All categories

3 years ago

Solve each equation by completing the square 6) m² + 16m – 8 = 0

Mathematics

1 answer:

Natali5045456 [20]3 years ago

3 0

Answer:

m = - 8 ± 6 $\sqrt{2}$

Step-by-step explanation:

Given

m² + 16m - 8 = 0 ( add 8 to both sides )

m² + 16m = 8

To complete the square

add ( half the coefficient of the m- term )² to both sides

m² + 2(8)m + 64 = 8 + 64

(m + 8)² = 72 ( take the square root of both sides )

m + 8 = ± $\sqrt{72}$ = ± $\sqrt{36(2)}$ = ± 6 $\sqrt{2}$

Subtract 8 from both sides

m = - 8 ± 6 $\sqrt{2}$

You might be interested in

Independent Practice

schepotkina [342]

Answer:

343 fourths

Step-by-step explanation:

343 fourths

6 0

2 years ago

Read 2 more answers

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is

kodGreya [7K]

We're looking for a scalar function $f(x,y)$ such that $\nabla f(x,y)=\vec F(x,y)$ . That is,

$\dfrac{\partial f}{\partial x}=2x-6y$

$\dfrac{\partial f}{\partial y}=-6x+6y-7$

Integrate the first equation with respect to $x$ :

$f(x,y)=x^2-6xy+g(y)$

Differentiate with respect to $y$ :

$-6x+6y-7=-6x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=6y-7$

Integrate with respect to $y$ :

$g(y)=3y^2-7y+C$

So $\vec F$ is indeed conservative with the scalar potential function

$f(x,y)=x^2-6xy+3y^2-7y+C$

where $C$ is an arbitrary constant.

6 0

2 years ago

Asking costs 5 points and then choosing a best answer earns you 3 points!

yKpoI14uk [10]

Thanks this came in handy bc I'm a beginner

4 0

3 years ago

Find the area 9cm 8cm 13cm 9cm 11cm

Viktor [21]

Answer:

460

Step-by-step explanation: multiply all numbers to get your answer

6 0

3 years ago

You were testing orange juice recipes it’s recipe calls for orange juice concentrate and water mix one has 4 cups of concentrate

Sav [38]

Answer:

First mixed is the most orangey.

Step-by-step explanation:

First:

$Orange\ juice\ concentrate=4\ cups\\\\Water=6\ cups\\\\Tota\ content=4+6=10\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{4}{10}\times 100=40\%$

Second:

$Orange\ juice\ concentrate=1\ cups\\\\Water=3\ cups\\\\Tota\ content=1+3=4\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{1}{4}\times 100=25\%$

Third:

$Orange\ juice\ concentrate=2\ cups\\\\Water=4\ cups\\\\Tota\ content=2+4=6\ cups\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{Orange\ juice\ concentrate}{Total\ amount}\times 100\\\\Percentage\ of\ orange\ juice\ concentrate=\frac{2}{6}\times 100=33.33\%$

First mixed has highest percentage of orange juice. Hence first mixed is the most orangey.

4 0

3 years ago