Mathematics, 05.06.2021 02:50 Treezy11

Someone please help me thank you

Answers: 2

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Answer from: xmengeo

$x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10}$

Step-by-step explanation:

Ensure that the equation is in the form of ax² +bx +c= 0.

5x² -x +1= 3

5x² -x +1 -3= 0 (-3 on both sides)

5x² -x -2=0

Here, a= 5, b= -1, c= -2.

Use the quadratic formula below to solve for x.

$\boxed{x = \frac{ - b± \sqrt{b^{2} - 4ac } }{2a} }$

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

$x = \frac{1± \sqrt{1 + 40} }{10}$

$x = \frac{1± \sqrt{41} }{10}$

$∴x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10}$

Answer from: ariloveshorses

Step-by-step explanation:

First, lets understand the question. When it says to find all the "real" solutions, that means you should not give any solutions containing an imaginary number. An imaginary number is basically where we accept that there exists an i (imaginary number) that is equal to $\sqrt{-1\\}$ (square root of negative 1). So we are not considering this concept in this question.

Let's start solving then. Can you think of an equation that may help you solve this problem? The biggest clue is that x is squared. If you said the quadratic formula, then you are perfectly correct!

Remember in order to use the quadratic formula, you must get your equation into the form:

$ax^{2} +bx +c=0$

Let's do it! Right now we have:

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

Get rid of the 3 by subtracting it from both sides:

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

Okay! it looks like our quadratic form now! By comparing it we can figure out what a, b, and c are in this case:

$a = 5,{ }\\ b = -1, { }\\c = -2$

Let's get out our quadratic formula now:

$\frac{ -b\frac{+}{} \sqrt{b^{2} -4ac} }{2a}$

All that's left to do is insert values and solve! (Be really careful when dealing with the negatives):

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

$=\frac{ -1\frac{+}{} \sqrt{41} }{10}$

Removing the plus/minus we get two answers:

$=\frac{ -1+ \sqrt{41} }{10}\\\\or\\\\=\frac{ -1-\sqrt{41} }{10}$

These are the most simplified forms! It turns out we didn't even have to worry about imaginary solutions because we didn't end up with a negative sign under the square root. Hope this helps, and good luck!

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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