/?f=100)
Answer:
Two imaginary solutions:
x₁= ![\frac{2}{3} -\frac{1}{3} i\sqrt{26}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20-%5Cfrac%7B1%7D%7B3%7D%20i%5Csqrt%7B26%7D)
x₂ = ![\frac{2}{3} +\frac{1}{3} i\sqrt{26}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%2B%5Cfrac%7B1%7D%7B3%7D%20i%5Csqrt%7B26%7D)
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](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-4ac%20%3D%204%5E%7B2%7D%20-4%28-3%29%28-10%29%20%3D%2016-120%3D-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}](https://tex.z-dn.net/?f=%5Cfrac%7B-4%2B%5Csqrt%7B-104%7D%20%7D%7B2%28-3%29%7D%20%5C%5C%5Cfrac%7B-4%2B%5Csqrt%7B-104%7D%20%7D%7B-6%7D%5C%5C%5Cfrac%7B-4%2B2%5Csqrt%7B-26%7D%20%7D%7B-6%7D%20%5C%5C%5Cfrac%7B-4%2B2i%5Csqrt%7B26%7D%20%7D%7B-6%7D%20%5C%5C%5Cfrac%7B2%7D%7B3%7D%20-%5Cfrac%7B1%7D%7B3%7D%20i%5Csqrt%7B26%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-%5Csqrt%7B-104%7D%20%7D%7B2%28-3%29%7D%20%5C%5C%5Cfrac%7B-4-%5Csqrt%7B-104%7D%20%7D%7B-6%7D%5C%5C%5Cfrac%7B-4-2%5Csqrt%7B-26%7D%20%7D%7B-6%7D%20%5C%5C%5Cfrac%7B-4-2i%5Csqrt%7B26%7D%20%7D%7B-6%7D%20%5C%5C%5Cfrac%7B2%7D%7B3%7D%20%2B%5Cfrac%7B1%7D%7B3%7D%20i%5Csqrt%7B26%7D)
These are our two solutions in the imaginary numbers.
Answer:
2
Step-by-step explanation:
<em>for </em><em>this </em><em>question</em><em> </em><em>you've </em><em>to </em><em>cross </em><em>multiply</em>
<em>-</em><em>2</em><em>2</em><em>/</em><em>9</em><em>r</em><em>=</em><em>1</em><em>1</em><em>/</em><em>9</em>
<em>9</em><em>9</em><em>r</em><em>=</em><em>-</em><em>1</em><em>9</em><em>8</em>
<em>then </em><em>you </em><em>divide</em><em> both</em><em> sides</em><em> by</em><em> </em><em>9</em><em>9</em><em> </em><em>inorder </em><em>to </em><em>remain </em><em>with </em><em>r </em><em>on </em><em>one </em><em>side</em>
<em>9</em><em>9</em><em>r</em><em>/</em><em>9</em><em>9</em><em>=</em><em>1</em><em>9</em><em>8</em><em>/</em><em>9</em><em>9</em>
<em>r=</em><em>2</em>
<em>I </em><em>hope </em><em>this </em><em>helps</em>