Translate "the product of z,x,and y into a mathematical expression

The​ number is 5 which sum of the square of a positive number and the square of 3 more than the number 89.

The quadratic function is defined as a function containing the highest power of a variable is two.

We have to determine the​ number which sum of the square of a positive number and the square of 3 more than the number 89.

Let the first number would be x

So second number = x + 3

According to the given condition,

⇒ x² + (x + 3)² = 89                    

⇒ x² + x² + 6x + 9 = 89                    

⇒ 2x² + 6x + 9 = 89

⇒ 2x² + 6x - 80 = 0

⇒ x² + 3x - 40 = 0

⇒ (x + 8)(x - 5) = 0

⇒ x + 8 = 0 or x - 5 = 0    

⇒ x = -8 or x = 5  

The answer is 5 because we are looking for a positive number.

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Final answer:

The positive number where the sum of its square and the square of 3 more than the number equals 89 is 5.

Explanation:

To determine the positive number where the sum of squares of the number and the square of 3 more than the number equals 89, we set up the following equation:

Let x be the positive number. Then:

x² + (x + 3)² = 89

Expanding the equation:

x² + x² + 6x + 9 = 89

Combining like terms, this becomes:

2x² + 6x + 9 = 89

Subtract 89 from both sides:

2x² + 6x - 80 = 0

We now have a quadratic equation. Dividing by 2 for simplicity:

x² + 3x - 40 = 0

Factor the quadratic equation:

(x + 8)(x - 5) = 0

Setting each factor equal to zero gives us two possible solutions for x:

Therefore, the positive number is 5.

To determine how many pounds of blueberries are left in the container after using 1/5 for muffins, calculate 4/5 of the initial amount, as this represents the remaining 80%. The ability to work with fractions and percentages is crucial here.

The question involves understanding percentages and unit conversion. If 1/5 of the remaining blueberries is used to make muffins, that means 80% (or 4/5) of the blueberries are left in the container. To find out how many pounds of blueberries are left, we first need to know the total quantity before using any for muffins. Assuming we had a specific weight to begin with, we would calculate 4/5 of that weight to determine what remains.

For example, if there were 10 pounds of blueberries initially, 2 pounds (1/5) would be used for muffins, leaving 8 pounds (4/5) of blueberries in the container. It's essential to be comfortable with fractions and percentage calculations when dealing with such problems in mathematics.

a. Each bowl contains 1/12 of the total blueberries.

b. There were 72 ounces of blueberries in the full container.

c. There are 3 pounds of blueberries left in the container.

a. What fraction of the blueberries is in each bowl?

Initially, 1/6 of the blueberries are poured equally into two bowls. Therefore, each bowl receives 1/6 * 1/2 = 1/12 of the total blueberries.

b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?

Since each bowl has 6 ounces of blueberries, and there are two bowls, the total amount of blueberries poured into the bowls is 6 * 2 = 12 ounces. Since this represents 1/6 of the total blueberries, we can set up the equation:

Total blueberries = 12 * 6 = 72 ounces

c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?

After pouring 1/6 of the blueberries into the bowls, 5/6 of the blueberries remain. Then, 1/5 of these remaining blueberries are used to make muffins. So, the fraction of blueberries remaining after making muffins is 5/6 * 4/5 = 20/30 = 2/3.

To convert the remaining blueberries to pounds, since 1 pound equals 16 ounces, we divide the total remaining ounces by 16:

Remaining blueberries in pounds = (72 ounces * 2/3) / 16 ounces/pound = (72 * 2) / (3 * 16) = 144 / 48 = 3 pounds

So, there are 3 pounds of blueberries left in the container.

The probable question maybe:

A container is filled with blueberries. 1/6 of the blueberries are poured equally into two bowls.

a. What fraction of the blueberries is in each bowl?

b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?

c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?

⁶⁾4/5 = ¹⁰⁾24/30 = 240/300

⁵⁾5/6 = ¹⁰⁾25/30 = 250/300

Rational numbers between 4/5 & 5/6​ :

241/300

242/300

243/300

.................

248/300

249/300

Yo sup??

There are infinite numbers possible but since we are asked to find only 2 we can say

4/5=0.8000

5/6=0.8334

Therefore the possible numbers are:

0.81=81/100

0.82=82/100=41/50

0.83=83/100

and so on

Hope this helps.

Answer:

y=-1/8x

Step-by-step explanation:

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

m=(-0.5-0.5)/(4-(-4))

m=(-1)/(4+4)

m=-1/8

y-y1=m(x-x1)

y-0.5=-1/8(x-(-4))

y-0.5=-1/8(x+4)

y=-1/8x-4/8+0.5

y=-1/8x-1/2+1/2

y=-1/8x

Option D

The trip lasts for [tex]6\frac{1}{4}\ hours[/tex]

Solution:

Mr Patel is planning to drive 325 miles

Average speed is 65 mph

He will stop one hour for lunch and take a 15 min rest break

Let us first find the time taken

[tex]Time = \frac{distance}{speed}[/tex]

[tex]Time = \frac{325}{65}\\\\Time = 5[/tex]

Thus he covers 325 miles in 5 hours

Also, given that, he will stop one hour for lunch and take a 15 min rest break

Therefore, total time taken for trip is:

Total time = 5 hours + 1 hour + 15 minutes

Total time = 6 hours 15 minutes

We know that,

1 hour = 60 minutes

Therefore,

[tex]6\ hours\ 15\ minutes\ = 6 + \frac{15}{60}\ hours = 6 + \frac{1}{4} = 6\frac{1}{4}\ hours[/tex]

Thus the trip lasts for [tex]6\frac{1}{4}\ hours[/tex]

Mr. Patel's trip will last a total of 6.25 hours, including his driving time, lunch break, and rest break. The calculation was done using the formula Time = Distance / Speed, and factoring in the break times.

First, we need to calculate how many hours Mr. Patel will spend driving. To do this, we use the formula Distance = Speed * Time. We rework this formula to find time, giving us Time = Distance / Speed. So, Mr. Patel’s total driving time is 325 miles divided by 65 mph (miles per hour), which equals 5 hours.

The next task is to factor in Mr. Patel’s lunch and rest breaks. He takes one hour for lunch and 15 minutes for a rest break. Note that 15 minutes is 0.25 of an hour. Add these two periods to our initial 5 hours of driving time, and we get a total of 6.25 hours. So, Mr. Patel's trip will last 6.25 hours, which corresponds to answer choice D).

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Answer:

Step-by-step explanation:

Answer:

71 ducks

Step-by-step explanation:

1. 56 + 20 = 76

2. 76 - 5 = 71

See the graph below

First of all, let's rename those expressions as follows:

[tex]\left\{ \begin{array}{c}y=10+3x\\y=4x\end{array}\right[/tex]

So we we have two lines written in slope-intercept form. In order to graph those lines, let's find two points for each:

First line:

[tex]For \ x=0: \\ \\ y=10+3(0) \\ \\ y=10 \\ \\ \\ For \ x=-10/3: \\ \\ y=10+3(-10/3) \\ \\ y=10-10 \\ \\ y=0 \\ \\ \\ So \ the \ line \ passes \ through \ (0,10) \ and \ (-10/3,0)[/tex]

This line is the green one shown below.

Second line:

[tex]For \ x=0: \\ \\ y=4(0) \\ \\ y=0 \\ \\ \\ For \ x=1: \\ \\ y=4(1) \\ \\ y=4 \\ \\ \\ So \ the \ line \ passes \ through \ (0,0) \ and \ (1,4)[/tex]

This line is the red one shown below.

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Answer:

9x +135

Step-by-step explanation:

9(x + 8) +63   (by PEDMAS distribute 9 into parentheses first)

= x(9) + 8(9) +63  

= 9x + 72 + 63

= 9x +135    [  =9(x+15)    ]

Answer: 9x+135

Step-by-step explanation:

9(x + 8) +63

9x+72+63

9x+(72+63)

9x+135

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)  

- Cutiepatutie ☺❀❤

Simple interest formula:

Total = principal x (1 + rate x years)

10 years:

Total = 15,000(1+0.04x10)

Total = $21,000

8 years:

Total = 15000(1+0.04x8)

Total = $19,800

Savings = 21,000 - 19,800 = $1,200

Final answer:

When dividing 0.7 by 0.1995, it is crucial to perform the calculation accurately and round it according to the significant figures of the original numbers. Calculators will provide an exact answer, but understanding significant figures is necessary for a correctly rounded result.

Explanation:

Dividing Decimals

When we divide 0.7 by 0.1995, we have to handle decimals properly. It's similar to how a calculator operates but with an understanding of significant figures. The division of decimals can be tricky because calculators give an exact numerical value, which may not respect the precision of the input numbers.

For instance, if we divide 12.2 by 1.7 using a calculator, we get many decimal places. But based on the initial data's significant figures, we must round our answer appropriately. Similarly, if we divide 1.9436 by various powers of 10, we get:

1.9436 ÷ 100 = 0.019436

1.9436 ÷ 1000 = 0.0019436

When dividing by powers of 10, we move the decimal point to the left for each power. In more complex divisions or when your calculator presents more decimals than necessary, it is important to round the answer to the correct number of significant figures.

The geometry sequence has the equation [tex]a(n)=5(3^{n-1})[/tex].

The 5 represents the first number of the sequence and the 3 represents the common ratio.

a(5) = [tex]5(3^{5-1})=5(3^{4})=5(81)=405[/tex]

answer: 405

Answer:

It is 405.

It is 405.

The answer is option C) 19,-19

Step-by-step explanation:

Given, z² = 361

To eliminate the square of z, take square root on both sides

z = √361

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

[tex]\mathsf{z^2 = 361}\\\\\large\text{Take the square root of the number 361}\\\\\mathsf{z = \pm \sqrt{361}}\\\\\large\text{Simplify it}\\\\\mathsf{z = -19\ or\ z = 19}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{z = 19\ or\ z = -19 \ (Option\ C.)}}\huge\checkmark[/tex]

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

Answer:

160 stickers

Step-by-step explanation:

32 x 5=160

Answer:

160

Step-by-step explanation:

     Let x =  sister's number of stickers

Then 5x = Nicole's number of stickers

           x = 32

         5x = 5 × 32 =160

Nicole has 160 stickers.

Answer:

The number of jumps that the game piece took, was 40.

Step-by-step explanation:

Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].

Now, the piece starts at point A = 7 and jumps to the right.

So, the number of jumps required by the piece to jump over B = 24 will be

[tex]\frac{24 - 7}{0.889} = 19.122[/tex] jumps ≈ 20 jumps {As the piece crosses the point B}

Now, as soon as the piece jumps over B = 24, it switches direction and jumps to the left. And the piece then stops at point A.

Therefore, the number of jumps that the game piece took, was (20 × 2) = 40. (Answer)

Final answer:

Calculating the jumps based on the jump size of 8 / 9 units, the piece makes 20 jumps to go from point A past point B, and then 23 jumps to return to point A, for a total of 43 jumps.

Explanation:

To solve the question, we must calculate the total number of jumps the game piece takes from the starting point A at 7, over point B at 24, and back to A. Each jump measures 8 / 9 units. To calculate the number of jumps to reach just past point B (24 units), we can set up a division problem to find the number of jumps it would take to first reach or pass 24 starting from 7. The formula for this is (B - A) / jump size.

So, the calculation for jumps to point B is: (24 - 7) / 8 / 9 = 17 × 9 / 8 = 153 / 8 = 19.125. Since the game piece cannot make a partial jump, we must round up to 20 jumps to reach beyond 24 units.

After the piece switches direction, we perform a similar calculation to find how many jumps it takes to go back to point A (7 units).

Here, since the piece is already beyond 24, it only needs to jump back to the next integer value before 7 which is 6.

Now, the game piece is at (20 × 8 / 9) + 7 = approximately 24.222 + 7 = approximately 31.222 units along the path.

To calculate the jumps back to 6, we have (31.222 - 6) / 8 / 9 which is approximately 22.556 jumps, and rounding up gives us 23.

Therefore, the total number of jumps made is the sum of the jumps to point B and back to point A,

which is 20 + 23 = 43 jumps.

Answer:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Step-by-step explanation:

Complete Question: What is the equation of line that is parallel to the line [tex]y=\frac{1}{5}+4[/tex] and passes through [tex](-2,2).[/tex]

[tex]Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}[/tex]

To find the equation of a line parallel to a given line and passing through a given point, use the point-slope form of a line.

To find the equation of a line parallel to the given line, we need to remember that parallel lines have the same slope. The given line has a slope of 1/5. So, the parallel line will also have a slope of 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get:

y - 2 = 1/5(x + 2)

To simplify the equation, we can multiply through by 5 to get rid of the fraction:

5y - 10 = x + 2

Finally, we can rearrange the equation to the standard form:

x - 5y = -12

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Final answer:

The coordinates of vertex W of parallelogram WXYZ, given vertices X(-2,-3), Y(0, 5), and Z(7, 7), are W(9, 15). This is found by calculating vector ZW as equal to vector XY and adding ZW to the coordinates of Z.

Explanation:

The coordinates of vertex W of parallelogram WXYZ can be found by using the properties of parallelograms. In a parallelogram, opposite sides are equal in length and parallel. Given vertices X(-2,-3), Y(0, 5), and Z(7, 7), we can first find the vector representation from X to Y and from Y to Z:

To find the vector from Z to W, which we'll call ZW, we use the fact that ZW must be parallel and equal in length to vector XY. Therefore:

Now we add vector ZW to the coordinates of Z to find W:

Thus, the coordinates of vertex W are (9, 15).

In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:

[tex]x\approx 2.9ft[/tex]

First of all, let's calculate the area of the original rectangular garden:

[tex]A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2[/tex]

Jake wants to increase the area by 50%, so the new area would be:

[tex]A'=168(1.5) \\ \\ A'=252ft^2[/tex]

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

[tex](12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives[/tex]

Finally:

In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:

[tex]x\approx 2.9ft[/tex]

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Answer:

y = -2

Step-by-step explanation:

Use the formula for slope: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

"m" means slope, and we know it is -1.

Decide which points will be point 1 and point 2

Point 1 (-2, y)    x₁ = -2  y₁ = y

Point 2 (0, -4)   x₂ = 0  y₂ - -4

Substitute the "x" and "y" values into the formula

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \frac{-4-y}{0-(-2)}[/tex]                Simplify

[tex]-1 = \frac{-4-y}{2}[/tex]                    Remember m = -1. Get rid of the fraction

[tex]2*-1 = 2*\frac{-4-y}{2}[/tex]           Multiply both sides by 2

[tex]-2 = \frac{2(-4-y)}{2}[/tex]                   The "2"s cancel out on the right

[tex]-2 = -4-y[/tex]                      Start isolating "y"

[tex]-2 +4= -4-y + 4[/tex]           Add 4 to both sides

[tex]2= -y[/tex]

[tex]2/-1= -y/-1[/tex]              Divide both sides by -1 to isolate "y"

-2 = y            Answer

y = -2            Variable on left side

Answer:

3 x 10^3

Step-by-step explanation:

The first is to identify the operation to be performed, it is a quotient between two potency.

Being two potency of the same base number (10), the property says that the quotient of two potency of the same base subtracts its exponent, and the base remains the same.

The corresponding exponents are 8 and 5.

The subtraction is 8-5 = 3.

The whole number that accompanies the base is divided in a current way, that is 12/4. Therefore, the result is 3.

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

Given:

Elena ate 2/8 of a pizza.

Dylan ate 1/5 of a pizza.

Question asked:

How much of the pizza did they eat ?

Solution:

By simply adding.

Elena ate of a pizza. = [tex]\frac{2}{8}[/tex]

Dylan ate of a pizza = [tex]\frac{1}{5}[/tex]

Total of a pizza they ate = [tex]\frac{2}{8}[/tex] + [tex]\frac{1}{5}[/tex]

By taking LCM of 8 and 5 ; 40

[tex]\frac{10 + 8}{40} = \frac{18}{40} = \frac{9}{20}[/tex]

Thus, [tex]\frac{9}{20}[/tex] f the pizza they eat.

Answer:

It will take 1/2 of a year or 6 months for these trees to be the same height.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Type A is 2 feet tall and grows at a rate of 25 inches per year.

Type B is 10 feet tall and grows at a rate of 9 inches per year.

2. Algebraically determine exactly how many years it will take for these trees to be the same height.

x = Number of years

Type A = 2 + 25x

Type B = 10 + 9x

Let's solve for x, using the following equation:

Type A =  Type B

2 + 25x = 10 + 9x

25x - 9x = 10 - 2

16x = 8

x = 8/16 = 1/2

It will take 1/2 of a year or 6 months for these trees to be the same height.

Let's prove it, this way:

2 + 25x = 10 + 9x

2 + 25 (1/2) = 10 + 9 (1/2)

2 + 25/2 = 10 + 9/2

29/2 = 29/2

14.5 = 14.5

Answer:

B- 240 cm²

Step-by-step explanation:

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Final answer:

To find the percent of discount, subtract the sale price from the original price, divide by the original price, and multiply by 100. The percent of discount is 30%.

Explanation:

To find the percent of discount, we need to calculate the difference between the original price and the sale price, and then divide it by the original price and multiply by 100.

Original price - Sale price = $129 - $90.30 = $38.70

Percent of discount = ($38.70 / $129) * 100 = 30%

Therefore, the percent of discount is 30%, which is option B.

Answer:

4

Step-by-step explanation:

-6g+36=12

-6g=12-36

-6g=-24

6g=24

g=24/6

g=4

Answer:

g= - 8

Step-by-step explanation:

Simplifying

-6g + -36 = 12

Reorder the terms:

-36 + -6g = 12

Solving

-36 + -6g = 12

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '36' to each side of the equation.

-36 + 36 + -6g = 12 + 36

Combine like terms: -36 + 36 = 0

0 + -6g = 12 + 36

-6g = 12 + 36

Combine like terms: 12 + 36 = 48

-6g = 48

Divide each side by '-6'.

g = -8

Simplifying

g = -8

Answer:

4/15

Step-by-step explanation:

P(drawing white marble and black marble)

= 6/10 × 4/9 [9 as there is no replacement]

= 4/15

Final answer:

The probability of drawing a white marble first and a black marble second without replacing the first one from a bag of 6 white and 4 black marbles is 12/45, which simplifies to 4/15.

Explanation:

The question is asking to find the probability of drawing a white marble first and then a black marble second from a bag of 6 white marbles and 4 black marbles, without replacing the first marble. To solve this, we calculate the probability of each event separately and then multiply them because the events are independent.

First, the probability of drawing a white marble is calculated by dividing the number of white marbles by the total number of marbles:
P(White first) = 6/10 or 3/5.

Since the first marble is not replaced, there are now only 9 marbles left in the bag, with 5 white and 4 black marbles. Next, the probability of drawing a black marble after drawing a white marble is the number of black marbles over the remaining total number of marbles:
P(Black second | White first) = 4/9.

To find the combined probability of both events happening in sequence, multiply the probabilities:
P(White first and Black second) = P(White first) × P(Black second | White first) = (3/5) × (4/9) = 12/45.

Therefore, the probability of drawing a white marble first followed by a black marble is 12/45, which simplifies to 4/15.

Answer:3/6

Step-by-step explanation:

68 is the 22nd term of the following sequence.

Step-by-step explanation:

the twenty second (22) term of the sequence 5, 8, 11, ...... is: D. 68.

Given the following data:

To find the twenty second (22) term of the sequence:

Mathematically, the [tex]n^{th}[/tex] term of a sequence is calculated by using the following formula;

[tex]a_n = a + (n - 1)d[/tex]

Where:

First of all, we would determine the common difference.

[tex]d = 2^{nd} \; term - 1^{st}\;term\\\\d = 8 - 5 \\\\d = 3[/tex]

Substituting the given parameters into the formula, we have;

[tex]a_{22} = 5 + (22 - 1)3\\\\a_{22} = 5 + (21)3\\\\a_{22} = 5 + 63\\\\a_{22} = 68[/tex]

Therefore, the twenty second (22) term of the sequence is 68.

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Answer:

Option C) 2=2 is the last step of Naomi and it is the correct answer

Step-by-step explanation:

Given that Naomi solves a system of equation by Substitution method :

The given system has infinite many solutions

Naomi's last step is 2=2

Then the system of equations has infinite many solutions

Therefore it must be 2=2

Hence option C) 2=2 is the last step and it is the correct answer

The correct last step in a solution with infinitely many solutions is option C, '2 = 2,' which shows that the system of equations is dependent and represents an identity.

When Naomi solves a system of equations using substitution and finds that the system has infinitely many solutions, this means that the two equations are essentially the same line. Therefore, the last step in her solution would demonstrate that the two expressions are identical. Option C, which states 2 = 2, would be the correct answer because it represents an identity, showing that the two sides of the equation are the same no matter what value is chosen for the variables. This is consistent with a situation where the system of equations is dependent, having an infinite number of solutions.

Answer:

A

Step-by-step explanation:

I'm not entirely sure but please let me know if I'm right

Answer: yes

Step-by-step explanation: 2.20 divided by 10 is .22, so one ounce is 22 cents. 2.64 divided by 12 is .22, 3.30 divided by 15 is .22, and 4.84 divided by 10 is .22. All the costs are the same per ounce, so it is a proportional relationship of .22.