All categories

2 years ago

X^2 - 8x = 3 by completing the square

Mathematics

1 answer:

Anit [1.1K]2 years ago

3 0

<h2>Solving Quadratic Equations by Completing the Square Method</h2><h3>Answer:</h3>

$x = 4 +\sqrt{19}$ and $x = 4 -\sqrt{19}$

<h3>Step-by-step explanation:</h3>

Recall:

$x^2 -2ax +a^2 = (x -a)^2$

$x^2 -8x = 3 \\ x^2 -8x +16 = 3 +16 \\ (x -4)^2 = 19 \\ x -4 = ±\sqrt{19} \\ x = 4 ±\sqrt{19}$

You might be interested in

Adele is paid a weekly salary of $685. She is paid an additional $23.50 for every hour of overtime she works. This week her tota

loris [4]

The answer is 7 overtime hours

7 0

2 years ago

Read 2 more answers

if alpha and beta are the zeroes of the polynomial f(x) = 6x² + x - 2, find the value of 1/alpha + 1/beta - alphabeta

finlep [7]

Answer:

let alpha be x and beta be y

Step-by-step explanation:

x+y= -b/a

x+y=-1/6

and xy= c/a

xy= -1/3

according to question

1/x+1/y -xy =(x+y)/xy-xy

(-1/6)/(-1/3)-(-1/3)

1/2+1/3

the answer is 5/6

7 0

2 years ago

A square outdoor patio with side length x feet is surrounded by a brick walkway that is 4 feet wide. What is the area of the wal

Masja [62]

Answer:

Area of walkway = 16(x+4) $ft^{2}$

Step-by-step explanation:

Length of the sides of the square outdoor = x feet

Area of the square outdoor = length x length

= x * x

= $x^{2}$ $ft^{2}$

The square outdoor is surrounded by 4 feet of walkway. So that,

length of the walkway = (x + 2(4))

= (x + 8)

Area of walkway with outdoor = (x + 8)*(x + 8)

= ( $x^{2}$ + 16x + 64) $ft^{2}$

Area of walkway = Area of walkway with outdoor - Area of the square outdoor

= ( $x^{2}$ + 16x + 64) - $x^{2}$

= 16x + 64

Area of walkway = 16(x+4) $ft^{2}$

7 0

2 years ago

The order pairs (0,0), (2,4), (4,8) and (6,12) represent a function. What is the rule for this function ?

Gala2k [10]

X double by 2
y double by 2

7 0

2 years ago

Read 2 more answers

It took Lou 2 1/2 gallons of paint to paint one fence. How many gallons to paint six fences that are small in size

rusak2 [61]

Answer:

15 gallons to paint six fences that are small in size.

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity 1 such as 3 miles per hour or 5 meter per seconds.

As per the statement:

It took Lou $2\frac{1}{2}$ gallons of paint to paint one fence.

$\text{Unit rate per fence}= \frac{\text{Number of gallons of paint}}{\text{number of fences}}$

Substitute the given value we have;

$\text{Unit rate per fence}= \frac{\frac{5}{2} }{1} = \frac{5}{2}$ gallons.

We have to find how many gallons to paint six fences that are small in size.

By definition of unit rate;

$\text{Number of gallons to paint 6 fences}= \text{Unit rate per fence} \times 6$

Substitute the given values we have;

$\text{Number of gallons to paint 6 fences}= \frac{5}{2} \times 6 = 5 \times 3 = 15$

Therefore, 15 gallons to paint six fences that are small in size.

3 0

2 years ago