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Alexeev081 [22]
3 years ago
14

Which of the following is the result of completing the square for x2 + 8x - 6 ?

Mathematics
2 answers:
sergey [27]3 years ago
7 0
X^2+8x-6=0
(x+8/2)^2-(8/2)^2-6=0
(x+4)^2-16-6=0
(x+4)^2-22=0

x+4= ± square root 22

x=-4 + square root 22 or x=-4 - square root 22
=0.6904 =-8.6904
melamori03 [73]3 years ago
5 0
STEP 1- since 6 doesn't contain the variable to solve for move it to the right side of the equation by subtracting 6 from both sides
X^2-8X=-6
STEP 2- create a trinomial square on the left side of the equation find the value that is equal to the square of half of b the coefficient of x 
(b/2)^2 =(-4)^2
STEP 3- add the term to each side of the equation
x^2-8x+(-4)^2=-6=(-4) 
STEP 4- simplify the equation
x^2-8x+16=10 
STEP 5- factor the perfect trinomial square into (x-4)^2
(x-4)^2=10
STEP 6-solve the equation for x
x=4= square root of 10

 
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A car used 11 1/2 gal of gasoline on a 345-mile trip. How many miles can this car travel on 1 gal of gasoline? ____mi
lyudmila [28]

Answer:

The answer to your question is: 30 miles can the car travel.

Step-by-step explanation:

Data

gasoline used = 11 1/2 gal

distance = 345 mile-trip

distance travel with 1 gal = ?

Process

Convert 11 1/2 to a improper fraction    11 1/2 = 23/2

Rule of three

                            23/2 gal -----------------------  345 miles

                              1 gal      ----------------------   x

                          x = (1 x 345) / 23/2

                          x = 345 / 23/2

                          x = 690/ 23

                          x = 30 miles

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Prove that an integer consisting of 3n ones is divisible by 3n (e.g. 111 is divisible by 3, 111,111,111 is divisible by 9, etc.)
mote1985 [20]

For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

<h3>Integers divisible by 3</h3>

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

<h3>Proof for the divisibility</h3>

111 = 1 + 1 + 1 = 3  (the sum is multiple of 3 = 3 x 1)  (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2)  (222/3 = 74)

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27 = 2 + 7 = 9  (the sum is multiple of 3 = 3 x 3)  (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

Learn more about divisibility here: brainly.com/question/9462805

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