Taco Johns is soon opening in Caledonia. It's massive news. Right now Caledonia has 13 fast food
restaurants. It's expected over the next 4 years the number of fast food restaurants in Caledonia will increase
to 21 restaurants. Write an equation to relate the number of fast food restaurants in Caledonia as a function of
time.

y² - 1 should be multiplied on both sides to solve the equation.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

(y² - 5) / (y² - 1) = (y² + y + 2) / (y + 1)

This can be written as,

y² - 1 = (y + 1) (y - 1)

So,

Multiplying y² - 1 on both sides.

(y² - 1) x (y² - 5) / (y² - 1) = (y² - 1) x (y² + y + 2) / (y + 1)

(y² - 5) = (y² + y + 2) (y - 1)

y² - 5 = y³ + y² + 2y - y² - y - 2

y² - 5 = y³ + y - 2

y³ - y² + y - 2 + 5

y³ - y² + y + 3

Thus,

Multiplying y² - 1 on both sides will solve the equation.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The coordinate of the image of the point (-3/2, -1/2) under reflection in the x-axis is (-3/2, 1/2).

When we want to reflect a point with respect to x-axis, the value of ordinate is negated. Reflection with respect to x-axis does not alter the value of abscissa but the ordinate value changes.

(i) The image coordinates of the point (2, -5) under reflection in the x-axis are (2, 5). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).

(ii) The image of the point (-3/2, -1/2) under reflection in the x-axis has the coordinates (-3/2, 1/2). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).

(iii) The image coordinates of the point (-7, 0) under reflection in the x-axis are (-7, 0). This signifies that the point's x-coordinate remains constant while its y-coordinate remains constant (zero).

To learn more about image of points, visit

brainly.com/question/26642069

#SPJ1

The complete question is: 1. Find the co-ordinates of the images of the following points under reflection in the x- axis:

(i) (2, -5)

(ii) (-3/2, -1/2)

(iii) (-7, 0)

Answer:

its ×2

Step-by-step explanation:

4×2 = 8

8×2=16

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

Answer:

8x^2-2x+1

The volumes of the structure are:

1. (8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)

2. (8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)

3. (8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]

A polynomial expression is an algebraic expression consisting of variables and coefficients, and involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Examples include 2x^3 - 5x^2 + 3x + 1 and 4y^2 + 7y - 2.

1.We can divide the structure into two rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of the second prism are 12(8 + x)(3 + x). To find the total volume, we can add the volumes of the two prisms:

(8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)

2.We can also divide the structure into three rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(3 + x), the dimensions of the second prism are 12(8 + x)(3 + x), and the dimensions of the third prism are 12(6 + 3x)(3 + x). To find the total volume, we can add the volumes of the three prisms:

(8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)

3.We can view the structure as one large rectangular prism with two smaller rectangular prisms removed, as shown in the sketch. The dimensions of the large prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of each small prism are 12(8 + x)(3 + x). To find the total volume, we can subtract the volumes of the two small prisms from the volume of the large prism:

(8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]

To know more about algebraic expression, visit:

https://brainly.com/question/953809

#SPJ1

so let's take a peek at the triangular pyramid, hmm it has a base of well, the base is a triangle, so we can say the triangle has a base of 10 and a height of 8, thus and area of (1/2)*10*8, and the pyramid has a height of 9.

[tex]\textit{Volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(10)(8)\\[1em] h=9 \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(10)(8) \right](9) \\\\\\ V=\cfrac{1}{3}(40)(9)\implies V=\cfrac{360}{3}\implies V=120~m^3[/tex]

Answer:

y= 13

Step-by-step explanation:

y+3x2+7

y=6+7

y=13

x     y

0     13

1       13

linear

Answer:this equation is not right.so,it does not have any solutions

Step-by-step explanation:

because if we try to solve it we get,

-2x-4=5-2x

-4-5=-2x+2x

-9=0

so,this equation is not right.

Answer:

equation has no solution

Step-by-step explanation:

- 2(x + 2) = 5 - 2x ← distribute parenthesis on left side

- 2x - 4 = 5 - 2x ( add 4 to both sides )

- 2x = 9 - 2x ( add 2x to both sides )

0 = 9 ← false statement

this false statement indicates the equation has no solution

Ben and Chris will meet after 3.5 hours.

The least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Ben and Chris start at the same time from places 96 miles apart to cycle toward each other,

Ben at 16mph and Chris at 12mph.

The LCM of 12 and 16 is,

= 48.

So, they will meet after 3.5 hours.

Therefore, they will meet after 3.5 hours.

To learn more about the LCM;

https://brainly.com/question/20739723

#SPJ1

Answer:

  ㏒₅₄168 = (1+ab)/(8a-5ab)

Step-by-step explanation:

You want ㏒₅₄168 written in terms of a and b, where ...

The rules of logarithms are relevant here:

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]

In order to simplify the writing in what follows, we want to define ...

Now, we can write the equations ...

  a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]

  b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]

Using these, we can solve for p and q:

  2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]

  (3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]

Using your favorite solution method for linear equations, you find ...

  p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)

  q = (-ar(3 -2b)/(-1) = ar(3 -2b)

Substituting these expressions into ...

  [tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]

__

Additional comment

The calculator confirms the result.

Answer:

120 student

Step-by-step explanation:

We know

45% of the students take the bus to school

100% - 45% = 55%

So, 55% travel by car or walk to school

400 x 0.55 = 220 students

So, 220 student travel by car or walk to school

We know

20 more students walk than travel by car

220 - 20 = 200 students

200/2 = 100 students

100 + 20 = 120 students

So, 120 students walk to school

Answer:

Step-by-step explanation:

Convert pounds to ounces:

2[tex]\frac{2}{3}[/tex] = 2.667

2.667 lb x 16 oz/lb = 42.7 oz

42.7 > 40, therefore Tuga has enough sweet potatoes to make chili

This graph is the rotation of 90° counterclockwise about the origin.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

We have the three points of the figure in graph as P(-2, 3), T(-3, 5) and J(-4, 4).

A point (x, y) after the rotation of 90° counterclockwise would be the point (-y, x).

P(-2, 3) after the rotation of 90° will be (-3, -2), which is the point P'.

T(-3, 5) after the rotation of 90° will be (-5, -3) which is the point T'.

J(-4, 4) after the rotation of 90° will be (-4, -4) which is the point J'.

Hence the image of the figure is the transformation of rotation of 90° counterclockwise.

Learn more about Rotation here :

https://brainly.com/question/12091224

#SPJ1

Your question is incomplete. The graph of possible figure is given below.

Answer:

d ≥ - 14

Step-by-step explanation:

6d ≥ - 84

Divide by 6 both sides

6d/6 ≥ - 84/6

d ≥ - 14

Answer:

angle 1 is 28 degrees  angle 2 is 62 degrees

DONT FORGET TO PUT THE DEGREES SIGN

Step-by-step explanation:

since it is a right angle, angle 1+ angle 2 is 90 degrees.

So,

2x+(x+48)=90

3x=90-48

3x=42

x=14

angle 1=28   angle 2=62

We can find the two linear equations by using the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

For the first equation:

Using the first point (-2, 8), we have m = (y2 - y1) / (x2 - x1) = (-3 - 8) / (-2 - (-2)) = -11/0, which is undefined. This means the first line is a vertical line.

The equation can then be written as x = -2, since the x-coordinate is constant.

For the second equation:

Using the second point (-1, 4), we have m = (y2 - y1) / (x2 - x1) = (-2 - 4) / (-1 - (-2)) = -2.

The equation can then be written as y - 4 = -2(x + 1), or y = -2x - 2.

Thus, the system of linear equations is:

x = -2

y = -2x - 2

Written in standard form:

x + 0y = -2

-2x + y = -2

Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.

What is area of a circle ?

Area of circle can be defined as product of pi and square of radius .

To find the area of the semicircle, we need to use the formula for the area of a circle, but divide it by 2 since we only have half of a circle. The formula for the area of a circle is:

A = πr²

where A is the area of the circle, and r is the radius.

In this case, we have a semicircle, so we need to use half of the formula:

A = (πr²)/2

We are given that R = 314, so we can substitute that into the formula:

A = (π(314)²)/2

Using a calculator and rounding to the nearest hundredth, we get:

A ≈ 49106.15

Therefore, Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.

To learn more about Area of circle from given link.

https://brainly.com/question/28642423

#SPJ1

Indicating whether the variable is relevant to the questions, and Identifying the variable as either categorical or quantitative.

Rather than straightforward explanations. Anything may be measured using it. It can also do mathematical calculations, which is essential for data analysis.

To completely understand all of the facets of quantitative data, statistical analysis—the discipline of obtaining, analysing, and presenting enormous volumes of data to uncover patterns and trends—is used. This calls for quantitative analysis employing a wide variety of data.

Categorical data is data that may be arranged into groups or categories using names or labels.

The approach is based on algorithms that assess each component of a data collection individually, compare them to other individual data sets, and look for particular similarities.

Learn more about Variables:

https://brainly.com/question/29670043

#SPJ4

Complete question:

identify and classify the variable(s) you will use.Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Group of answer choices

Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.

Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc. 

According to the information in the question:

Deposit = $50

Rent cost per day for the car = $20

Total amount that Justice has to pay = $490

∴ Total number of days that Justice kept the car = (490 - 50)/20

                                                                                 = 440/20

                                                                                 = 22 days

To know more about rent, visit the link below

https://brainly.com/question/26268428

#SPJ1

The number of days did he have the car are 22.5 days.

a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.

Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.

To find out how many days he had the car, we can set up an equation:

$50 + (number of days x $20) = $490.

Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.

So Justice had the car for approximately 22.5 days.

To know more about Dollar visit:

brainly.com/question/29846475

#SPJ1

Answer:

25 copies rented

Step-by-step explanation:

r = r1 - 5t, t is time in weeks, r is the number of copies rented, r1 how many people were renting at the start

we know on the 6 weeks passed and 4 copies were rented

4 = r1 - 5(6)

4 = r1 - 30; add 30 on both sides

34 = r1

r = 34 - 5t now plug t = 2 in for this function

r = 34 - 5(2)

r = 35 - 10

r = 25 copies rented

Answer:

1. D

2. C

3.D

4.D

5.C

6. A

7.B

Answer:

a couple different obes

Step-by-step explanation:

there are five

An amount of $ 13,200 has a total comission of 856.

Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:

C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)

C = 856

The graduate must pay a total comission of $ 856 for an amount of $ 13,200.

To learn more on interest rates: https://brainly.com/question/13735414

#SPJ1

The value of the expressions will be:

x + y + x + y + 2x + 2z.= 4x + 2y + 2z

6a² - 5a²b - 4a² - 3a²b = 2a² - 8a²b

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

3x(2 + x) - x² = 2x² + 6x

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The value of the expressions will be:

x + y + x + y + 2x + 2z

= 4x + 2y + 2z

6a² - 5a²b - 4a² - 3a²b

= 2a² - 8a²b

2(x + 3y) - 2x

= 2x + 6y - 2x

= 6y

3x(2 + x) - x²

6x + 3x² - x²

= 2x² + 6x

Learn more about expressions on:

brainly.com/question/1859113

#SPJ1

The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. Then the rate is given as,

⇒ $22.50 / 5

⇒ $4.5 per game

But the early-bird special on Saturday morning offers 8 games for $30. Then the rate is given as,

⇒ $30 / 8

⇒ $3.75 per game

The difference is given as,

D = $4.5 - $3.75

D = $0.75 per game

The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.

More about the rate link is given below.

https://brainly.com/question/14731228

#SPJ1

Answer:

a = - 2

Step-by-step explanation:

Since the point (x, y) = (1, a) lies on the line, substituting this value of x = 1 should give the corresponding value of y which is a

y = 3x - 5

At  (1, a)
a = 3(1) - 5

a = 3 - 5

a = - 2

Answer

Answer:

x = [tex]-3[/tex]; y = 11

Step-by-step explanation:

These two equations are linear simultaneous equations. They can be solved either by substitution, elimination or graphical method:

Substitution:

[tex]y = 8 - x[/tex] ------- (equation i)

[tex]y = 2x + 17[/tex] ---- (equation ii)

Substitute (equation i) into (equation ii):

[tex]8 - x = 2x + 17[/tex]

Bring all the like terms together. In addition x has to be isolated and made the subject of the equation:

[tex]8 - 17 = 2x + x[/tex]

[tex]-9 = 3x[/tex]

x = [tex]-\frac{9}{3}[/tex]

∴ x = [tex]-3[/tex]

Substitute this value of x in any of the equations to solve for y:

[tex]y = 8 - (-3)[/tex]

[tex]y = 8 + 3[/tex]

∴ y  = 11

This ordered pair of [tex](-3, 11)[/tex] is a solution for both linear simultaneous equations. In addition, this particular pair is known as the 'point of intersection'.

The company need to use for the family size box use a scale factor of 15.625 times greater.

To find the scale factor, we first need to determine the ratio of the volume of the family size box to the volume of the single serving box. The volume of a rectangular prism is given by the product of its length, width, and height. Let's assume the single serving box has dimensions l, w, and h. The volume of the single serving box is then lwh.

The volume of the family size box is 18.75 ounces, and since the single serving box is 1.2 ounces, the scale factor is the ratio of the volume of the family size box to the volume of the single serving box:

(18.75)/(1.2) = 15.625

Therefore, the company needs to use a scale factor of 15.625 to create the family size box from the single serving box. This means that the length, width, and height of the family size box will each be 15.625 times greater than the corresponding dimension of the single serving box.

Learn more about Box Volume Scale Factor Calculation here:

https://brainly.com/question/16890238

#SPJ4

Answer:

y = 7x -9

Step-by-step explanation:

This is a linear equation.

The change in y over the change in x is 9.  The y-intercept will be (0, -9).

If you follow the pattern as x is -1 and you go up 1 to zero, the the y goes up 7 from -16 to get -9

Answer:

y = 7x - 9

Step-by-step explanation:

y = 7x - 9

Let checks

-16 = 7(-1) - 9

-16 = -16

-23 = 7(-2) - 9

-23 = -23

So, y = 7x - 9 is the correct answer.