si la función madre f(x) = [x] se transforma en h(x) = [x] + 3, ¿que transformación ocurre de f(x) a h(x)? ¿Como se ven afectados el vértice y el rango de h(x)?

The solution of the given quadratic equation are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

What is quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a ≠ 0 is true is known as a quadratic equation.

Consider, the given equation:

2y^2 + 11y + 10 = 0

Compare this equation with [tex]ay^2 + by + c = 0[/tex]

⇒  a = 2,  b = 11, c = 10

Consider, the quadratic formula

[tex]y = \frac{-b+-\sqrt{xb^2-4ac} }{2a}[/tex]

Plug the values of a, b, c in the quadratic formula.

⇒

[tex]y = \frac{-11+-\sqrt{11^2-4(2)(10)} }{2(2)} \\y = \frac{-11+-\sqrt{121-80} }{4}\\ y = \frac{-11+-\sqrt{41} }{4} \\y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex]

Hence, the solution of the given quadratic equation are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

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Y-axis divides the line segment formed by the points ( -3 ,2) and ( 6,1) in the ratio equals to 1 :2.

As given in the question,

Coordinates of the line segment is given by :

( x₁ , y₁ ) = (-3, 2)

(x₂ , y₂ ) = ( 6,1)

Let the ratio of the given line segment divided by the y -axis that is          ( x, y) = ( 0, y ) be   m : n given by the formula:

( x, y ) = [ ( mx₂ + nx₁) /(m +n) , (my₂ + ny₁ ) / ( m + n ) ]

Substitute the values we get,

( 0 ,y ) =  [ ( 6m -3n) /(m +n) , (1m + 2n ) / ( m + n ) ]

⇒ ( 6m -3n) /(m +n)  = 0

⇒ 6m -3n = 0

⇒ 6m = 3n

⇒m : n = 1 : 2

Therefore, y-axis divides the given line segment into the ratio 1 : 2.

The above question is incomplete, the complete question is :

In what ratio is the line segment joining the points (- 3 2) and (6,1) is divided by Y-axis?

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Question 10

[tex]\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}[/tex]

However, the second case does not satisfy the angle sum of a triangle, so [tex]x \approx 60.7^{\circ}[/tex].

Question 12

[tex]\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

The least count of Vernier calipers is 0.01cm and The length of the line is 10.23cm

Mean scale division:

The main scale is graduated with one division value equal to 1 mm. The length of the Vernier scale is the same as the n- scale of the Vernier scale and the (n-1) scale of the main scale.

Vernier Scale Division:

The minimum Vernier caliper number is also called the Vernier constant. Defined as the difference between the major and Vernier scales is represented mathematically as:

          VC = 1 MSD – 1 VSD

If the Vernier scale has n divisions, it matches the (n-1) divisions of the main scale. Vernier Caliper :

LC = ( 1 - [tex]\frac{n-1}{n}[/tex])  MSD

According to the problem

1MSD= 1mm

MSR = 10.2cm

Here, 10VSD  = 9MSD

          1VSD   = (9/10)MSD

                      =(9/10)×1mm

                      = (9/10)mm

Least count of Vernier calipers L.C = 1MSD - 1VSD

                                                           =1mm - (9/10)mm

                                                           =0.01mm

Therefore, Least Count (LC) = 0.01cm

Therefore,

Length of the line = MSR + (VSD × L.C)

                             = 10.2 + (3 × 0.01)

                             = 10.2+(0.03)p

                             = 10.23 cm

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Therefore , the solution of the given problem of combination comes out to be  479001.6.

Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.

Here,

Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..

and n ways for seating 8 people.

Thus , to find this permutation- combination arrangement .

So,

nPr => 6 P 6 and * 12P6

nPr =>  665280 * 720

nPr = > 47,90,01,600

and divide it by 1000 .

So ,

=> 479001600/1000

=> 479001.6

Therefore , the solution of the given problem of combination comes out to be  479001.6.

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As y varies directly with x, The value of y when x = -4 is 8/5.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Direct variation is expressed as;

y ∝ x

Then, y = k(x)

Where k is the proportionality constant.

Given that y = -8 and x = 20.

First determine the constant of proportionality k.

y = k(x)

-8 = k( 20 )

-8/20 = k

k = -8/20

k = -2/5

Next, we determine the value of y when x = -4.

y = k(x)

Plug in k = -2/5 and x = -4

y = -2/5( -4 )

y = -2/5 × -4

y = 8/5

Therefore, the numerical value of y is 8/5.

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The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Given equation,
y=x³+4x²+3x+12

To determine the x-intercept put equation y = 0

0 = x³+4x²+3x+12

Factorize the above equation

0=(x²+3)(x+4)

One of the factors from above is given as

x+4=0  

x = -4

The x-intercept is (-4,0)

For the y-intercepts, x=0 and solve.

y = 12

y = 12

The y-intercept is (0,12)

Now equation of the line passing these points is given as.

m = (y₂ - y₁) /  (x₂ - x₁)
m = 12/3
m = 3

C, we already have C=12

So the equation of the line is
y = mx + c
y=3x+12

Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

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Yes, the set of all real numbers is uncountably infinite but "infinity" is not   a member of the set of real numbers.

Basically, The real numbers R is the set of "all the numbers" on the number line that  includes the rationals and irrationals together.

The real numbers are an uncountably infinite set – there actually are far more real numbers than there are natural numbers, and there is no way to line up the reals and the naturals so that we are assigning exactly one real number to each natural number. Hence there is no possible way of counting the number it can be considered in the category of uncountably infinite. If the domain of a function is all real numbers, you can represent this using interval notation as (−∞,∞), however "infinity" is not a member of the set of real numbers.

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A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.

1. Calculate the means of the two samples.

2. Calculate the standard deviation of the two samples.

3. Calculate the degrees of freedom (df) by subtracting 1 from the total

number of samples.

4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.

5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.

6. Compare the calculated t-statistic with the critical value of t.

7. Make a decision – accept or reject the null hypothesis.

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Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.

Each point in the plane whose distance from that other point is a certain value forms a circle (center). It is therefore a curve composed of vertices that are spaced apart from one another in the plane by a specific amount. Furthermore, it is symmetrical about the center at all angles in terms of rotation. The closed, two-dimensional plane of a circle has all pairs of endpoints equally separated from the "center." When a line is drawn through the circle, a circle symmetry line is created. Furthermore, it rotates equally from all angles about the center.

Here,

The circle of the rear wheel is equal to circle = diameter x π, or 2.5 feet by 12 inches, or 30 inches.

The length of the front axle is 30 x 2 = 60 inches.

The diameter of the front wheel, C, is equal to 60 x Pi, or 60π, in inches.

The diameter of a back wheel is 4 x 2 = 8 inches.

The circumference of back wheel is C = 8 x Pi = 8π in inches.

750 revolutions are equal to

100 × [60Pi/8π] = 6,000π/8π.

100 rotations of the front tire will be made by the back wheel.

Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.

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7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are 49.

Calculating the sum of two or more numbers is the process of multiplication. It is stated as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation. Most word problems incorporate some type of narrative, hence they are sometimes called "story problems," and the quantity of technical jargon they employ can vary.

Given that 7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are:

Hats = (7)(7) = 49.

Hence, there are a total of 49 hats.

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For Sydney with $100 at 5%, monthly, for 10 year we get 229050.

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).

Let the equation be

A = [ p(1 + r/n)nt ] + [ PMT ((( 1 + r/n)nt - 1) / (r / n)) ]

For Sydney with $100 at 5%, monthly, for 10 year

A = [ 100(1 + 0.05/12)(12)(10) ] + 100 (((1 + 0.05/12)(12)(10) - 1) / (0.05 / 12)) ]

= 229050

Therefore, the correct answer is 229050.

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The required proportion of side lengths is JK/LK= JM/LN.

The Side-Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it splits those sides proportionally. In the case of triangle J K L, with line segment M N drawn parallel to side J L and intersecting sides J K and L K, the proportion of the lengths of the sides that are split can be determined by the ratio of the corresponding segments on each side.

Let's call the length of side J K as x, the length of side J L as y, and the length of side L K as z. Let the length of segment J M be a and the length of segment L N be b.

According to the side-splitter theorem, the proportion of the length of side J K to side L K is equal to the proportion of the length of segment J M to segment L N. This means that:

x/z = a/b

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The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The customer can send a package for $5, plus an additional $2 per pound.

The cost, y, can be represented by the equation y = 5 + 2x,

where x represents the amount of pounds of the package.

Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.

so, we get,

2x + 5 = 15

x = 5

Hence, The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

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Answer:

D: A package that weighs 5 pounds will cost $15 for both options.

Step-by-step explanation:

2x + 5 = 15

x = 5

Thus, the person above me is correct :)

The range, variance, and standard deviation are 8, 21.10, 445.21.

The range, variance, and standard deviation are 99, 40.14,1612

What is data?

Data is a collection of measurements or observations used as a source of information. There are numerous types of data and numerous ways to represent data.

Given data is

43, 41, 48, 47, 49

Arrange them in ascending order:

41, 43, 47, 48,49

The range is (49 - 41) =8

The mean is (41+43+47+48+49)/5 =45.6

Data      deviation from mean    square  deviation

41                         4.6                         21.16

43                         2.6                        6.76

47                         -1.4                        1.96

48                         -2.4                        5.76

49                         -3.4                        11.56

Total                                                  47.2

The standard deviation is s = √[(x-μ)²/N] = 21.10

The variance is s² = 445.21

Given data is

100, 1, 3, 95, 70, 4, 6, 10, 5

Arrange them in ascending order:

1, 3, 4, 5, 6, 10, 70, 95, 100

The range is (100 - 1) = 99

The mean is (1+3+4+6+5+10+70+95+100)/9 =32.67

Data      deviation from mean    square  deviation

1                         31.67                         1002.99

3                         29.67                       880.31

4                         28.67                        821.97

5                        27.67                         756.63

6                         26.67                        711.29

10                         22.67                      513.93

70                        -37.33                       1393.52

95                        -62.33                      3885.03

100                         -3.33                        4533.33

Total                                                     14508.0001

The standard deviation is s = √[(x-μ)²/N] = 40.14

The variance is s² = 1612

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We may apply the simple interest formula to find the due date for repayment from Mikos is 5 months.

I = P*r*t, where I represents interest, P the principal (initial sum), r the interest rate, and t the period of time in years.

The maturity value formula can be used to calculate interest given that the loan's principal is $100,000 and its maturity value is $104,375:

Where MV is the maturity value, P is the principal, and I is the interest, the formula is: MV = P + I.

With the above data, we obtain: 104,375 = 100,000 + I

  I = 4,375.

Now we can use this value of I to find the time t in years:

I = P*r*t

4,375 = 100,000 (0.105) t

t = 4.375 / (100,000 x 0.105)

t = 4.375 / 10,500

t = 0.417 years or approximately 5 months

 So, it takes approximately 5 months to repay the pay back amount .

Therefore, Mike must repay the amount by April 14, which is around five months after the day he took out the loan.

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A degree 3 polynomial has either 1 real root, 2 real roots, or 3 real roots. It is possible for the polynomial to have imaginary roots as well, but these are not counted.

A polynomial of degree 3 is a equation in the form of ax3 + bx2 + cx + d = 0. For a polynomial of degree 3, the number of roots it has depends on the value of the discriminant, which is calculated using the formula b2 - 4ac.  If the discriminant is positive, the polynomial has three real roots. If the discriminant is equal to zero, the polynomial has two real roots. If the discriminant is negative, the equation has one real root and two imaginary roots. In the case of one real root, the polynomial can be factored into (x - r) (ax2 + bx + c). In the case of two real roots, the polynomial can be factored into (x - r1) (x - r2). In the case of three real roots, the polynomial can be factored into (x - r1) (x - r2) (x - r3).

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Answer:

A) 4x4 – 3x3y + 8x2y2 – 7xy3

Step-by-step explanation:

The polynomial written in standard form is: 4x4 + 8x2y2 - 3x3y - 7xy3. Option C

In standard form, a polynomial is written with the highest exponents first and positive numbers in front of each term.

This means that the term with the greatest power comes first, followed by the terms in decreasing order of powers.

The polynomial is organized in option C like this.

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Answer: 15/2

Step-by-step explanation: -5/2 + 1/4W = -5/8

-    1/4W = -5/8 + 5/2

-    1/4W = 15/8

-     W = 15/8 × 4

-      W = 15/2

The surface area is approximately 100.5m².

Surface Area = πrl + πr²

Where r is the radius of the base and l is the slant height.

Surface Area = π(2m)(4m) + π(4m)²

Surface Area = 100.5m²

The surface area of a right circular cone can be calculated by using the formula surface area = πrl + πr². In this particular case, the height of the cone is 4m and the radius of the base is 2m. Therefore the surface area of the cone is calculated as follows: π(2m)(4m) + π(4m)² = 100.5m². This surface area includes both the base and sides of the cone.

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The approximate cost per ounce of a container of gochujang at the market is given as follows:

$0.5.

As we have the graph of the linear function, the best way to define it is in slope-intercept form, as follows:

y = mx + b.

For which the parameters are given as follows:

The cost per ounce is represented by the slope.

From the graph, we have that the graph starts at the origin, and when the number of ounces increases by 4, the cost increases by 2, hence the slope representing the cost per ounce is given as follows:

m = 2/4

m = $0.5.

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Answer:

4 km wide and 6 km long.

Step-by-step explanation:

Let the width be x, then the length is x+2 km.

Area = width * length

Substituting the given values:

24 = x(x + 2)

24 = x^2 + 2x

x^2 + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

As x must be positive, then x = 4.

So, the dimensions are 4 and 4+2

= 4, 6,

Answer:

width = 3.46 km and length = 6.93 km

Step-by-step explanation:

let the width be : X km

then the length would be: 2X km

as area is length x width

therefore:

2X x X = 24

2X² = 24

X² = 24/2

X² = 12

X = [tex]\sqrt{12}[/tex]

X=  3.46

the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km

The can is a cylinder with the smallest height and a radius that is the square root of the volume divided by 2[tex]\pi[/tex].

The formula to calculate the volume of a cylinder is given by the product of the base area and its height. The volume of a cylinder = πr2h cubic units.

To find the dimensions of a 12-oz can that can be constructed with the least amount of metal, we need to minimize the surface area of the can while maintaining a volume of [tex]355 cm^3[/tex]. The surface area of a cylindrical can is given by [tex]2\pi r(r+h)[/tex] where r is the radius of the base of the can and h is the height of the can.

Minimizing the surface area of the can is equivalent to minimizing the total material used in constructing the can. This can be achieved by making the height of the can as small as possible while maintaining a volume of 355 cm^3. The volume of a cylindrical can is given by πr^2h,

So the equation is:

[tex]\pi r^2h= 355cm^3[/tex]

We can get the value of h in terms of r by dividing both sides by πr^2

[tex]h= 355cm^3 / (\pi r^2)[/tex]

Now we can substitute this value of h in the equation for the surface area:

[tex]2\pi r(r+h) = 2\pi r(r + 355cm^3 / (\pi r^2))[/tex]

Now we can differentiate the above equation with respect to r and set it equal to zero to find the minimum value of the surface area.

[tex]d(2\pi r(r+h))/dr = 2\pi r + 2\pi (355cm^3 / (\pi r^2)) = 0\\r = sqrt(355cm^3 / (2\pi ))[/tex]

Now we can substitute this value of r back into the equation for the volume of the can to find the corresponding value of h:

[tex]\pi r^2h = 355cm^3[/tex]

h = [tex]355cm^3 / (\pi r^2) = 355cm^3 / (\pi (355cm^3 / (2\pi ))^2)[/tex]

The dimensions of the 12-oz can that can be constructed with the least amount of metal are a radius of sqrt(355cm^3 / (2π)) and a height of 355cm^3 / (π (355cm^3 / (2π))^2).

Hence, the can is a cylinder with the smallest height and a radius that is the square root of the volume divided by 2π.

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Complete question: A soda can is to hold 12 fluid ounces. Find the dimensions that will minimize the amount of material used in its construction, assuming the thickness of the material is uniform?

Answer:

B

Step-by-step explanation:

the 4 is how far along you go on the x-axis (horizontal line).

the -2 is saying it needs to be 2 boxes below 0 on the y-axis (vertical line).

therefore the answer is b

Answer:

38

Step-by-step explanation:

4/2+33-2+5=2+33-2+5=35-2+5=33+5=38

The answer is C) 195/8

First, we can use the fact that A, B, C, D, E, and F are concyclic and that D, E, and F are the midpoints of AB, BC, and AC respectively.

Let r be the radius of the circumcircle of triangle ABC. Then using the Pythagorean theorem, we can find that r = (151413) / (4*K) where K is the area of the triangle.

Now we can use the property that the perpendicular bisectors of any triangle pass through the circumcenter of the triangle. We know that the midpoint of a line segment is the foot of the perpendicular from that point to the other endpoint. Then we can use the property that the radius from the circumcenter of the triangle to the midpoint of a side is half the length of that side.

Therefore, the circumcenter of triangle BDE is located at X = (BD/2, DE/2) = (13/2, 7/2) and the circumcenter of triangle CEF is located at X = (CE/2, EF/2) = (15/2, 7/2).

So the coordinates of X are (13/2, 7/2) and since the circumcenter of a triangle is equidistant from each vertex of the triangle, we can find that XA = XB = XC = r = r = (151413) / (4*K)

Therefore, XA + XB + XC = 3r = 3(151413) / (4*K) = (195/8)

So the answer is c. 195/8.

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Answer:

1) 33.422

2) 0.37

3) 34.034567

4) 19.501

5) 38.07

6) 51.02

7) 65.38

8) 0.072

Cheers

Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

It is given by:

f(x) = 9x² - 54x - 144.

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0,

hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.

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let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.

[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-\sqrt{5}i\hspace{5em}\stackrel{conjugate}{-1+\sqrt{5}i} \\\\\\ (-1-\sqrt{5}i)(-1+\sqrt{5}i)\implies (-1)^2~~ - ~~(\sqrt{5}i)^2\implies (-1)^2~~ - ~~(\sqrt{5})^2 i^2 \\\\\\ 1~~ - ~~(\sqrt{5^2})i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}[/tex]

The amount it would cost to buy 3.9 pounds of steak is $2.59

From the question, we are to determine how much it would cost to buy 3.9 pounds of steak

Let the cost be $x

From the given information, we have that

55 pounds of steak cost $36.50

If 55 pounds of steak cost $36.50

Then,

3.9 pounds of steak will cost $x

Thus,

55 × x = 3.9 × 36.50

55x = 142.35

x = 142.35/55

x = 2.588

x ≈ 2.59

Hence, the cost is $2.59

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