Which statement is true about the voting results?​

The equation that can be used to find the cost of each binder n in dollars is 861=7n.

Given that the cost of 7 binders is $8.61.

We are required to form an equation that represents the total cost of each binder n in dollars.

Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.

Suppose the cost of 1 binder is n dollar.

We know that the total cost is basically the product of price of 1 unit and number of quantities of units.

Total cost=Price of 1 unit* number of units

8.61=n*7

8.61=7n

Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.

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Answer:

This questions seems to be incomplete but generally tan with x is expressed as

tan(x) =

Answer:

d ≈ 21.26 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 8 ) and (x₂, y₂ ) = (13 - 6 )

d = [tex]\sqrt{13-(-3))^2+(-6-8)^2}[/tex]

   = [tex]\sqrt{(13+3)^2+(-14)^2}[/tex]

   = [tex]\sqrt{16^2+196}[/tex]

   = [tex]\sqrt{256+196}[/tex]

   = [tex]\sqrt{452}[/tex]

   ≈ 21.26 units ( to 2 dec. places )

Answer:

The distance is 21.3

Step-by-step explanation:

The solution is in the attached image

The equivalent expression of  2x√44x - 2√11x  is 2x√11x

An equivalent expression can be find when simplified or factorised.

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

The expression equivalent to 2x√44x - 2√11x is as follows:

2x√44x - 2√11x

factorise

2x√44x - 2√11x = 2(x√44x - √11x³)

Hence,

2(x√44x - √11x) = 2(x√4 × 11x  - √11x³)

2(x√4 × 11x  - √11x) =  2(2x√11x  - x√11x)

Therefore,

2(2x√11x  - x√11x) = 4x√11x - 2x√11x

4x√11x - 2x√11x = 2x√11x

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Utilizando la distribución binomial, la probabilidad de resolver un problema de n problemas propuestos, es p^n.

La fórmula es:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

La probabilidad de que todos los problemas sean resolvidos es dada por P(X = n), asi:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = n) = C_{n,n}.p^{n}.(1-p)^{n-n}[/tex]

P(X = n) = p^n

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Answer: 30%

Step-by-step explanation:

the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%

Answer:

30%

Step-by-step explanation:

For Connexus students its 30% :)

The voltage of the circuit is 8 + i .  Option C

From the information given, we have that;

E = IZ

Where;

We have that;

I = 3 + 2i

Z = 2 - i

Substitute into the formula

E = IZ

E = ( 3 + 2i) ( 2 - i)

Making the product of complex numbers we have:

E = ( 3 × 2 - i ) + ( 4i - 2i²)

E = ( 6 - 3i ) + ( 4i - 2 ( -1) )

E = ( 6 + 2) + ( 4 - 3 ) i

E = 8 + i

Thus, the voltage of the circuit is 8 + i .  Option C

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Answer:

It's C

Step-by-step explanation:

The average rate of change obtained from the ratio of change in y to the change in x is 27

The average rate of change can be obtained using the relation :

Rate of change = (y2 - y1) ÷ (x2 - x1)

at; x1 = -3

y1 can be calculated from the function ;

y1= 3(-3³)-1

y1=-82

At ; x2 = 3

y2 can be calculated from the function ;

y2 = 3(3³)-1

y2=80

The rate of change can be calculated thus : (y2 - y1) ÷ (x2 - x1)

[80-(-82)]/[3-(-6])

162/6

27

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The closest point is (3.5, 1.9) and the distance is 1.96 units

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

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The given triangle has three angles with measurements: ∠A = 69°, ∠B = 52°, and ∠C = 59° respectively. Using the law of cosines, these angles are calculated from the given lengths of the triangle.

The law of cosines gives the relationship between the lengths of sides and the angles of the triangle ABC.

According to the law of cosines:

Cos A = (b² + c² - a²)/2bc

Cos B = (a² + c² - b²)/2ac

Cos C = (a² + b² - c²)/2ab

For the given triangle ABC,

a = 75, b = 63, and c = 69

So, using the law of cosines,

Cos A = (b² + c² - a²)/2bc

⇒ Cos A = (63² + 69² - 75²)/2×63×69

⇒ Cos A = 5/14

⇒ A = Cos⁻¹(5/14) = 69.07

∴ ∠A = 69°

Similarly,

Cos B = (a² + c² - b²)/2ac

⇒ Cos B = (75² + 69² - 63²)/2×75×69

⇒ Cos B = 31/50

⇒ B = Cos⁻¹(31/50) = 51.6 ≅ 52

∴ ∠B = 52°

Cos C = (a² + b² - c²)/2ab

⇒ Cos C = (75² + 63² - 69²)/2×75×63

⇒ Cos C = 179/350

⇒ C = Cos⁻¹(179/350) = 59.2

∴ C = 59°

Thus, the angles of the triangle ABC are 69°, 52°, and 59° respectively.

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Answer:

Step-by-step explanation:

Begin by filling in x as -2 and y as √12 in the given expression:

[tex]2(3(-2)^3+2(\sqrt{12})^2)[/tex].  Work inside the parenthesis first and deal with those exponents:

(-2)³ is the same as (-2)(-2)(-2) which is -8;

(√12)² is the same as (√12)(√12) which is √144 which is 12.

Filling those simplifications in:

[tex]2(3(-8)+2(12))=2(-24+24)=2(0)=0[/tex]

Answer:

Step-by-step explanation:

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Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

According to thermodynamics, heat is a type of energy that crosses a thermodynamic system's border due to a temperature differential across the barrier. In a thermodynamic system, heat is not present.

But the phrase is also frequently used when referring to the thermal energy that makes up a system's internal energy and is reflected in the system's temperature. Heat is a type of energy in both senses of the word. Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

Therefore, heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

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Answer:

Area = 32feet²

Step-by-step explanation:

Perimeter of a rectangule = 2(length+width)

Then:

g = 2w               Eq. 1

2(g+w) = 24       Eq. 2

g = length

w = width

From Eq. 2:

(2*g + 2*w) = 24

2g + 2w = 24      

2w = 24 - 2g            Eq. 3

Matching Eq. 1  and Eq. 3

g = 24 - 2g

g + 2g = 24

3g = 24

g = 24/3

g = 8 feet

From Eq. 1

g = 2w

8 = 2w

8/2 = w

w = 4 feet

Check:

From Eq. 2

2(g+w) = 24

2(8+4) = 24

2*12 = 24

Answer:

Area of a rexctangle = length * width

Then:

Area = 8feet * 4feet

Area = 32feet²

The expression representing the given statement is 7×(6+3)-(4÷2). Option A is correct.

Given the statement is Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.

Firstly, we will break the statement in two parts that is Multiply 7 by the sum of 6 and 3 and second part is subtract the quotient of 4 and 2.

Multiply 7 by the sum of 6 and 3 means there is addition sign between 6 and 3 and the addition of 6 and 3 is multiply with 7, we get

7×(6+3)    ......(1)

subtract the quotient of 4 and 2 means 4 is divisible by 2 and this is subtract means there is a minus sign, we get

-(4÷2)   .....(2)

Combine equation (1) and (2), we get

7×(6+3)-(4÷2)

Hence, the expression which represents the given statement Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2 is 7×(6+3)-(4÷2).

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The probability that of 6 randomly selected patients, 4 will recover is 0.03295

The chance of an event occurring is defined by probability.

Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.

Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]

                                = 0.03295

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a) The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function g(x) in factored form is g(x) = [(x - 6) · (x + 3)] / (x - 2). there is no slant asymptotes.

c) There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

a) In the first part of this question we need to determine the equation of a polynomial in expanded form, derived from its factor form defined below:

f(x) = Π (x - rₐ), for a ∈ {1, 2, 3, 4, ..., n}         (1)

Where rₐ is the a-th root of the polynomial.

If we know that r₁ = 6, r₂ = - 1 and r₃ = - 3, then the polynomial in factor form is:

f(x) = (x - 6) · (x + 1) · (x + 3)

f(x) = (x - 6) · (x² + 4 · x + 4)

f(x) = (x - 6) · x² + (x - 6) · (4 · x) + (x - 6) · 4

f(x) = x³ - 6 · x² + 4 · x² - 24 · x + 4 · x - 24

f(x) = x³ + 10 · x² - 20 · x - 24

The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function is introduced below:

g(x) = (x³ + 10 · x² - 20 · x - 24) / (x² - x - 2)

g(x) = [(x - 6) · (x + 1) · (x + 3)] / [(x - 2) · (x + 1)]

g(x) = [(x - 6) · (x + 3)] / (x - 2)

The slope of the slant asymptote is:

m = lim [g(x) / x] for x → ± ∞

m = [(x - 6) · (x + 3)] / [x · (x - 2)]

m = 1

And the intercept of the slant asymptote is:

n = lim [g(x) - m · x] for x → ± ∞

n = Non-existent

Hence, there is no slant asymptotes.

c) There is vertical asymptote at a x-point if the denominator is equal to zero. There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

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Answer:

Simplified: 4X^3

Step-by-step explanation:

Simplify the expression.

1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.

2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.

3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.

4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.

Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.

Affordability can be measured as a Debt To Income (DTI) ratio.

Current monthly income = $3,500

Monthly mortgage payment = $900

Monthly student loan payment = $350

Total monthly debt payment = $1,250

Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)

Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.

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The answer to the questions of volumes are given as follows

a) [tex]v=128 \pi[/tex]

b) [tex]v=\frac{128}{3} \pi[/tex]

 c)[tex]v=\frac{1024}{5} \pi[/tex]

d)[tex]V=\frac{13568}{15} \pi[/tex]

Generally, the questions are  mathematically solved below

[tex]y=\sqrt{x}, y=4, x=0[/tex]

a) x-axis

if $y=4, x=16, x=0$

Using disk method

[tex]} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\[/tex]

[tex]v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\[/tex]

[tex]v=\frac{\pi}{2} \times 16 \times 16 \\[/tex]

[tex]v=128 \pi[/tex]

b)  line y=4

if x=0, y=0 ;

[tex]y=\sqrt{x} \Rightarrow x=y^{2}[/tex]

Using shell method

[tex]v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\[/tex]

[tex]v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y[/tex]

[tex]v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\[/tex]

[tex]v=\frac{2 \pi}{12}[1024-768] \\[/tex]

[tex]v=\frac{512 \pi}{12} \\[/tex]

[tex]v=\frac{128}{3} \pi[/tex]

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

[tex]v=\pi \int_{0}^{4} y^{4} d y$[/tex]

[tex]v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\[/tex]

[tex]v=\frac{1024}{5} \pi[/tex]

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

[tex]V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$[/tex]

[tex]V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\[/tex]

[tex]V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\[/tex]

[tex]V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\[/tex]

[tex]V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\[/tex]

[tex]V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)[/tex]

[tex]V=\frac{256}{15}(5+48) \pi \\[/tex]

[tex]V=\frac{256 \times 53}{15} \pi \\[/tex]

[tex]V=\frac{13568}{15} \pi[/tex]

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Using the triangle midsegment theorem, the length of AC in the given triangle is: 40 units.

The midsegment of a triangle can be defined as the line segment that intersects two sides of a triangle at their midpoints. This means that, the sides they intersect is bisected forming two equal halves.

In a typical triangle, there are three midsegments in the triangle. For example, in the image given in the attachment below, the midsegments of the triangle are: DF, FB, and BD. All midsegments are parallel to the third sides of a triangle.

What is the Triangle Midsegment Theorem?

According to the triangle midsegment theorem, the length of the midsegment (i,e. DF) is parallel to the third side (i.e. AC) and also half the length of the third side (AC).

We are given the following:

EC = 30

DF = 20

Applying the triangle midsegment theorem, we have:

DF = 1/2(AC)

Substitute

20 = 1/2(AC)

2(20) = AC

40 = AC

AC = 40 units.

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The volume (in cubic centimeters) of a box) given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

V = 6h

Where,

If the height = 6 cm

Fixed base area = 6 cm²

V = 6h

= 6 cm² × 6 cm

V = 36 cm³

Therefore, the volume of the box given the fixed base area of 6cm² and height of 6 cm is 36 cm³.

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Answer:

f(4)=14

Step-by-step explanation:

a) u do it by substituting 4 in places where there r 'x'

since this one say f(4) it only can go to the function which says f(x)
f(x)=4x-2
f(4)=4(4)-2, so according to BODMAS rule multiplication comes first rather than subtraction

so, f(4)=16-2=14
f(4)=14
do the others based on this, hope i explained well, if i did, please gimme brainliest :)

First, I will subtract 53 from 697.

697 - 53 = 644

Next, I will divide the total by 2.

644 / 2 = 322.

This means the cost of the garden table is 322.

I will add 53 back to the total.

322 + 53 = 375.

The cost of the bench is $375.

The price at which equilibrium is achieved is $20.

The equilibrium point is the point where the lines of the demand and supply functions meet.

From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).

Also from the question, the lines intersect at point (15, 20).

The y-coordinate of the intersection point is 20 in this scenario.

Hence, the price at which equilibrium is achieved is $20.

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Answer:

b

Step-by-step explanation:

Answer:

[tex]t = \cfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]4(t+\cfrac{1}{4})=3[/tex]

Divide both sides by 4:

[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]

Subtract 1/4 from both sides:

[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]

[tex]t = \cfrac{2}{4}[/tex]

Simplify:

[tex]t = \cfrac{1}{2}[/tex]

Answer:

[tex]t = \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]4(t + \frac{1}{4} ) = 3[/tex]

Divid the whole equation by 4.

[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]

[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]

[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]

Take 1/4 to right side.

[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]

[tex]t= \frac{2}{4} [/tex]

To simplify the answer more divide the numerator and denominator by 2.

[tex]t = \frac{1}{2} [/tex]

[tex]\boldsymbol{\sf{6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Convert 6 to the fraction 18/3.

                       [tex]\boldsymbol{\sf{\dfrac{18}{3} -\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.

                       [tex]\boldsymbol{\sf{\dfrac{18+1}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 \ \longmapsto \ \ [Add \ 18+1] }}[/tex]

                              [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 }}[/tex]

Subtract [tex]\bf{\frac{1}{2}x }[/tex] on both sides.

                               [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x-\dfrac{1}{2}x=5 }}[/tex]

Combine [tex]\bf{-\frac{3}{4}x}[/tex] and [tex]\bf{-\frac{1}{2}x}[/tex] to get [tex]\bf{-\frac{5}{4}x}[/tex].

                                [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{5}{4}x=5 }}[/tex]

Subtract 19x from both sides.

                                       [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=5-\dfrac{19}{3} }}[/tex]

Convert 5 to the fraction 15/3.

                                      [tex]\boldsymbol{\sf{-\dfrac{4}{5}x=\dfrac{15}{3}-\dfrac{19}{3} }}[/tex]

Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.

                             [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=\dfrac{15-19}{3} \ \longmapsto \ \ [Subtract \ 15-19] }}[/tex]

                                 [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=-\dfrac{4}{3} }}[/tex]

Multiply both sides by -4/3, the reciprocal of -4/3.

                                    [tex]\boldsymbol{\sf{x=-\dfrac{4}{5}\left(-\dfrac{4}{5}\right) }}[/tex]

Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

                   [tex]\boldsymbol{\sf{x=\dfrac{-4(-4)}{3\times5} \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}[/tex]

                                 [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=\frac{16}{15} }}}}}[/tex]

Answer:

Step-by-step explanation:

To solve this, you have to divide this fraction from left to right.

Fraction is a division or part of a whole number.

First, do apply the fraction rule.

[tex]\rightarrow: \sf{\dfrac{A}{B}\div \dfrac{C}{D}=\dfrac{A}{B}\times \dfrac{D}{C}}[/tex]

[tex]\sf{-\dfrac{1}{50}\times \dfrac{100}{1}}[/tex]

Cancel the common factor of 50.

[tex]\sf{-\dfrac{2}{1} }[/tex]

Divide.

-2/1=-2

[tex]\rightarrow: \boxed{\sf{-2}}[/tex]

So, the final answer is -2.

I hope this helps, let me know if you have any questions.

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Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.

The expected winnings for Steve are a function of the probability of some predictable outcomes.

In this situation, the predictable outcome is the size of the lottery prize.

The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.

Sale price per ticket = $5

Lottery prize = $300

Value of lottery prize to Steve if he wins = $295 ($300 - $5)

Probability of winning = 1% (1/100 x 100)

Expected win = $3 ($300 x 1%)

Thus, Steve's expected win is $3, which outweighs the cost of a ticket.

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Answer:

  none

Step-by-step explanation:

The domain of the equation can be found by looking at the requirements ...

For n+2 ≥ 0, we find ...

  n ≥ -2 . . . . . . . . subtract 2 from both sides

For -16-5n ≥ 0, we find ...

  -16 ≥ 5n . . . . . add 5n

  -3.2 ≥ n . . . . . divide by 5

Together, these domain restrictions require that ...

  n ≥ -2

  n ≤ -3.2

These intervals do not overlap, so there are no values of n that can satisfy this equation.

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Additional comment

The solutions would appear on the attached graph as points where the curves intersect above the x-axis. They do not intersect, hence the equation has zero solutions.

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If we were to solve this without regard to domain restrictions, we would square both sides to get ...

  (n +2)² = -16 -5n

  n² +9n +20 = 0 . . . . . put in standard form

  (n +4)(n +5) = 0 . . . . . factor

  n = {-5, -4} . . . . . . . . . both are extraneous solutions.

These "solutions" do not satisfy the requirement that the square root be positive.

Answer:

y = 2x² − 12x + 8

Step-by-step explanation:

FIRST METHOD :

y = 2x² − 12x + 8

  = (2x² − 12x) + 8

  = 2 (x² − 6x) + 8

  = 2 (x² − 6x + 9 − 9 ) + 8

  = 2 (x² − 6x + 9) − 2×9 + 8

  = 2 (x² − 6x + 9) − 18 + 8

  = 2 (x² − 6x + 9) − 10

  = 2 (x − 3)² − 10

Then ,the equation has a extremum value of (3,-10)

Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0

(2 > 0) , the graph (parabola) opens upward

Therefore ,the extremum (3,-10) is a minimum.

SECOND METHOD :

the graph of a function of the form f(x) = ax² + bx + c

has an extremum at the point :

[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]

in the equation : f(x) = 2x² − 12x + 8

a = 2  ; b = -12  ; c = 8

Then

[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]

Then

[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]

the graph of a function f(x) = 2x² − 12x + 8

has an extremum at the point (3 , -10)

Since the parabola opens up ,then the extremum (3,-10) is a minimum.