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3 years ago

How do you solve these? Please explain steps as well. Thanks.

Mathematics

1 answer:

posledela3 years ago

3 0

$7x-3=2x-33 \\
7x-2x=-33+3\\
5x=-30\\
x=-6\\\\
3(x-2)=2(2x-1)\\
3x-6=4x-2\\
4x-3x=-6+2\\
x=-4
$

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The distance between -18 and 15 is equal to ______.

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Answer:

It would be equal to 15 - (18)

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2 years ago

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Select the two values of x that are roots of this equation 3x^2 + 1 =5x

Zina [86]

Answer:

x = 1.434 and x=0.232

Step-by-step explanation:

To find the root of the equation stated above we need to:

(1) Write the polynomial equation with zero on the right hand side:

$3x^{2} + 1 = 5x$ ⇒ $3x^{2} -5x + 1 = 0$

(2) Divide the whole equation by 3

$3x^{2} -5x + 1 = 0$ ⇒ $x^{2} -\frac{5}{3}x + \frac{1}{3}= 0$

(3) Use the quadratic formula to solve the quadratic equation:

The quadratic formula states that the two solutions for a quadratic equation is given by:

$\frac{-b±\sqrt{b^{2} - 4ac}}{2a}$ (1)

In this case, a = 1, b = $-\frac{5}{3}, c= \frac{1}{3}$

Substituiting a, b and c in equation (1) We get:

$\frac{-\frac{5}{3}±\sqrt{(-\frac{5}{3})^{2} - 4(1)(\frac{1}{3})}}{2(1)}$ (1)

The two solutions are:

x = 1.434 and x=0.232

8 0

2 years ago

Which equation has the solutions x = -3 ± √3i/2 ?

Maurinko [17]

Answer:Answer is option C : [ $x^{2}$ + 3x + 3 ] =0

Note: None of options matches with given question.

instead of "-3" , there should be "- $\frac{3}{2}$ ".

Step-by-step explanation:

Note: None of options matches with given question.

instead of "-3" , there should be " $\frac{3}{2}$ ".

Here, First thing you have to observe the nature of roots.

∴ x = - $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i and x = - $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$

∴ [ x+( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) ][ x+( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + x( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i)+ x( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + $\frac{3}{2}$ x + $\frac{\sqrt{3}}{2}$ ix + $\frac{3}{2}$ x - $\frac{\sqrt{3}}{2}$ ix + (3- $\frac{\sqrt{3}}{2}$ i)(3+ $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{\sqrt{3}}{2}$ i)( $\frac{\sqrt{3}}{2}$ i) ] =0