3 years ago

Which pair of numbers is made up of prime numbers?

Mathematics

1 answer:

tester [92]3 years ago

8 0

37 and 89 are prime numbers

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Find the solutions to the equation 102x 11 = (x 6)2 – 2. Which values are approximate solutions to the equation? Select two answ

otez555 [7]

You can try finding the roots of the given quadratic equation to get to the solution of the equation.

There are two solutions to the given quadratic equation

$x = 0.202, x = 113.798$

<h3>How to find the roots of a quadratic equation?</h3>

Suppose that the given quadratic equation is $ax^2 + bx +c = 0$

Then its roots are given as:

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

<h3>How to find the solution to the given equation?</h3>

First we will convert it in the aforesaid standard form.

$102x + 11 = (x-6)^2 - 2\\102x + 11 + 2 = x^2 + 36 - 12x\\0 = x^2 -114x + 23\\x^2 -114x + 23 = 0\\$

Thus, we have

a = 1. b = -114, c = 23

Using the formula for getting the roots of a quadratic equation,

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{114 \pm \sqrt{114^2 - 92}}{2} \\\\ x = 0.202 (\text{used "-" sign})\\\\x = 113.798 ( used "+" sign})$

Thus, there are two solutions to the given quadratic equation

$x = 0.202, x = 113.798$

Learn more here about quadratic equations here:

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Solve the following equation by factoring.<br><br> 5x103+32x73−64x43=0

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3 years ago

What value of x makes this equation true? 12x - 15 = 6 - 3x *

Marina86 [1]

Answer:

x = 1.4 (or 21/15)

Step-by-step explanation:

12x - 15 = 6 - 3x

+3x +3x

-----------------------

15x - 15 = 6

+15 +15

-----------------------

15x = 21

/15 /15

----------------------

x = 21/15 or

x = 1.4

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