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Dmitrij [34]
2 years ago
9

100 points PLEASE ANSWER ASAP thank you so much Please show work

Mathematics
2 answers:
vivado [14]2 years ago
5 0

Answer:

The mistake is that the equation on both sides is multiplied by 8. Both sides should be divided by 8.

Step-by-step explanation:

8x^2-x-1=0
8x^2-x=1   Divide both sides of the equation by 8
x^2-\frac{1}{8} x=\frac{1}{8}
x^2-\frac{1}{8} x+?=\frac{1}{8} +? Add the same value to both side
x^2-\frac{1}{8} x+\frac{1}{256} =\frac{1}{8} +\frac{1}{256}              
Use a^2-2ab+b^2=(a-b)^2
(x-\frac{1}{16} )^2 = \frac{33}{256}
x-\frac{1}{16}=+-\frac{\sqrt{33} }{16}
x_{1} =\frac{-\sqrt{33}+1 }{16}
x_{2} =\frac{\sqrt{33}+1 }{16}


shutvik [7]2 years ago
4 0

Answer:

x=\dfrac{1 \pm \sqrt{33}}{16}

Step-by-step explanation:

Given:

8x^2-x-1=0

Add 1 to both sides:

\implies 8x^2-x=1

Factor out the 8 from the left side:

\implies 8\left(x^2-\dfrac{1}{8}x\right)=1

Divide both sides by 8:

\implies x^2-\dfrac{1}{8}x=\dfrac{1}{8}

Add the square of half the coefficient of x to both sides:

\implies x^2-\dfrac{1}{8}x+\dfrac{1}{256}=\dfrac{1}{8}+\dfrac{1}{256}

Factor the left side and simplifyy the right:

\implies \left(x-\dfrac{1}{16}\right)^2=\dfrac{33}{256}

Square root both sides:

\implies x-\dfrac{1}{16}=\pm\sqrt{\dfrac{33}{256}}

Simplify:

\implies x-\dfrac{1}{16}=\pm\dfrac{\sqrt{33}}{16}

Add 1/16 to both sides:

\implies x=\pm\dfrac{\sqrt{33}}{16}+\dfrac{1}{16}

Simplify:

\implies x=\dfrac{1 \pm \sqrt{33}}{16}

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Soloha48 [4]
The numbers are "x" and "y", therefore, we suggest this system of equations:
x-y=14
xy=1800
We can solve by substitution method.
x=14+y

(14+y)y=1800
14y+y²=1800
y²+14y-1800=0

Now, we solve this square equation:
y=[-14⁺₋√(196+7200)] / 2=(-14⁺₋86)/2
We have two solutions:

y₁=(-14-86)/2=-50     ⇒x=14+y=14-50=-36
y₂=(-14+86)/2=36    ⇒x=14+y=14+36=50

Answer: we have two solutions:
Solution1: The first number is -36 and the other number is -50
Soltuion2: The first number is 50 and the other number is 36
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Bond [772]

Answer:

You would save $18

Step-by-step explanation:

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5 0
3 years ago
Find the simple interest: Principal: $3020 Interest Rate: 5% Time: 6 months​
Andrews [41]

Answer:

A = $3094.58

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

Simple Interest Rate Formula: A = P(1 + r)ⁿ

  • A is the final amount
  • P is the principal amount
  • r is the rate
  • n is the time (in years)

Step-by-step explanation:

<u>Step 1: Define variables</u>

A = ?

P = 3020

r = 0.05

t = 6 months = 0.5 years

<u>Step 2: Solve for </u><em><u>A</u></em>

  1. Substitute:                    A = 3020(1 + 0.05)^0.5
  2. Add:                              A = 3020(1.05)^0.5
  3. Evaluate:                       A = 3020(1.0247)
  4. Multiply:                        A = 3094.58

And we have our final answer!

5 0
3 years ago
Can u help me with this problem 1/2+-2/5t-1=1/5t+t
Temka [501]
1/2+-2/5t(+2/5)=1/5t+t(+2/5)
simplify
1/2=2 and 3/5t
change to a decimal
.5 = 2.6t
divide both sides by 2.6
.5/2.6 2.6t/2.6
you get T= .3125
8 0
3 years ago
Read 2 more answers
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