$0.60 bottle of iced tea marked up $1.35

To solve the system of equations x - y = 7 and 0.5x + y = 5, convert both to y = mx + b form, graph them, and identify the intersection point as the solution.

To solve the system of linear equations:

we aim to express each equation in the

y = mx + b

form, where

m

is the slope and

b

is the y-intercept, to make them easy to graph.

Rearrange the first equation to isolate y:

The second equation rearranges to:

Both equations are now in a form where they can be graphed easily.

When these equations are graphed, the point where they intersect is the solution to the system. For simplicity, this explanation does not involve the actual graphing, but you can use graph paper or a graphing calculator:

The intersection point gives the solution to the system.

Answer:

The height of the fox in Huseyin's drawing is, 16 units

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

As per the statement: Huseyin draws a fox with a scale of 3 units on his graph paper represents 15 cm. The fox has an actual height of 80 cm.

⇒ We are given Scale of 3 units.

On graph paper the length of fox is 15 cm.

The fox has an actual height = 80 cm

let x be the height in units of the fox in Huseyin's drawing.

By definition of proportion;

[tex]\frac{3}{15} = \frac{x}{80}[/tex]

by cross multiply we get;

[tex]3 \times 80 = 15x[/tex]

Simplify:

240 = 15x

Divide both sides by 15 we get;

x = 16 units.

Therefore, the height of the fox in Huseyin's drawing is, 16 units

Answer:

16 units

Step-by-step explanation:

khan academy

Answer:

22 days  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Nonmember:

swim: $5

exercise: $9

Per day:  9 + 5 = $14

Member:

$300 per year plus $4 per day for an exercise class.  $0 for swimming

300 ÷ 14 = 21.428      21 days x $14 = $294     22 days x $14 = $308

So.... if he goes to the gym at least 22 days he will save money with the membership.

Answer:

The answer is D.) 5d+9d = 300 + 4d

Step-by-step explanation:

The equation states that for each day he attends to the gym to swim and exercise without a membership he has to pay for both, which is $5 and $9 respectively. This is each day that he attends.

However, if he HAS a membership, he only has to pay the $300 yearly fee once, and then $4 everyday he attends afterwards to do both swimming and exercising.

Now, in order to find out when the membership is worth it you need to find out when the membership cost and the non-membership cost is equal. so on one side of the equation you'll need the non-membership costs, and on the other side we'll put the membership cost.

So, for the non-membership cost, every day he goes it'll cost him $5 to swim and $9 to exercise, meaning that one side of the equation is 5d (d represents days) + 9d

And for the membership side we have the $300 initial, one-time fee, and then the $4 a day he has to pay to attend. This is equivalent to 300+4d

Finally, we put both equations together in a way to show that we want both sides to be equal, i.e

5d+9d = 300+4d

Thus our answer is D

Answer:

Stock Yield = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]

Step-by-step explanation:

Stock yield is found by the annual dividend divided by the current stock price.

There is an inverse relationship between the stock yield and the current  stock price.

For example, let's assume we have some shares of Company ABC, which pays $1.20 per share in annual dividends and the current stock price is $12.00, then by using the formula above we can calculate the stock yield of the Company ABC as,

Stock Yield  of company ABC = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]

                                                  = [tex]\frac{\$1.20}{\$12.00}[/tex]

                                                   = 0.1

                                                  = 10%

[tex]\dfrac{25}{35}=\dfrac{25:5}{35:5}=\dfrac{5}{7}\to\boxed{D)}[/tex]

Let the Length of River D be : P

Given : River C is 100 Miles Longer than River D

⇒ Length of River C = P + 100

Given : The Sum of Both Rivers is 5570 Miles

⇒ P + (P + 100) = 5570

⇒ 2P + 100 = 5570

⇒ 2P = 5570 - 100

⇒ 2P = 5470

⇒ P = 2735

⇒ Length of River D is : 2735 Miles

⇒ Length of River C is : (P + 100) = (2735 + 100) = 2835 Miles

Answer:

75 weeks

Step-by-step explanation:

Let the number of weeks be x

10x + 45 = 789          Subtract 45 from both sides

10x = 789 - 45           Combine

10x = 744                   Divide by 10

x = 744/10                  Divide

x= 74.4 weeks.          It will not hurt her to save the extra week to get the phone

Answer:

The average U.S. citizen throws away about 133.8 pounds of garbage a month.

Step-by-step explanation:

First take the total amount of trash thrown away in a year (1,606), and divide it by the number of months in a year (12).

1,606 / 12 = 133.833333

You would get 133.833333 and would round it to the nearest tenth and get 133.8.

Answer:

133.83 lb/month, or  133.8 lb/month to the nearest tenth.

Step-by-step explanation:

Here we need to find the unit rate of throwing stuff away.

To do this, divide 1,606 lb by 12 months, since we want the answer in pounds per month:

1,606 lb

------------- = 133.83 lb/month, or 133 5/6 lb/month

12 mos

Answer:

(x-3, y+4) hope this helps.

Answer:

The correct answer option is (x + 3, y - 4).

Step-by-step explanation:

If we are talking about the translation rule with respect to the origin (0, 0), then the correct option will be (x + 3, y - 4).

Since moving to the right on the x axis means a positive addition so moving three units right will mean 'plus 3'.

While moving down means that the value of y is going in negative so it will be (y - 4)

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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

[tex]100-2^3\times3+8^2\div4\\\\=100-8\times3+64\div4\\\\=100-24+16\\\\=76+16\\\\=\boxed{92}[/tex]

Answer:

The median of the histogram is scores ranging from 70-80

Step-by-step explanation:

Median of a histogram is always the "class interval" in which the MIDDLE NUMBER falls in.

If we add up all the bars (y-axis), we see HOW MANY NUMBERS in total there are. So we have:

[tex]1+2+1+2+6+9+13+5=39[/tex] numbers in total

What is the middle number out of 39 numbers?

It is: [tex]\frac{n+1}{2}[/tex] th number where [tex]n=39[/tex] for this problem

So, the middle number is : [tex]\frac{39+1}{2}=\frac{40}{2}=20[/tex]th number

Which class interval does the 20th number fall into?

So, definitely, 20th number falls into the sixth class interval which is "70-80".

Hence, the median of the histogram is scores ranging from 70-80.

(1 & 2/3) ft = (1 ft) + (2/3 ft)

(1 & 2/3) ft = 12 inches + 12*(2/3) inches

(1 & 2/3) ft = 12 inches + 8 inches

(1 & 2/3) ft = 20 inches

If the tree grows 5 inches per year, then it will take 4 years to get to 20 inches since 5*4 = 20. You can also divide to get 20/5 = 4.

So it takes 4 years for the tree to grow 1&2/3 feet tall.

Answer:

4 years

Step-by-step explanation:

Okay, so basically write a proportion

5 inches/per year

Then, find out how many inches are in  1 2/3 feet

1 2/3 = 1 8/12

Meaning there 1 2/3 feet is 1 foot and 8 inches. We know a foot is 12 inches. so then you just add 12 + 8 which is 20

Now going back to your proportion

5 inches/ per year =20 inches/x years

We know 5 goes into 20 4 times. Meaning to get to 20, your'e going to have to multiply the numerator by 4. But whatever you do to the numerator, you must do to the denominator. So multiply 1 x 4 which is 4 meaning it is going to take 4 years for the tree to grow 1 2/3 feet.

Given : Water Level in the Pool decreases by 6.35 × 10⁻¹ cm each Day

⇒ In One Day : The Level decreases by 6.35 × 10⁻¹ cm

⇒ In [8.64 × 10⁻⁴] Seconds : The Level decreases by 6.35 × 10⁻¹ cm

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = (\frac{6.35 \times 10^-^1}{8.64 \times 10^4})}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 0.73 \times 10^-^5}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 7.3 \times 10^-^6}[/tex]

First Blank : 7.3

Second Blank : 10⁻⁶

Answer:

5/8

Step-by-step explanation:

62.5% = 62.5/100

       =0.625

=0.625/1 x 1000/1000

=625/1000

=5/8

Answer:

8.3 * 10 ^5

Step-by-step explanation:

830000

To change this to scientific notation, we move the decimal 5 places to the left.  The exponent will be positive 5 because we moved it to the left

8.3 * 10^ +5

8.3 * 10 ^5

Answer:

x = 91.5

Step-by-step explanation:

for 30.5 miles travelled gas used is 1 gallon ← unit rate

To calculate distance travelled multiply gas used by 30.5

For 3 gallons used

distance travelled = 3 × 30.5 = 91.5 miles

⇒ x = 91.5

Check out the attached image below. It shows the bar graphs of each school. As you can see in figure 2 (Cleveland highschool), the data is more spread out compared figure 1. So this has a higher standard deviation. The standard deviation measures spread. The larger the standard deviation is, the more spread out the values will be. It can be thought of as a measure of how distant each value is from the mean.

Answer:

Yes. The statement is absolutely True

Step-by-step explanation:

Answer:

Yes the statement is true for real numbers.

Step-by-step explanation:

Yes. Every real number has two qualities: a sign and a distance from zero

Real numbers are points along a continuous infinite number line with its midpoint at 0.

These have a sigh either positive or negative. Like the numbers less than zero, or on the left side of zero on a number line are negative and the numbers on the right are positive.

Answer:

Symbols (or letters) in an equation can be important.

Step-by-Step Explanation:

The symbol [or letter (x, m, n, etc.)] is usually not important because the symbol represents a number. Sometimes it is important because each symbol (or letter) can represent another number.

for example: n+3 = 4-m (the symbol/ letters are different because they represent a different number).

for another example: n+3 = 4 (the symbol/ letter is only one letter).

The choice of letter or symbol to represent an unknown number in mathematics is arbitrary. It doesn't impact the mathematical operation or relationships, as the fundamental principles of algebra apply universally to any symbol.

It doesn't matter what letter or symbol is used to represent an unknown number because the essence of algebra and mathematical expressions is based on abstraction and generality. Mathematical symbols are placeholders for values and can be interchanged without changing the underlying mathematical relationships. Here's why it doesn't matter:

1. Universality of Symbols: Mathematical symbols and variables are universally understood and follow consistent rules. Whether you use "x," "y," "a," "b," or any other symbol, the principles of mathematics remain the same.

2. Abstraction: Algebra allows us to work with general concepts rather than specific numbers. The choice of symbols is arbitrary and doesn't affect the mathematical operations. The symbols represent placeholders for any number that satisfies the given conditions.

3. Flexibility: Different symbols can be used for different contexts or problems. For example, "x" is often used for unknowns in equations, "a" for constants, and "y" for dependent variables in functions. However, this is a convention, and other symbols can be used interchangeably.

4. Consistency: The rules of algebra, such as the commutative, associative, and distributive properties, hold true regardless of the symbols used. Algebraic manipulations and equations remain valid irrespective of the choice of symbols.

In summary, mathematical symbols are versatile and interchangeable because they serve as placeholders for values. The principles of algebra and mathematics are symbol-independent, allowing for flexibility in representation while maintaining the same underlying mathematical relationships.

For more such questions on mathematical operation:

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Answer:

Point-Slope form:  [tex]y+1=-\frac{6}{15}(x+5)\\[/tex]

standard form:  [tex]2x+5y=-15[/tex]

Step-by-step explanation:

The standard form is given by: [tex]Ax+By=C[/tex]

The point-slope form is given by: [tex]y-y_1=m(x-x_1)[/tex]

point [tex](10,-7)[/tex] as point [tex](x_2,y_2)[/tex]

Let's find the slope:

[tex]m=\frac{-7-(-1)}{10-(-5)}=-\frac{6}{15}[/tex]

1. So, point slope form can be written as:

[tex]y-(-1)=-\frac{6}{15}(x-(-5))\\y+1=-\frac{6}{15}(x+5)\\[/tex]

2. Rearranging this equation and bringing all x's and y's to one side and the number to another side will give us the standard form. So:

[tex]y+1=-\frac{6}{15}x-2\\y+\frac{6}{15}x=-2-1\\y+\frac{6}{15}x=-3[/tex]

But A, B, and C (standard form) needs to be integers, so to get rid of the denominator , we multiply the whole equation by 15. So we have:

[tex]y+\frac{6}{15}x=-3\\15y+6x=-45[/tex]

We can factor out a 3, so it becomes:

[tex]15y+6x=-45\\5y+2x=-15[/tex]

So standard form is [tex]2x+5y=-15[/tex]

Answer:

Step-by-step explanation:

Find x

Find y

Answer:

Step-by-step explanation:

OK... You have to use this formula: Y2 - Y1

                                                          X2 - X1

Y2 - Y1

X2 - X1

-5 - 7

2 - - 2

-12

-2

Simplify by dividing both -12 & -2 by 2: -6

                                                                 -1

It's either -6 or it's just -6 by itself... Really sorry if I'm wrong...

                -1  

Well, a linear equation should look like this: y = ax + b.

So if the slope is 0, then y = a*0 + b = b.

If y = b, then the line is a horizontal line like this:    ______________

Now, we look at the points that were given in the question: (-2, 7), (2, -5)

If the slope is 0, then the value of y, should not change, but the value of x will constantly be changing. So it means that as x increases, y is always the same.

If we look at the y place on the points: The y values are the bold numbers:

(-2, 7), (2, -5)

As you can see, 7 is not the same as -5. So the line's slope is not 0. The slope would be a negative number. Why? Well, 7 is above the x-axis and -5 is below the x-axis. For the x values, -2 is smaller than 2, so the point (-2, 7) is located at the top left quadrant and the point (2, -5) is located at the bottom right quadrant.

So to answer your question, the slope is not zero. The slope is negative.

Answer:

a. opens: upward

b. a.o.s.: x = 1

c. vertex: (1, -4)

d. x-intercepts: (-1, 0), (3, 0); y-intercept: (0, -3)

Step-by-step explanation:

By looking at the graph, we can see that the parabola opens upward. This means that its a-value is positive.

The axis of symmetry is the line that passes exactly through the center of the parabola. It always starts with x = __, because it is a vertical line.

The center of this parabola is at the x-value of 1, so we can say that the equation of the axis of symmetry is x = 1.

The vertex is at the highest or lowest point of the parabola, also known as the maximum or minimum point. Since this graph opens up, the vertex is at the minimum point.

Look at the graph and find the point where the parabola opens upwards. This point is at the x-value of 1 and the y-value of -4, so the vertex of the parabola is at (1, -4).

Again, look at the graph provided to find the x and y-intercepts. On the x-axis, the parabola crosses through at the x-values of -1 and 3, so the x-intercepts are (-1, 0) and (3, 0).

The parabola crosses the y-axis at the y-value of -3, so the y-intercept of the parabola is (0, -3).

Answer:

4.7

Step-by-step explanation:

Multiply 15 by 2.2. And get 33

Divide 33 by 7 and get 4.7

Hope it helps!

Final answer:

To accommodate 15 people, the elevator must be approximately 4.7 feet wide.

Explanation:

The question is asking us to calculate the width of the elevator box that can legally accommodate 15 people, given that the elevator building code requires at least 2.2 square feet per person and the depth of the elevator is 7 feet.

First, we need to find out the total area required for 15 people:

Total area = Number of people × Area per person = 15 × 2.2 square feet

Total area = 33 square feet

As we have the depth of the elevator, we can now calculate the width:

Total area = Width × Depth

Width = Total area / Depth

Width = 33 sq ft / 7 ft

Width ≈ 4.7 feet

Therefore, the elevator must be approximately 4.7 feet wide to accommodate 15 people as per the building code's requirements.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-2)}{6-0}\implies \cfrac{0+2}{6}\implies \cfrac{2}{6}\implies \cfrac{1}{3} \\\\\\ \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-(-2)=\cfrac{1}{3}(x-0) \\\\\\ y+2=\cfrac{1}{3}x\implies y=\cfrac{1}{3}x-2[/tex]

By using the properties of angle bisectors and congruent triangles, we can demonstrate that ABCD has both pairs of opposite sides parallel, proving it is a parallelogram.

Proof that ABCD is a Parallelogram

To prove that quadrilateral ABCD is a parallelogram:

DE bisects AC, meaning D is the midpoint of AC, and E is the midpoint of BD.

Since <1 is congruent to <2, triangles ADE and CDE are congruent by the Angle-Side-Angle (ASA) criterion.

If these triangles are congruent, then AD = DC and AE = EC by corresponding parts of congruent triangles (CPCTC).

Since DE bisects AC and BD, triangles ADE and CDE are mirror images.

Consequently, AD is parallel to BC, and AB is parallel to CD.

Because opposite sides are congruent and parallel, we conclude that ABCD is a parallelogram.

The bolt with a diameter of 0.52 inch has a percent error of approximately 5.45% from the advertised 0.55 inch, which is within the acceptable margin of less than 6%. Therefore, it should be included in the package.

The question revolves around determining if a bolt with a diameter of 0.52 inch should be packaged given that the labeled diameter is 0.55 inch and the allowable percent error is less than 6%. To calculate the percent error, we use the formula: Percent Error = (|Actual Value - Theoretical Value| / Theoretical Value) × 100%. Applying the numbers: Percent Error = (|0.52 - 0.55| / 0.55) × 100% = (0.03 / 0.55) × 100% ≈ 5.45%.

Since the percent error of 5.45% is less than 6%, the bolt with a diameter of 0.52 inch should be included in the package. This decision is based on the calculated percent error being within the accepted tolerance level.

The given lines 'x=-2' and 'y=8' are indeed perpendicular as they intersect at a right angle of 90 degrees, which defines perpendicularity.

In the context of coordinate geometry, the equations 'x=-2' and 'y=8' represent two lines in a 2D space. The line x=-2 is a vertical line that passes through -2 on the x-axis, while y=8 is a horizontal line that passes through 8 on the y-axis.

These lines are indeed perpendicular because they intersect at a right angle, which is a primary characteristic of perpendicular lines. Perpendicularity in 2D space is defined by a 90-degree angle between two lines, and in this case, the vertical line (x=-2) and horizontal line (y=8) do, indeed, intersect perpendicularly.

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Hello!

The number of tickets is dependent on age, so age is the independent variable.

Think of it as a y = mx equation. In this equation, x is the input, and y changes depending on the value of x inputted.

In this situation, y is the number of tickets, as y changes depending on the age x inputted. x is age, the independent variable.

Answer:

Its C) the number of tickets

Step-by-step explanation: