Eating at all you can eat buffet at your favorite restaurant cost $18.50, and increases its cost by 6% each year .


1. Write a function that correctly depicts the scenario.

2. How much will the buffet cost 10 years from now round your answer to the nearest cent

3. How much did the buffet cost 15 years ago ?round your answer to the nearest cent

The value of the variable based on the triangle given is 5.5 units.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Add each side of the triangle.

3z + z + 1 + 4z - 3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z -2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

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Answer:

x < -2  or  x > 4

Step-by-step explanation:

This is an absolute value inequality of the form

|X| ≥ b

where X is an expression with a variable, and b is a non-negative number.

An absolute value inequality of this form is solved by changing the form into a compound inequality using the word "or."

To solve

|X| ≥ a,

solve the compound inequality

X < - a or X > a

In other words, when the absolute value of an expression is greater than (or greater than or equal to) a number, rewrite the absolute value inequality as

expression < -number or expression > number

In your problem, you have

|2x - 2| ≥ 6

The expression is 2x - 2.

The number is 6.

You change the absolute value inequality to the following compound inequality:

2x - 2 ≤ -6  or  2x - 2 > 6

Now you solve each inequality always keeping the word "or" in between them.

2x - 2 ≤ -6  or  2x - 2 > 6

2x < - 4  or  2x > 8

x < -2  or  x > 4

I hope you understand the solution and explanation. If you have any questions, ask in the comments.

Answer:

y = -0.2x + 4.6

Step-by-step explanation:

We can set up a point-slope form to calculate for the equation:

y - y1 = m (x - x1)

Before we plug the coordinate into the formula, we need m, the slope of L, we know that L is perpendicular to the straight line, and the slope of the straight line is 5:

Perpendicular slope form is: opposite reciprocal of m, which is:

-1/5 or -0.2

Now we plug all the numbers into the previous equation:

y - 5 = -0.2 (x + 2)

y = -0.2 (x + 2) + 5

y = -0.2x + -0.4 + 5

y = -0.2x + 4.6

Now this is a slope-intercept form.

The distance between the given two points on the coordinate grid is 17 units.

A coordinate grid has two perpendicular lines, or axes labelled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.

Given that, are two points (7, 8) and (-8, 0) on a coordinate grid, we need to find the distance between the points

We know that, the distance between two points on a coordinate grid is given by;

D = √(x₂-x₁)²+(y₂-y₁)²

Here, x₁ = 7, x₂ = -8 and y₂ = 0, y₁ = 8

Therefore,

D = √(-7-8)²+(0-8)²

D = √(-15)²+(-8)²

D = √225+64

D = √289

D = 17

Hence, the required distance is 17 units.

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Answer:

7 1/2

Step-by-step explanation:

9 4/5 - 2 3/10 =

(9 + 4/5) - (2 + 3/10) =

(9 + 4/5) - 2 - 3/10 =  ==> distribute the minus sign to 2 and 3/10

9 + 8/10 - 2 - 3/10 =  ==> change 4/5 to 8/10 to have common denominators

9 - 2 + 8/10 - 3/10 =  ==> combine like terms

7 + 5/10 = ==> simplify

7 + 1/2 = 7 1/2

The value of the angle ∠U using the exterior angle theorem is calculated as; D: 34°

An exterior angle of a triangle is created by extending one side of the triangle. Now, the theorem of exterior angle of a triangle is that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Now, since we are given that m∠V = 95°, and m∠Z = 129°, then it means we can say that;

∠X, ∠Y = ∠Z

Similarly;

∠U + ∠V = ∠W

By congruency and external angles theorem, we can say that;

∠U + ∠V = ∠Z

Thus;

∠U +  95° = 129°

Thus;

∠U = 129 - 95

∠U = 34°

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Answer: I don’t know

Step-by-step explanation:

If Jordan is taking out a 2-week payday loan for $600. He will be charged $95 interest for the 2-week loan. The APR for this loan is 412.8%.

Using this formula to find the Annual percentage rate (APR)

APR =Loan interest /loan amount ÷ Number of loan length / 365

Let plug in the formula

APR = 95/600 ÷ (2 × 7 days)/365 days

APR = 95/600 ÷ 14 days/365 days

APR = 4.1279 × 100

APR = 412.8% ( Approximately)

Therefore we can conclude that the APR is 412.8%.

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Answer:

Eden planted 2 basil plants and 8 mint plants.

Step-by-step explanation:

Here's one possible way to write a system of equations to represent the information given in the problem:

Let x be the number of basil plants and y be the number of mint plants.

The first equation represents the total number of plants:

x + y = 10 (because Eden is planting a total of 10 herbs)

The second equation represents the total cost of all the plants:

x* $0.50 + y* $0.25 = $3

Elimination Method:

Multiply the first equation by $0.50

x* $0.50 + y* $0.50 = $5

subtracting this equation from the second equation

y* $0.25 = $3-$5 = -$2

y = 8

then substitute the value of y in first equation

x + 8 = 10

x = 2

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The total number of different 4-digit numerals that can be written using the 10 digits is 7.

Numbers are represented by digits, which include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A group of digits known as numerals is used to represent a number. 1234 2314 56111, for example, are numerals.

The number of different permutations of 4 digits can be calculated using the formula nPr = n! / (n-r)!.

2. In this case, n = 10 and r = 4, so nPr = 10! / (10-4)! = 10! / 6! = 5040 / 720 = 7!.

Since each digit can only be used once, there are no duplicate combinations. Therefore, the total number of different 4-digit numerals that can be written using the 10 digits is 7!

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The matching of the first row of expressions with the second row of expressions are;

1) 2√(3x²y) → x√(12y)

2) 2x√(6xy²) → y√(24x³)

3) 2y√(2x⁴) → x²√(8y²)

4) 3x²√(2y⁴) → xy√(18x²y²)

1) 2√(3x²y)

This can be broken down into the expression;

2x√(3y)

2) 2x√(6xy²)

This can broken down into;

2xy√(6x)

3) 2y√(2x⁴)

This can be simplified into;

2x²y√2

4) 3x²√(2y⁴)

This can be simplified into;

3x²y²√2

The second row of expressions are simplified as;

xy√(18x²y²)

= 3x²y²√2

x√(12y)

= 2x√3y

x²√(8y²)

= 2x²y√2

y√(24x³)

= 2xy√6x

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Answer:

Step-by-step explanation:

u just add the two equations together.

14w +56

The answer to the given equation is 240.

We can con solve the equation in the following ways:

6 f(x) dx = 6 * (4x) dx for x ≥ 4

Here, we will do the derivative and integration of the given equations as required. That will take us to the simplified statement. Note: we need to take into consideration the greater than equal  sign as it will directly affect the result of the equation.

= 24 * ∫x dx from 4 to 6

= 24 * (x^2/2)|4 to 6

= 24 * (6^2/2 - 4^2/2)

= 24 * (18 - 8)

= 24 * 10

= 240

Therefore, The answer to the given equation is 240.

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Answer:

Use the Cosine Rule to find unknown sides and angles

Step-by-step explanation

The extraneous solution of the equation x - 1 = √x + 1 is x = 0

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

x - 1 = √x + 1

Take the square of both sides

So, we have

x² - 2x + 1 = x + 1

Evaluate the like terms

x² - 3x = 0

So, we have

x(x - 3) = 0

Solving for x, we have

x = 3 and x = 0

Substitute x = 3 and x = 0 in x - 1 = √x + 1

3 - 1 = √3 + 1

2 = 2 ---- true

0 - 1 = √0 + 1

-1 = 1 ---- false

Hence, the extraneous solution is x = 0

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Answer:The greatest possible error of a measurement is considered to be one-half of the measuring unit. If you measure a length to be 4.3 cm. (measuring to the nearest tenth), the greatest possible error is one-half of one tenth, or 0.05. This means that any measurements in the range from 4.25 cm. to 4.35 cm. are perceived as correct.

Step-by-step explanation:

Answer:

The greatest possible error for a measurement of 0.05 metric tons would depend on the accuracy of the measurement device or technique being used. Without more information about the specific measurement method, it is impossible to determine the greatest possible error.

Step-by-step explanation:

There are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.

To calculate the number of even numbers, we can first calculate the total number of combinations of all the digits. This is done by multiplying the total number of digits (5) by the total number of combinations of each digit (4). This gives us 5 x 4 = 20.

To calculate the number of even numbers, we then divide this number in half, as half of the combinations will be even numbers. Therefore, 20 divided by 2 = 10 even numbers. Hence, there are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.

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The equation of the line that passes through these points X -2,0,2,3 and Y -17, -5, 7, 13 is given by y = 6x - 30

The slope, m of the linear function is calculated using the points on the form the table (0, -5) and  (2, 7)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-5 - 7) / (0 - 2)

m = (-12) / (-2)

m = 6

equation passing through point (0, 5)

(y - y₁) = m (x - x₁)

y - 0 = 6 (x - 5)

y = 6x - 30

The equation of the line for the table is solved to be  y = 6x - 30

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Answer:

Step-by-step explanation:

point form:

(-24,-13)

Equation form:

x = -24  y = -13

The value of [tex]x[/tex] and [tex]y[/tex] is [tex]x=-24[/tex] and [tex]y=-13[/tex]

The two given equation are

                       [tex]2x-3y=-9\\x-5=-29[/tex]

We need to find [tex]x[/tex] and [tex]y[/tex]

 that is ,

           [tex]x=-29+5\\x=-24[/tex]

We can substitute the value of [tex]x[/tex] in equation [tex]2x-3y=-9[/tex]

       that is ,

                      [tex]2(-24)-3y=-9\\-48-3y=-9\\-3y=-9+48\\-3y=39\\y=-13[/tex]

The value of [tex]x=-24,y=-13[/tex]

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The complete question is , Find the value of [tex]x[/tex] and [tex]y[/tex] if [tex]2x-3y=-9 , x-5=-29[/tex] in the substitution form.

Answer

[tex]\sqrt[3]{4^{2} }[/tex]

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

[tex]\sqrt[3]{2x-3}[/tex] = 3 ( cube both sides to clear the radical )

( [tex]\sqrt[3]{2x-3}[/tex] )³ = 3³

2x - 3 = 27 ( add 3 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

The value is evaluated to 5 1/4

A fraction can be described as the part of a whole value, variable or element.

The different types of fractions are;

From the information given, we have that;

1 + (-2/3) - (-m)

If the value of m = 9/2, let's substitute the value, we have;

1 - 2/8 - ( 9/2)

expand the bracket

1 - 2/8 + 9/2

Find the LCM

8 - 2 +  36 /8

42/8

5 1/4

Hence, the value is 5 1/4

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In order to solve problems involving triangles that require constructions, you can use a straightedge and compass.

Here are the steps you can follow:

First, identify the information that is given in the problem and what you need to find.

Draw a diagram of the triangle, including any given segments or angles.

Use the given information to construct any points or lines that are required.

Use the straightedge to draw any necessary lines, and use the compass to construct any circles or arcs that are required.

Use the properties of triangles and the given information to solve for the unknown quantity. It's important to note that not all problems involving triangles can be solved using constructions. In some cases, you may need to use other techniques, such as the Pythagorean Theorem or the Law of Sines.

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Answer:

-45, -46

Step-by-step explanation:

-45 + (-46) = -91

Each of Liam, Anika, and Sai is figuring out the identical equation for x. 12x+4=20x-12 in the original equation. 12x+16=20x was the outcome of Sai's initial action.

Getting the variable on one side is the first step in solving an equation with a variable on both sides once it has been simplified. To do this, one of the words with the variable's addition or subtraction is reversed.

12 x + 4 = 20 x - 12 x 4 = 20 x - 12 x - 12 x 4 = 8x - 12

The linear term was then simply merged.

12 on each side is added. Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x + 4 = 20 x - 12 is the analysis.

12 on each side added

Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x from both sides 16 = 20 x - 12 x 16 = 8x x = 2.

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Brandon ' s rate of change , give the graph on the amount of savings per period, is C. 75

The rate of change can be found by the formula :

= Rise / Run

The rise can be found by subtracting an earlier value of the amount in savings, from a later value of the amount in savings .

The run can be found by subtracting an earlier value in periods from a later value in periods . Therefore , the first step is to pick two points on the graph.

Points picked are ( 2 , 150 ) and ( 4 , 300 )

The rise is :

= 300 - 150

= 150

The run is :
= 4 - 2

= 2

The rate of change is :
= 150 / 2

= 75

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To solve this equation, we need to get x by itself on one side of the equation. To do this, we can start by adding 8 to both sides of the equation to get:

2/3 x - 8 + 8 = 24 + 8

This simplifies to:

2/3 x = 32

Then, we can divide both sides of the equation by 2/3 to get:

(2/3) / (2/3) * x = 32 / (2/3)

This simplifies to:

x = 48

So the solution to this equation is x = 48.

The net force on particle q2 is 32203.65N

The sum total of all the forces which are acting on an object is known as the net force. A mass that can accelerate due to net force on an object. Whether a body is at rest or in motion, it is a subject to another force. When there are a lot of forces which are acting on a system, the term net force is used to denote it.

Given;

r₁₂ = 0.550m r₂₃ = 0.550m. Then the distance from the first charge to the third one will be;

r₁₃ = r₁₂ + r₂₃ = 0.550 + 0.550 = 1.1m

Now, according to the Coulomb's law, the net force on particle q₂ will be equal to the sum of the forces on particle q₂ from the particle q₁ and q₃.

F₃+ = F₁₃ +F₂₃ = q₁q₂/r²₁₃ + k q₃q₂/r²₂₃

Where, k = 9 × 10⁹ N m²/C²

Substituting numerical values;

F₃ = 9 × 10⁹ (-66.3 × 10⁻⁶)(-43.2 × 9 × 10⁻⁶)/ 1.45² + 9 × 10⁹ × 108 × 10⁻⁶ (-43.2 × 10⁻⁶) / 0.550²

F₃= 231.996x 41.9904/0.3025

F₃= 32203.65

Therefore, the net force will be 32203.65N

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Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!