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3 years ago

Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 8x + 6

Mathematics

1 answer:

irga5000 [103]3 years ago

4 0

Answer:

Minimum at (-4, -10)

Step-by-step explanation:

x² + 8x + 6

The coefficient of x² is positive, so the parabola opens upward, and the vertex is a minimum.

Subtract the constant from each side

x² + 8x = -6

Square half the coefficient of x

(8/2)² = 4² = 16

Add it to each side of the equation

x² + 8x + 16 = 10

Write the left-hand side as the square of a binomial

(x + 4)² = 10

Subtract 10 from each side of the equation

(x+ 4)² -10 = 0

This is the vertex form of the parabola:

(x - h)² + k = 0,

where (h, k) is the vertex.

h = -4 and k = -10, so the vertex is at (-4, -10).

The Figure below shows your parabola with a minimum at (-4, -10).

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Find the minimum sample size needed to be 99% confident that the sample's variance is within 30% of the population's variance.

liq [111]

The Minimum sample size table is attached below

Answer:

$X=173$

Step-by-step explanation:

From the question we are told that:

Confidence Interval $CI=99\%$

Variance $\sigma^2=30\%$

Generally going through the table the

Minimum sample size is

$X=173$

7 0

3 years ago

Solve for w.<br> -3(-8w+1) -w=5(w-1)-1<br> Simplify your answer as much as possible.<br> W =

oksian1 [2.3K]

Answer:

W = - 6

Step-by-step explanation:

-3(-8w+1) - w = 5(w-1) - 1 -> (Original equation)

24w - 3 - w = 5w - 5 - 1 -> (Expanded version)

23w - 3 = 5w - 6 -> (Simplified version)

18w - 3 = - 6 -> (Subtract 5w from both sides)

18w = - 3 -> (Add 3 to both sides)

w = 18/-3 which is - 6 -> (Doing 18/-3)

5 0

3 years ago

Factorize 2a^2+7a-15

loris [4]

$\huge\bf \pink {\underline{Solution :-}}$

$2 {a}^{2} + 7a - 15$

$= 2 {a}^{2} + 10a - 3a - 15$

$= 2a(a + 5) - 3(a + 5)$

$= (a + 5)(2a - 3)$

$\sf \red{Hence, Answer \: is \: (a + 5)(2a - 3).}$

$\\$

$\bf \purple{ \underline{ Important \: Formulas \: for \: Factorization :-}}$

$• \: {a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}$

$• \: (a + b)(a - b) = {a}^{2} - {b}^{2}$

$• \: {a}^{2} - 2 ab + {b}^{2} = {(a - b)}^{2}$

$• \: {a}^{3} + 3 {a}^{2} b + 3a {b}^{2} + {b}^{3} = {(a + b)}^{3}$

$• \: {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{3}$

$• \: {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )$

$• \: {(a + b)}^{2} - {(a - b)}^{2} = 4ab$

$• \: (a + b)( {a}^{2} -ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

$• \: (a - b)( {a}^{2} + ab + {b}^{2} ) = {a}^{3} - {b}^{3}$

$• \: {( \frac{a + b}{2} )}^{2} - ( {\frac{a - b}{2} } )^{2} = ab$

5 0

3 years ago

Read 2 more answers

Graph the solution to the inequality<br> |y+5|> 2

kirill [66]

Answer:

y>-3 y>-7

Step-by-step explanation:

-(y+5)>2

y<-7

7 0

3 years ago

Why did the cow give only buttermilk

Anastaziya [24]

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5 0

3 years ago