The area of the rectangle to the right is 18x² - 6x, and its width is 6x. Find the length of the rectangle.​

Answer:

It's A. x and y are proportional. k=8

Step-by-step explanation:

x and y are proportional since they are related by the equation 8 = xy. To find the constant of proportionality, we can solve for y in terms of x:

y = 8/x

This shows that y is inversely proportional to x, and the constant of proportionality is 8.

Therefore, the correct answer is A. x and y are proportional, and the constant of proportionality is k = 8.

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We can see that the signs of the coefficients are different for the terms with x, so the two products are not equal.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Part a:

To find the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6), we need to distribute each term in the first expression to each term in the second expression, and then combine like terms.

(3x – 4) (5[tex]x^{2}[/tex] – 2x + 6)

= 3x(5[tex]x^{2}[/tex] ) – 3x(2x) + 3x(6) – 4(5[tex]x^{2}[/tex] ) + 4(2x) – 4(6)

= 15[tex]x^{3}[/tex]– 6[tex]x^{2}[/tex]  + 18x – 20[tex]x^{2}[/tex]  + 8x – 24

= 15[tex]x^{3}[/tex] – 26[tex]x^{2}[/tex]  + 26x – 24

Therefore, the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6) is equal to 15x^3 – 26[tex]x^{2}[/tex]  + 26x – 24 in standard form.

Part b:

No, the product of (3x – 4) and (5[tex]x^{2}[/tex]  – 2x + 6) is not equal to the product of (4 – 3x) and (5[tex]x^{2}[/tex]  – 2x + 6).

(4 – 3x) (5[tex]x^{2}[/tex]  – 2x + 6)

= 4(5[tex]x^{2}[/tex] ) – 4(2x) + 4(6) – 3x(5[tex]x^{2}[/tex] ) + 3x(2x) – 3x(6)

= 20[tex]x^{2}[/tex] – 8x + 24 – 15[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]  – 18x

= -15[tex]x^{3}[/tex]+ 26[tex]x^{2}[/tex]  - 26x + 24

Therefore, We can see that the signs of the coefficients are different for the terms with x, so the two products are not equal.

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Answer:

x = -3

y = -6

Step-by-step explanation:

We are given the following system of equations:

y = 2x

-3x - 15 = y

We can use the substitution method to solve this system.

Substitute y = 2x from the first equation into the second equation and solve for x:

-3x - 15 = 2x

-5x = 15

x = -3

Now that we have found x, we can use the first equation to find y:

y = 2x = 2(-3) = -6

Therefore, the solution to the system of equations is (x, y) = (-3, -6).

The ratio of x to z is equal to 15 : 42.

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Based on the information provided above, we have the following ratio parameters:

x : y = 5 : 6 ⇒ x/y = 5/6

z : y = 7 : 3 ⇒ z/y = 7/3

Therefore, we can logically deduce the following:

x/z = x/z × y/y

x/z = x/y × y/z

x/z = 5/6 × 3/7

x : z = 15 : 42

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The side length to the nearest tenth of a centimeter is 5.57

A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other.  also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles)

The range of the sides is 30 to 31

the area of a square is

A = l² where l = length of side

√30 = l

L= 5.48 or

l = √31 = 5.57

The side length is the mean of the range of numbers

l = (5.48+5.57)/2  = 5.53

My estimate is reasonable because 5.53² = 30.5809 which is a number between 30 and 31

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Due to the fact that a square's area is proportionate to its square of side length, a minor change in the area corresponds to a small change in the side length, making this estimate acceptable.

Let's call the side length of the square "s". We know that the area of the square is between 30 cm² and 31 cm², so we can write:

30 < s² < 31

Taking the square root of all three sides of this inequality, we get:

√30 < s < √31

Using a calculator, we can approximate the square roots to the nearest tenth of a centimeter:

√30 ≈ 5.5

√31 ≈ 5.6

So, we can estimate that the side length of the square is between 5.5 cm and 5.6 cm, to the nearest tenth of a centimeter.

This estimate is reasonable because the area of a square is proportional to the square of its side length, so a small change in the area corresponds to a small change in the side length.

Since the difference between the upper and lower bounds of our estimate is only 0.1 cm, it makes sense that the area of the square is very close to the given range.

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Answer: C

Step-by-step explanation:

Find the positive difference between the x and y values to get the other end pt.

[tex]1-(-3)\\1+3\\4[/tex]

Which represents the change in x.

[tex]-2-(-8)\\-2+8\\6[/tex]

Change in y

Add the change to the x and y coordinates to the coordinates of the midpoint and that will be the answer

[tex](1+4,-2+6)\\(5,4)[/tex]

Which is Option C

Answer:

A. F(5,4)

Step-by-step explanation:

x(E) = [x(D) + x(F)]/2

2(1) = -3 + x(F)

x(F) = 2 + 3 = 5

y(E) = [y(D) + y(F)]/2

2(-2) = -8 + y(F)

y(F) = -4 + 8 = 4

=> F(5,4)

Therefore , the solution of the given problem of area comes out to be the kite's surface size is roughly 42.8 square inches. (A) 90 is the best match, but it's not the right response.

Calculating how much room is needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capability of a cuboid is given by the total of the borders connected to each of its six rectangular edges.

Here,

The following method must be used to determine a kite's area:

=>  Diagonal 1 x Diagonal 2 / 2 =  Area

where "diagonal 1" and "diagonal 2" denote the kite's two diagonal lengths, respectively.

We can see from the provided illustration that:

=>  17.1 inches are the length of Diagonal 1 (OD).

The length of Diagonal 2 (OS) is 5 inches.

We can enter these numbers into the formula to determine the area:

=> Area = (17.1 x 5) / 2 Area

=>  (diagonal 1 x diagonal 2) / 2 Area

=> 42.75

To the closest tenth, we round and obtain:

=> Area ≈ 42.8

Consequently, the kite's surface size is roughly 42.8 square inches. (A) 90 is the best match, but it's not the right response.

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Answer:

1) y = (1/15)x + 18

2) y = (5/144) (x - 16)^2 + 20

Solution:

1) The solution consists in establishing the equations that model the two paths.

2) Let's start with the easiest one. It is the linear path.

You have that the equation is a line that passes through the points (0,18) and (30,20). This equation is found using this formula:

[tex]\dfrac{y-b}{x-a} =\dfrac{d-b}{c-a}[/tex]

where the two points are (a,b) and (c,d)

So, for the two points given:

[tex]\dfrac{y-18}{x-0} =\dfrac{20-18}{30-0} =\dfrac{2}{30}[/tex]

=> [tex](y - 18)\times30 = x\times2[/tex]

=> [tex]30y - 540 = 2x[/tex]

=> [tex]30y = 2x + 540[/tex]

=> [tex]y = 2x \div 30 + 540 \div 30[/tex]

=> y = x/15 + 18 ---------------> this is the first equation of the system.

3) Now, find the equation for the path modeled by the quadratic function.

The vertex form of a quadratic function is: [tex]y = A (x - h)^2 + k[/tex]

where the vertex is (k,h).

Then, so far you can write [tex]y = A (x - 16)^2 + 20[/tex]

Now, replace the coordinates of the point (4,25) to find the value of A:

[tex]25 = A (4 - 16)^2 + 20[/tex]

=> [tex]25 = A (-12)^2 + 20[/tex]

=> [tex]25 = A\times144 + 20[/tex]

=> [tex]144A = 25 - 20[/tex]

=> [tex]144\ A = 5[/tex]

=> [tex]A = 5 \div 144[/tex]

=> y = (5 / 144) (x - 16)^2 + 20 ---------> this is the second equation of the system.

System:

1) [tex]y = (\frac{1}{15} )x + 18[/tex]

2)[tex]y = (\frac{5}{144} )\ (x - 16)^2 + 20[/tex]

In respοnse tο the given questiοn, we can state that As a result, the functiοn turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))). With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

Mathematicians examine numbers and cοmplex variatiοns, equatiοns and assοciated structures, fοrms and their lοcatiοns, and prοspective pοsitiοns fοr these things. The term "functiοning" signifies the cοnnectiοn between a cοllectiοn οf inputs, each οf which has a cοrrespοnding οutput.

A functiοn is a cοnnectiοn οf inputs and results in which each input leads tο a single, identifiable οutcοme. Each functiοn is assigned a dοmain, a cοdοmain, οr a scοpe. The letter f is widely used this tο denοte functiοns (x). The symbοl fοr admissiοn is an x. The fοur primary types οf usable functiοns are οn οperatiοns, οne-tο-οne capabilities, sο multiple functiοnality, in capabilities, and then οn functiοns.

Optiοn (D) is a design that might depict the graph οf y = x³ - 4x since it cοntains a single hump with a rοοt at x = 0 and intersects the y-axis at y = 0.

We may use the fοllοwing prοcedures tο sοlve the functiοn y = x³ - 4x:

The value οf the y-intercept is (0, 0).

We set y = 0 and sοlve fοr x tο determine the x-intercepts:

[tex]x^3 - 4x = 0[/tex]

[tex]x( x^2 -4) = 0[/tex]

[tex]x = 0 , x = -2 , x = 2[/tex]

As a result, the x-intercepts are (-2, 0), (0, 0), and (2, 0).

[tex]3x^2 - 4 = 0[/tex]

x = ±√(4/3)

As a result, the turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))).

With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

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Answer:

(q²-p)(p²-q), 240

Step-by-step explanation:

Q1     p²q²+pq-q³-p³=(p²q²-q³)+(pq-p³)

                               =q²(p²-q)-(p³-pq)

                               =q²(p²-q)-p(p²-q)

                                =(q²-p)(p²-q)

Q2  If p=4 and q=-4

(4)²(-4)²+(4) x(-4)-(-4)³-4³=256-16+64-64=240

Answer:

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The value of the variable x is 253 degrees

From the question, we have the following parameters that can be used in our computation:

Circle and intersecting tangent lines

Using the theorem of angle between intersecting tangents and arcs, we have the following equation

1/2 * (x - 360 + x) = 73

Multiply by 2

(x - 360 + x) = 146

So, we have

2x - 360 = 146

Evaluate the like terms

2x = 506

Divide by 2

x = 253

Hence, the value of x is 253 degrees

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A company's break-even point is the level of sales or revenue that the company needs to generate in order to cover all of its expenses and to neither make a profit nor incur a loss.

The amount of sales or revenue that a business must achieve in order to pay all of its costs while not turning a profit or suffering a loss is known as the break-even point. The company's total income and entire costs are equal at the break-even point.

In other words, the firm reaches its break-even point when its entire income matches the sum of its total variable expenses and total fixed costs. Raw materials, labor, and commissions are examples of expenses known as variable costs that fluctuate in response to variations in the volume of production or sales. Rent, salary, and insurance are examples of fixed expenditures that don't fluctuate while output or sales alter.

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Part a: The amount of leather needed to create both drum heads is 2769.48 cm².

Part b: Total surface area of Iranian cylindrical drum: 4022.34 cm².

A cylinder is just a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface.

Part a: The amount of leather needed to create both drum heads.

Amount of leather = 2 * area of circle

Amount of leather = 2 * πr²

Amount of leather = 2 * 3.14 * 21²

Amount of leather = 2769.48 cm².

Thus, the amount of leather needed to create both drum heads is 2769.48 cm².

Part b: Total surface area of Iranian cylindrical drum:

TSA = 2πr(h + r)

TSA = 2*3.14*21*(21 + 9.5)

TSA =

Thus, the total area of wood used to make the body of the drum 4022.34 cm².

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The statement "If I make more money than the cost of the ingredients, then the following is true, c > 1 and c < 13" provides support for Jane's claim that she must sell at least one but no more than 12 cakes to make a profit.

What is statement ?

A statement is a declarative sentence that expresses a fact, an opinion, or a proposition that can be either true or false. It is a linguistic expression that can be either a complete sentence or a part of a sentence, and it conveys a meaning that can be evaluated as true or false.

The statement that provides support for Jane's claim is:

"If I make more money than the cost of the ingredients, then the following is true, c > 1 and c < 13"

This statement implies that if Jane makes more money than the cost of the ingredients, then she must have sold at least one cake (since c > 1) but not more than 12 cakes (since c < 13). This makes sense because if she sells fewer than one cake, she will not make any profit, and if she sells more than 12 cakes, the profit she makes per cake will be reduced since the cost of the ingredients is fixed.

The other statements do not provide support for Jane's claim:

"She cannot sell less than 0 cakes, so c must be >= 0" is true, but it does not provide any information about the range of values for c that support Jane's claim.

"| e = 0 then she has not lost or earned any money." is true, but it does not provide any information about the range of values for c that support Jane's claim.

"c = 1 then she has earned a small amount of money." is true, but it only provides information about one specific value of c, not a range of values that support Jane's claim.

"c equals a negative integer then she did not sell any cakes" is true, but it only provides information about one specific value of c, not a range of values that support Jane's claim. Additionally, the statement is not relevant to Jane's claim since negative values of c are not included in the range c > 1 and c < 13.

Therefore, the statement "If I make more money than the cost of the ingredients, then the following is true, c > 1 and c < 13" provides support for Jane's claim that she must sell at least one but no more than 12 cakes to make a profit.

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For the given map, the scale factor is shown as 1 unit = 557 miles or 1:557.

What is a scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor. The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger. The ratio of one unit of distance on a map to the comparable distance on the ground is commonly used to describe a map's scale. The ratio of a distance on a map to its actual distance on the ground is known as the map scale.

Here it is given at the bottom of the map:

1 unit = 557 miles.

This is the scale factor of the map.

The unit is not mentioned. So the 1 unit can be in cm, m,  inches and so on. This unit is equal to 557 miles on the ground.

So if the distance between two places is 20 cm on the map, then the actual distance is 20*557 = 11,140 miles.

Therefore for the given map, the scale factor is shown as 1 unit = 557 miles or 1:557.

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After answering the given query, we can state that The square is 6 inches long as a result.

According to Euclidean mathematics, a square has four equal sides and four equal angles, making it an equilateral quadrilateral. Another name for it is a rectangle with two adjacent edges that are the same length. An equilateral quadrilateral is one that has four equal sides and four equal angles, like a rectangle. 90 degree or straight angles are square angles. The square's diagonals are also divided at a 90-degree angle and are evenly spaced. a rectangle with two equal edges that is adjacent. a quadrilateral with four equal edges and right angles on all four sides. a parallelogram with two adjacent sides that are equal and make a right angle. rhombus with square sides.

Let's use the symbol x inches to represent the square's edge length.

The square's circumference, or the overall length of tape used, is 16 inches. Therefore:

4x = 16

When we simplify the solution, we obtain:

x = 4

Thus, the cube has sides that are 4 inches long.

Let's think about the parallelogram now. Its breadth is stated to be half the square, which translates to:

breadth equals 1/2 * 4 inches.

2 (length plus width) equals 16.

The result of substituting the number of the width we just discovered is:

length plus 2 equals 16,

When we simplify the solution, we obtain:

lenght + 2 equals 8

By taking 2 away from both edges, we arrive at:

width = 6

The square is 6 inches long as a result.

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We can say that after answering the offered question We may simulate inequality and address numerous issues in disciplines like economics, engineering, and science by employing variables and inequalities.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

Choose a scenario where a specific number or quantity must be larger than or equal to 5 for a specific condition to be satisfied in order to write a real-life circumstance for the inequality * 5.

Another illustration might have to do with a fitness objective. The inequality in this case would be " 5," meaning that you must weigh less than or equal to 5 in order to reach your objective.

Inequalities are typically employed to symbolise restrictions or limitations in real-world contexts, such as minimum or maximum demands, financial restraints, or safety standards. We may simulate and address numerous issues in disciplines like economics, engineering, and science by employing variables and inequalities.

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The expression that is equivalent to 10 > 5/154x8 is x > 1/ 2464 or 2464x > 1.

To see why this works, we can first simplify 5/154x8 . We can then simplify this to 5/1232x, by multiplying 5/(154*8) by x and simplifying the result. We can then substitute this expression into the original inequality to get:

10 > 5/1232x

x > 0, which means that x is a positive number

Divide both sides by 10 and multiply by x, then

x > 5/(1232*10)

x > 1/ 2464

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Answer:

If AB represents 300%, the length of a line segment that represents 100% is equal to one-third of the length of AB or simply 100%.

Step-by-step explanation:

If AB represents 300%, then AB is three times the length of a line segment that represents 100%.

So if we let the length of the line segment that represents 100% be x, then we can write:

AB = 3x

Solving for x, we get:

x = AB/3

Since AB represents 300%, we know that AB is three times the size of a line segment that represents 100%. Therefore, x is equal to one-third of AB, or:

x = AB/3 = (300%)/3 = 100%

So the length of a line segment that represents 100% is equal to one-third of the length of a line segment that represents 300%, or simply 100%.

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The volume of the triangular pyramid is 2 cubic feet.

what is triangle ?

A triangle is a 2-dimensional geometric shape that has three straight sides and three angles. The sum of the angles of a triangle is always 180 degrees.

The first step to solving this problem is to find the area of the base of the pyramid. Since the base is a right triangle, its area can be calculated using the formula for the area of a triangle:

Area of triangle = 1/2 * base * height

In this case, the base is a right triangle with legs of 2 feet, so its area is:

Area of base = 1/2 * 2 * 2 = 2 square feet

Next, we can use the formula for the volume of a pyramid to calculate the volume of the triangular pyramid:

Volume of pyramid = 1/3 * area of base * height

Substituting in the values we have, we get:

Volume of pyramid = 1/3 * 2 * 3 = 2 cubic feet

Therefore, the volume of the triangular pyramid is 2 cubic feet.

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The inequality expression (2/3)y - 4 ≥ 2 when evaluated is y ≥ 3

Inequality expressions are those statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

From the question, we have the following inequality expression given as

(2/3)y - 4 ≥ 2

Add 4 to both sides of the inequality

So, we have the following representation

2/3y ≥ 2

Multiply both sides of the inequality expression by 3/2

y ≥ 3

Hence, the solution to the given inequality expression is y ≥ 3

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4 x minus 3 y is the expression which is equivalent to (3 x minus 5 y) + (x + 2 y)?

To simplify the expression (3x - 5y) + (x + 2y), we can combine the like terms.

Starting with the x-terms, we have 3x + x = 4x.

Moving on to the y-terms, we have -5y + 2y = -3y.

Therefore, the simplified expression is 4x - 3y, which is equivalent to option B.

We can check this by plugging in some values for x and y. For example, if x = 2 and y = 1, then:

(3x - 5y) + (x + 2y) = (3(2) - 5(1)) + (2 + 2(1)) = (6 - 5) + (2 + 2) = 3 + 4 = 7.

And using the simplified expression, we get:

4x - 3y = 4(2) - 3(1) = 8 - 3 = 5.

So we can see that both expressions give the same result, confirming that option B is equivalent to the given expression.

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Answer

          4x-3y

(｡･∀･)ﾉﾞ

Step-by-step explanation:

The down payment and the amount financed are given as follows:

The down payment and the amount financed are obtained applying the proportions in the context of the problem.

Anna wants to add a $15,280 sunroom to her house. Her bank requires 20% down before lending her any money, hence the down payment is given as follows:

0.2 x 15280 = $3,056.

The amount financed is the part of the price that is not part of the down payment, hence it is given as follows:

15280 - 3056 = $12,224.

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Answer:

x = 18.1

Step-by-step explanation:

1) 12x - 5 + 8x + 3 = 360

2) Subtract 5 from both sides

3) Add 2 on both sides

4) Divide both sides

5) x = 18.1

The range of f(x) is {f(x) ∈ ℝ | f(x) ≥ –3}, which means that the possible values of f(x) are all real numbers greater than or equal to –3.

The range of a function is the set of all possible output values.

For the function f(x) = |x| – 3, we can think about the possible values that f(x) can take on.

First, consider the absolute value. For any input x, the absolute value |x| is always non-negative, so |x| – 3 is at least –3.

Next, think about the effect of subtracting 3. This shifts all the values down by 3 units. So the range of f(x) is all the values that can be obtained by subtracting 3 from the absolute value of x.

Therefore, the range of f(x) is {f(x) ∈ ℝ | f(x) ≥ –3}, which means that the possible values of f(x) are all real numbers greater than or equal to –3.

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Answer:

A)

Step-by-step explanation:

When reflecting over the X-axis, you change the sign on the number in the Y's position(+ - and vice versa).

Answer:

A

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(- 1, 6 ) → (- 1, - 6 )

(- 3, 2 ) → (- 3, - 2 )

Shop A sells 16 ounces of peanut butter for $3.99 (24.94 cents/oz), but Store B sells 32 ounces for $6.49 (20.28 cents/oz). At 20.28 cents/oz, Shop B is offering a better price.

To save money while shopping, it is important to compare unit pricing of supermarket items. In this analysis, we contrasted the unit costs of peanut butter at two various retailers. Shop A sells 16 ounces for $3.99, which works out to 24.94 cents per ounce; Store B sells 32 ounces for $6.49, which works out to 20.28 cents per ounce. With a cheaper unit price of peanut butter, Shop B is the preferable option. Comparing unit prices makes it simple to identify which retailer is providing the greatest bargain for the item we need to purchase.

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For the value of a = 7, the expression is true.

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2.

Now in the given question,

1/2 a - 5 1/2 = 5 - a

We first simplify the expression as:

a/2 -11/2 = 5 - a

⇒ (a-11)/2 = 5 - a

⇒ a - 11 = 10 - 2a

⇒ a+ 2a = 10 + 11

⇒ 3a = 21

⇒ a = 7.

Therefore, for the value of a = 7 the expression is true.

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