What is an equation of the line that passes through the points (2, -8) and (1, -7)

Answer:

The answer is -10/9

Step-by-step explanation:

10*x=(-1.111...*10 .) second equation

10x=-11.111....

subtruct second equation from the first equation

10x=10*-11.111.

-

x=-1.1111.

9x=10

x=10/9

The surface area of the solid cuboid 7m 6m and 3m. total surface area of cuboid is 162 [tex]m^{2}[/tex].

A cuboid is a six-sided solid known as a hexahedron in the geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces. A cuboid is a convex polyhedron with the same polyhedral graph as a cube in mathematics.

A cube with six square faces, a rectangular prism, rectangular cuboid, or a rectangular box with six rectangle faces are special situations. In both circumstances, the faces of the cube and the rectangular prism come together at a right angle.

total surface area of cuboid

= 2(lb+bl+lh)

=2(7×6+6×3+3×7)

=2(81)

=162 [tex]m^{2}[/tex]

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The probability of getting 2 at least once is 1/6.

So, the probability of getting a 2 at least once:

Formula of probability: P = favourable events/total events

Now, substitute the values in the formula as follows:

Therefore, the probability of getting 2 at least once is 1/6.

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The expression of the number 0.133333 as a fraction would give us 133333/1000000.

Let us recall that the term fraction is used to show that there is a top and a bottom part in the expression. The top part of the fraction is called the numerator while the bottom part of the fraction is called the denominator.

If we want to convert the fraction as we have it back to the decimal then we just have to divide the numerator by the denominator and we are back to the decimal. The decimal is marked by the presence of a decimal point.

To convert 0.133333 to fraction, we would take the decimal point as 1 and all other digits after it as zero thus we have;

133333/1000000.

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The fraction of the  blue T-shirts that are on sale and are size medium are 1/7.

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

Of all the shirts in the shop , 2/3 of the t-shirts are blue.

Of the blue shirts, 3/7 are on sale.

= 2/3  x 3/7

= 2/7

Out of all the shirts, 2/7 shirts are blue and are on sale.

Of the blue shirts on sale, 1/2 are size medium.  

= 2/7 x 1/2

= 1/7

The fraction of the  blue T-shirts that are on sale and are size medium are 1/7.

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the answer is 29 hope this helps

Lines through the given points are as follow:

a. Line1 is perpendicular to line2.

b. Line1 is neither perpendicular nor parallel to line2.

c. Line1 is parallel to line2.

As given in the question,

Slopes of the lines through the given points are as follow:

Let m₁ and m₂ be the slope of line1 and line2 respectively.

a. Line1 ( 2,-3) , (-4, -6) and Line2 (-3,2) ,  (2,-8)

m₁=(-6+3)/ (-4-2)

    =1/2

m₂=(-8-2)/ (2+3)

    =-2

m₁ × m₂ = -1

Line1 and line2 are perpendicular.

b. Line1(-4, -5) , (4,1) and line2 (6,10) , (-3,-2)

m₁=(1+5)/ (4+4)

    =3/4

m₂=(-2-10)/ (-3-6)

    =4/3

m₁ × m₂=1

Line1 and line2 are neither perpendicular nor parallel .

c. Line1 (0,-4) , (-2,-8) and line2 (-1,5), (1,9)

m₁=(-8+4)/ (-2-0)

    =2

m₂=(9-5)/ (1+1)

    =2

m₁=m₂

Line1 and line2 are parallel

Therefore, lines through the given points are as follow:

a. Line1 is perpendicular to line2.

b. Line1 is neither perpendicular nor parallel to line2.

c. Line1 is parallel to line2.

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the answer is x= -48

solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!

9:

By taking the quotient between the total debt and what they earn in a sold-out show, we conclude that they need to sell a total of 7 sold-out shows.

10:

A discount of 30%. Correct option is B.

Answering part 9:

We know that they asked for a loan of $8,000, such that an interest of the 6% is applied to this, so the total amount that they need to return is:

$8,000*(1 + 6%/100%) = $8,000*(1.06) = $8,480

Now we know that the theater has 150 seats, and each ticket costs $8.50, so for every sold-out show they earn a total of:

T = 150*$8.50 = $1,275

Then the number of sold-out shows that they need is given by the quotient:

$8,480/$1,275 = 6.65

Rounding to the next whole number we get to 7. To cover the debt, they need to sell a total of 7 sold-out shows.

10. The original price is $180 and she pays $126, then the discount k is:

$180*k = $126

k = $126/$180 = 0.7

and 1 - 0.7 = 0.3

So the discount is of the 30%.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -6= 2 (x +2) \\\\\\ y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}[/tex]

Answer:

17%

Step-by-step explanation:

Hello!

Out of the 6 options, only 1 option will be correct. This can be represented as a ratio of 1:6.

If you randomly guess, there is an equal chance of choosing any of the 6 options.

To find the percentage of guessing the correct option, simply divide 1 by 6 (1 option is correct out of 6), and multiply the outcome by 100 (for percentage).

The probability of getting an answer correct would be 17%.

The probability of getting an answer wrong would be 83%, which can be found by subtracting 17% from 100%.

The rate at which the grocery store clerk can scan products is 2 products per second.

Rate is the speed at which an activity can be carried out. Rate can be determined by dividing the total products that are bagged by the time it takes to bag the product.

Division is used to determine the product of two or more numbers. The sign that represent division is ÷. Division is a mathematical operations. Other mathematical operations include addition, subtraction and multiplication. Division entails grouping a number into equal groups using another number.

Rate = number of products ÷ time

1 ÷ 1/2

1 x 2 = 2 products per second

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Based on the population density of the area in 1980 and the area, the population in 1980 was 807,750 people

The population density of an area is based on the population of the area and the area. The formula is:

Population density = Population of area / Surface area

Given that the surface area is 750 square miles and the population density in 1980 was 750 square miles, the population of the area can be found by the formula:

Population in 1980 = Population density in 1980 x surface area

Population in 1980 = 1,077 x 750

= 807,750 people

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The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros

Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.

Simple interest = principal × rate × time

= 14,000 × 0.01 × 12

= 1,680 Euros

In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.

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Answer:

5u

Step-by-step explanation:

9-4=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9u - 4u}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (9u - 4u})\\\mathsf{= 9u - 4u}\\\mathsf{= 5u}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{\mathsf{5u}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The number of days that Rosa can continue to buy breakfast and lunch with the money is; 12 days

We are given the following parameters;

Amount held by Rosa = $254

Amount per breakfast = $7

Amount per Lunch = $13

Thus;

Amount spent each day = $7 + $13

Amount spent each day = $20

Now, to find out how many days this money can last her if she doesn't get any more income is;

Number of days = 254/20 = 12 days with $14 left

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The most appropriate choice for cost function and average cost function will be given by -

[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]

The number of flashdrive is very large, the average cost will come down to as low as $6.

What is cost function and average cost function?

Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.

Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.

Here,

C(x) = 17000 + 6x

[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]

        [tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]

        =   [tex]\frac{17000}{x}+6[/tex]

[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]

                    = 0 + 6

                    = 6

This means as the number of flashdrive is very large, the average cost will come down to as low as $6

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Complete Question

The cost​ (in dollars) for manufacturing a particular flashdrive is 17000 + 6x ​, where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per​ flashdrive, denoted by ​, is found by dividing​ c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2x-4}{2}[/tex] = 0

multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

2(x + 2) - 3(2x - 4) = 0 ← distribute parenthesis on left side and simplify

2x + 4 - 6x + 12 = 0

- 4x + 16 = 0 ( subtract 16 from both sides )

- 4x = - 16 ( divide both sides by - 4 )

x = 4

------------------------------------------------------------

[tex]\frac{5x}{2}[/tex] + [tex]\frac{x-2}{8}[/tex] = 2 ( multiply through by 8 to clear the fractions )

4(5x) + x - 2 = 16

20x + x - 2 = 16

21x - 2 = 16 ( add 2 to both sides )

21x = 18 ( divide both sides by 21 )

x = [tex]\frac{18}{21}[/tex] = [tex]\frac{6}{7}[/tex]

-----------------------------------------------------------

[tex]\frac{x-5}{4}[/tex] - [tex]\frac{3x-1}{5}[/tex] = - [tex]\frac{3}{2}[/tex]

multiply through by 20 ( the LCM of 4, 5, 2 ) to clear the fractions

5(x - 5) - 4(3x - 1) = - 30 ← distribute parenthesis on left side and simplify

5x - 25 - 12x + 4 = - 30

- 7x - 21 = - 30 ( add 21 to both sides )

- 7x = - 9 ( divide both sides by - 7 )

x = [tex]\frac{9}{7}[/tex]

-------------------------------------------------------------

[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{x^2-1}[/tex] ← x² - 1 is a difference of squares , then

[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{(x-1)(x+1)}[/tex]

multiply through by (x - 1)(x + 1) to clear the fractions

x + 1 + x - 1 = 4x + 2

2x = 4x + 2 ( subtract 4x from both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

If we substitute this value back into the original equation, we find

[tex]\frac{1}{-1-1}[/tex] + [tex]\frac{1}{-1+1}[/tex] = [tex]\frac{4(-1)+2}{(-1)^2-1}[/tex]

[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{1-1}[/tex]

[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{0}[/tex]

division by zero is undefined

thus x = - 1 is an extraneous solution

the equation has no solution

Answer:

[tex]\textsf{1.} \quad x=4[/tex]

[tex]\textsf{2.} \quad x=\dfrac{6}{7}[/tex]

[tex]\textsf{3.} \quad x=\dfrac{9}{7}[/tex]

[tex]\textsf{4.} \quad \textsf{No solution}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{x+2}{3}-\dfrac{2x-4}{2}=0[/tex]

[tex]\textsf{Add \; $\dfrac{2x-4}{2}$ \; to both sides of the equation}:[/tex]

[tex]\implies \dfrac{x+2}{3}-\dfrac{2x-4}{2}+\dfrac{2x-4}{2}=0+\dfrac{2x-4}{2}[/tex]

[tex]\implies \dfrac{x+2}{3}=\dfrac{2x-4}{2}[/tex]

Cross multiply:

[tex]\implies 2(x+2)=3(2x-4)[/tex]

[tex]\implies 2x+4=6x-12[/tex]

Subtract 2x from both sides:

[tex]\implies 2x+4-2x=6x-12-2x[/tex]

[tex]\implies 4=4x-12[/tex]

Add 12 to both sides:

[tex]\implies 4+12=4x-12+12[/tex]

[tex]\implies 16=4x[/tex]

[tex]\implies 4x=16[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{16}{4}[/tex]

[tex]\implies x=4[/tex]

--------------------------------------------------------------------------

Given equation:

[tex]\dfrac{5x}{2}+\dfrac{x-2}{8}=2[/tex]

Multiply the numerator and denominator of the first fraction by 4:

[tex]\implies \dfrac{5x \cdot 4}{2\cdot 4}+\dfrac{x-2}{8}=2[/tex]

[tex]\implies \dfrac{20x}{8}+\dfrac{x-2}{8}=2[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{20x+x-2}{8}=2[/tex]

[tex]\implies \dfrac{21x-2}{8}=2[/tex]

Multiply both sides by 8:

[tex]\implies \dfrac{(21x-2) \cdot 8}{8}=2 \cdot 8[/tex]

[tex]\implies 21x-2=16[/tex]

Add 2 to both sides:

[tex]\implies 21x-2+2=16+2[/tex]

[tex]\implies 21x=18[/tex]

Divide both sides by 21:

[tex]\implies \dfrac{21x}{21}=\dfrac{18}{21}[/tex]

[tex]\implies x=\dfrac{18}{21}[/tex]

Reduce the fraction by dividing the numerator and denominator by 3:

[tex]\implies x=\dfrac{18 \div 3}{21 \div 3}[/tex]

[tex]\implies x=\dfrac{6}{7}[/tex]

--------------------------------------------------------------------------

Given equation:

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

Multiply the numerator and denominator of the first fraction by 5, and the numerator and denominator of the second fraction by 4:

[tex]\implies \dfrac{(x-5) \cdot 5}{4\cdot 5}-\dfrac{(3x-1)\cdot 4}{5\cdot 4}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{5x-25}{20}-\dfrac{12x-4}{20}=-\dfrac{3}{2}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{5x-25-(12x-4)}{20}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{5x-25-12x+4}{20}=-\dfrac{3}{2}[/tex]

[tex]\implies \dfrac{-7x-21}{20}=-\dfrac{3}{2}[/tex]

Cross multiply:

[tex]\implies 2(-7x-21)=-3(20)[/tex]

[tex]\implies -14x-42=-60[/tex]

Add 42 to both sides:

[tex]\implies -14x-42+42=-60+42[/tex]

[tex]\implies -14x=-18[/tex]

Divide both sides by -14:

[tex]\implies \dfrac{-14x}{-14}=\dfrac{-18}{-14}[/tex]

[tex]\implies x=\dfrac{18}{14}[/tex]

Reduce the fraction by dividing the numerator and denominator by 2:

[tex]\implies x=\dfrac{18 \div 2}{14 \div 2}[/tex]

[tex]\implies x=\dfrac{9}{7}[/tex]

--------------------------------------------------------------------------

Given equation:

[tex]\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{x^2-1}[/tex]

Factor the denominator of the fraction on the right side of the equation:

[tex]\implies \dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

Multiply the numerator and denominator of the first fraction by (x+1), and the numerator and denominator of the second fraction by (x-1):

[tex]\implies \dfrac{x+1}{(x+1)(x-1)}+\dfrac{x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{x+1+x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

[tex]\implies \dfrac{2x}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]

Multiply both sides by (x+1)(x-1):

[tex]\implies \dfrac{2x(x+1)(x-1)}{(x+1)(x-1)}=\dfrac{(4x+2)((x+1)(x-1)}{(x+1)(x-1)}[/tex]

[tex]\implies 2x=4x+2[/tex]

Subtract 4x from both sides:

[tex]\implies 2x-4x=4x+2-4x[/tex]

[tex]\implies -2x=2[/tex]

Divide both sides by -2:

[tex]\implies \dfrac{-2x}{-2}=\dfrac{2}{-2}[/tex]

[tex]\implies x=-1[/tex]

However, if we substitute x = -1 into the original equation we get:

[tex]\implies \dfrac{1}{(-1)-1}+\dfrac{1}{(-1)+1}=\dfrac{4(-1)+2}{(-1)^2-1}[/tex]

[tex]\implies -\dfrac{1}{2}+\dfrac{1}{0}=\dfrac{-2}{0}[/tex]

A number divided by zero is undefined.  Therefore, there is no solution for this equation.

The interest rates required to get a total amount of $2,420 from compound interest on a principal of $2,000 compounded 1 times per year over 2 years is 10% per year.

The interest on savings that is calculated on both the initial principal and the interest accrued over time is known as compound interest.

The concept of compound interest, also known as "interest on interest," is thought to have first appeared in Italy in the 17th century. It will accelerate the growth of a sum more quickly than simple interest, which is calculated only on the principal sum.

Money is multiplied more quickly through compounding, and the more times it is compounded, the higher the compound interest will be.

Using the formula A = P(1 + r/n)^nt

Solving for rate r as a decimal

r = n[(A/P)^(1/nt) - 1]

r = 1 × [(2,420/2,000)^{1/(1)(2)} - 1]

r = 0.1

Then convert r to R as a percentage

R = r × 100

R = 0.1 × 100

R = 10%/year

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The answer to 32z - 48 using factoring is 3/2.

Given,

32z - 48

We have to find the answer using factoring:

Factoring:

Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.

Here,

32z - 48 = 0

Add 48 to both sides

32z - 48 + 48 = 0 + 48

32z = 48

Divide 32 on both sides

32z/32 = 48/32

z = 48/32

Now, we can factorize 48/32

Take 2 as common factor

(48/2) / (32/2) = 24/16

Again, take 2 as common factor

(24/2) / (16/2) = 12/8

Now, take 4 as common factor

(12/4) / (8/4) = 3/2

Here, z = 3/2

That is, the answer for 32z - 48 using factoring is 3/2.

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We can conclude that (A) "Yes since the appropriate probability is greater than​ 0.05, it is a significantly high numbe"r is the correct reason for the question.

So,

Number of Girls x

​P(x)

(0)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Results from groups of 8 births from 8 different parent sets are shown in the accompanying table.

Therefore, (A) "yes, since the appropriate probability is greater than​ 0.05, it is a significantly high number" is the correct reason for the question.

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Answer:

36.

Step-by-step explanation:

I get this answer as I know 30 is divisible by six, so I start to investigate by how much It is divisible by.

30 / 6 = 5

Since I now know that, I can infer that 6x6 is 36.

And since 30 would give you 5/6, I imagine the answer is 36.

Answer:

95% of adult males have diastolic blood pressure readings that are at least 102 mmHg

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 80 mmHg and the standard deviation is 11 mmHg.

2 standard deviations = 2 × 11= 22

80+ 22= 102 mmHg

Therefore, 95% of adult males have diastolic blood pressure readings that are at least 102 mmHg.

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Answer:

d(-6,-9),e(3,-9),f(3,-3),g(-6,-3

Step-by-step explanation:

first you look at the location of the point and follow in the direction of which number it is on the X line, then in the direction of which number it is on the Y line and in the parentheses of the coordinates, first write the number from the X line, then from the Y line

ps: I hope I helped you a bit :)

One possibility for resolving the inequality is (20, 60) in which x represents the number of tacos sold, and y the number of burritos sold

When graphing inequalities, the dependent variable, or y, is placed on the left side of the equation, while the other variables are placed on the right side.

The parameters are as follows:

Hudson has enough ingredients to make 90 tacos.

Each taco costs $3 to purchase.

Each burrito costs $7 to purchase.

Hudson must sell $420 worth of tacos and burritos per day.

x = number of tacos sold

y = the number of burritos sold

We need to graphically represent and solve the system of inequalities, and to identify one possible solution

The inequalities in the system are as follows:

x + y ≤ 90

3·x + 7·y ≥ 420

We have the following graphs to plot the above inequalities:

y ≤ 90 - x

y ≥ 420/7 - 3·x/7

y ≥ 60 - 3·x/7

The vertices of the feasible region's triangle are as follows from the inequality graph:

(0, 90), (0, 60), and the third vertex is found as follows for accuracy;

90 - x = 60 - 3·x/7

x = 52.5

y = 90 - x

∴ y = 37.5 at the vertex

The third vertex is (52.5, 37.5)

Therefore, the feasible region's vertices are (0, 90), (0, 60), and (52.5, 37.5), and one possible solution within the feasible region is (20, 60)

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Answer:

each chicken cost 3.65

Step-by-step explanation:

divide 18.25 by 5 and you'll get 3.65

The expression for the cube of the sum of a number and 3 is  (x+3)³

Algebraic expressions are simply defined as arithmetic expressions made up  of variables, terms, coefficients, factors and constants

They may also be known to consist of certain mathematical operations, such as;

Based on the information given, we have;

cube of the sum of a number and 3

Let the number be x

We have the expression to be;

x + 3

Find the cube

(x+3)³

Hence, the expression is (x+3)³

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The complete question is;

Write the expression for The cube of the sum of a number and 3