Sally is near the end of a three year lease on a car with an original MSRP of $38,000. Her leasing company claims that the car is now worth only $28,500. Which percentage represents the residual value of Sally’s leased car?a.25%b.33%c.67%d.75%

The main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

Both exponential equations are in the form y = ab^x - c, where a is the vertical scaling factor, b is the horizontal scaling factor (also known as the growth factor), and c is the vertical translation. The difference between the two equations lies in the values of the parameters a, b, and c.

The first equation, 2 (1/5)x-5, has a vertical scaling factor of 2, a horizontal scaling factor of 1/5, and a vertical translation of -5. The graph of this equation will increase at a slower rate than the graph of the second equation.

The second equation, 3 (1/2)x-3, has a vertical scaling factor of 3, a horizontal scaling factor of 1/2, and a vertical translation of -3. The graph of this equation will increase at a faster rate than the graph of the first equation.

In summary, the main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

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The sum of all the angles of triangle is 180°

We have the following angles:

The sum of all these angles will be equal to 180°

[tex] \sf \: 70 + 90 + 2x + 6 = 180[/tex]

[tex] \sf166 + 2x = 180[/tex]

[tex] \sf2x = 180 - 166[/tex]

[tex] \sf2x = 14[/tex]

[tex] \sf2x \div 2 = 14 \div 2[/tex]

[tex] \boxed{ \tt \: x = 7}[/tex]

The given angle is 2x+6, So put the value of x in this and find the value of angle

The number of cubes that has 1 face in red will be 54 which is placed at the center of all faces.

Samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.

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Answer:

4/49

Step-by-step explanation:

1 week : 5 working days

5*$4= $20

20/245= 4/49

Answer:

Step-by-step explanation:

Number of guests who called for room service = 45

Total number of guests = 45 + 200 = 245

Percentage of guests who called for room service = (45/245) x 100% ≈ 18.4%

Therefore, approximately 18.4% of the hotel's guests called for room service.

To create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Yaseen can produce 15 kits, the cost per kit she should charge is

p = 10 + 0.5q

p = 10 + 0.5(15) (15)

p = $17.50

She can produce 15 kits, the cost per kit she should charge is:

p = 30 - 0.5(15) (15)

p = $22.50

She can provide 60 kits, the cost per kit should be as follows:

p = 10 + 0.5q

Here, q=60

p = 10 + 0.5(60)

p = $40

She can produce 60 kits, the cost per kit should be set at:

p = 30 - 0.5(60) (60)

p = $15

Therefore, to create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

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Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:

(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.

In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:

t = 4 / (4 + 5) = 4 / 9

Plugging in the values into the formula:

x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9

y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9

So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).

Step-by-step explanation:

The accepted method for representing both integer and non-integer numbers is the decimal numeral system.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal between decimals is a decimal number that lies between two other decimal numbers.

For example, if you have two decimal numbers 0.2 and 0.3, a decimal between them would be any number that is greater than 0.2 and less than 0.3.

Some examples of decimals between 0.2 and 0.3 include 0.25, 0.26, 0.27, and so on.

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The question when translated in English is, "What is a decimal between decimals?"

Answer: la response est 1,235 je pense

Step-by-step explanation: trois decimal veux dire trois chiffre après la virgule donc on decale la virgule de 3 vers la gauche

The value of the variables y and z are 18

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

The special right triangle

The special right triangle has one of its angles to be 45 degrees

This means that

Legs = Hypotenuse/√2

Using the above as a guide, we have the following:

Legs = 18√2/√2

Evaluate

Legs = 18

Hence, the value of y and z are 18

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Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

ii

350x + 200y - 4200 = 0

Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:

350x + 200y - 4200 = 0

To find the x-intercept, we set y to zero and solve for x:

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

3.50x + 2.00y = 42.00

3.50x + 2.00y - 42.00 = 0

Multiplying both sides by 100 to eliminate the decimals, we get:

350x + 200y - 4200 = 0

x-intercept means what is x when y is 0

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

y-intercept means what is y when x is 0

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

To find the y-intercept, we set x to zero and solve for y:

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

The length of the arc AB is 6 cm when BC is 2 cm, ∠BOC = 32°, and ∠AOB = 96°.

The arc length is the portion of the circumference of a circle. It is directly proportional to the central angle formed by an arc.

The center of the circle is O, where BC = 2 cm, ∠BOC = 32°, and ∠AOB = 96°. Draw the diagram as per the given data.

As 96° = 3×32°, it follows that ∠AOB = 3×∠BOC.

As the central angle formed by an arc is proportional to its length. It follows that AB = 3×BC.

Since, BC = 2 cm, it can be got that AB = 3×2 cm = 6 cm.

Therefore, the required answer is 6 cm.

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4v + (9 x 7)= 4v +56

Answer:

Below

Step-by-step explanation:

I will assume they are all there on day 1

 then the LCM of  4  6  2  and 3   is 12 days

    every 12 days they are there together

       12 weeks = 12 x 7 = 84 days

                 84 / 12 = 7 times

day   1    13     25    37    49    62    74

The factorization of the given polynomial is 10x²(x+1).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is 10x³+10x².

Here, factors of the terms 10x³ and 10x² are

10x³= 2×5×x×x×x

10x²= 2×5×x×x

GCF of the terms is 2×5×x×x=10x²

10x²(x+1)

Therefore, the factorization is 10x²(x+1).

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Answer:

m∠6 = 142°

m∠7 = 38°

Step-by-step explanation:

You will be using postulates and theorems to solve this question.

Two parallel lines are cut by a transversal          (Given)

- m∠1 = 38°                         (Given)

- m∠1 ≅ m∠3                      (Vertical Angles Theorem)

  ∴ m∠3 = 38° (Definition of Vertical Angles Theorem)

- m∠3 ≅ m∠5                     (Alternate Angles Theorem)

 m∠3 = 38° ∴ m∠5 = 38° (Definition of Alternate Angles Theorem)

- m∠5 ≅ m∠7                     (Vertical Angles Theorem)

 m∠5 = 38° ∴ m∠7 = 38° (Definition of Alternate Angles Theorem)

m∠7 + m∠6 = 180°            (Corresponding Angles Postulate)

m∠7 = 38°                          (Given above)

Plug in 38 for m∠7 and solve for m∠6:

(38) + m∠6 = 180

Isolate m∠6. Note the equal sign, what you do to one side, you do to the other. Subtract 38 from both sides of the equation:

m∠6 + 38 = 180

m∠6 + 38 (-38) = 180 (-38)

m∠6 = 180 - 38

m∠6 = 142°

-

Answers:

m∠6 = 142°

m∠7 = 38°

~

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Value of composite functions (g-f)(x)  and (f/g)(x) are x² - 2x - 8 and

(x+1)/(2x - 3) respectively.both of these functions don't have the same

domain and range.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given functions,

f(x) = x² - 3x - 4

g(x) = 2x² - 5x - 12

1. (g - f)(x)

= g(x) - f(x)

= 2x² - 5x - 12 - (x² - 3x - 4)

= 2x² - 5x - 12 - x² + 3x + 4)

= x² - 2x - 8

x is defined for all real numbers

Domain = (-∞, ∞)

let y = x² - 2x - 8

x = √y + 2(x) - 8

Function is defined for y ≥ 9

Range is {y∈R , y ≥ 9}

2. (f/g)(x)

= f(x)/g(x)

= (x² - 3x - 4)/(2x² - 5x - 12)

= (x² - 4x + x - 4)/(2x² - 8x + 3x - 12)

= (x(x - 4) + 1(x - 4))/(2x(x - 4) + 3 (x - 4))

= (x+1)(x-4)/(2x+3)(x-4)

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

function is defined for x ≠ 3/2, Domain is {x ∈ R : x ≠ 3/2}

Let y = (x+1)/(2x - 3)

y.2x - 3y = x + 1

-3y - 1 = x - 2xy

x = (-1 - 3y)/(1 - 2y)

function is defined for y ≠ 1/2, Range is {y ∈ R : y ≠ 1/2}

Domain and range are not same for both functions.

Hence,  Value of composite functions (g-f)(x) = x² - 2x - 8 and

(f/g)(x) = (x+1)/(2x - 3), Domain and range is not same for both functions.

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Answer:

1:8

Step-by-step explanation:

since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.

16=1/2(2)h

32=2h

16=h

the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8

The system of equations are y = ( 5/4 )x and y = 6 - 3x where the value of x and y are 1.4117 and 1.765 respectively

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first equation be P

y = ( 5/4 )x   be equation (1)

Let the second equation be Q

y = 6 - 3x   be equation (2)

Substituting the values in the equation , we get

( 5/4 )x = 6 - 3x

Adding 3x on both sides of the equation , we get

6 = ( 5/4 + 3 ) x

( 17/4 )x = 6

Multiply by 4 on both sides of the equation , we get

17x = 24

Divide by 17 on both sides of the equation , we get

x = 24/17 = 1.4117

Substitute the value of x in equation (1) , we get

y = ( 5/4 ) ( 24/17 )

y = ( 30/17 )

y = 1.765

Hence , the equations are solved and the value of x and y are 24/17 and 30/17 respectively

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We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the short cut "x". Then, we can set up the following equation:

x^2 = 60^2 + 80^2

Expanding the squares:

x^2 = 3600 + 6400

x^2 = 10000

Taking the square root of both sides:

x = sqrt(10000)

x = 100

So, the length of the short cut up the flight of stairs is 100 meters.

Answer: Θ = [tex]45[/tex]

Step-by-step explanation:

tan x=sinx/cosx

and tan x is negative in the first and third quadrants.

tan x=1 for 45 degrees so tan x=-1 in the first quadrant 135 degrees and the third quadrant= 315 degrees

Answer: x = -7

explanation:

2(x+4)= -6

2x+8= -6

-8 -8

2x -14

Divide both sides by 2

X = -7

Answer:x=-7 I hope this helps

Step-by-step explanation:

2(x+4)=-6

Divide both sides of the equation by 2

X+4=-3

Move the constant to the right-hand side and change its sign

X=-3-4

Calculate the difference which means subtract-3 minus 4 which give you -7

X=-7

And that how you solve for X

The solution is, the remainder is 9.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

        0        4        10

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

        4        10       9 -> Remainder

So the remainder is 9.

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The Equation of Circle is (x+ 6)² + (y - 3)² = 9².

The equation for a circle is given by:

(x-h)² +(y-k)² = a²

Where (h,k) is the center and a is the radius of the circle.

Given:

We have the points A(-6, 3), B(-15, 3), and C(3,3).

Using Distance Formula

AB = √(-15 + 6)² + (3-3)²

AB = √9²

AB= 9 unit

BC= √(3 + 15)² + (3-3)²

BC = 18 unit

and, AC = √(3+6)² + (3-3)²

AC = 9 unit

As, AB = AC then A has to be the center (-6, 3) with radius 9 unit.

Thus, the Equation of Circle is

(x+ 6)² + (y - 3)² = 9²

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The balance amount when compounded daily at a rate of 4.075% after 6 months is  $269,320.60.

What is meant by compound interest?

The interest you earn on interest is known as compound interest. Compound interest, also known as interest on principal & interest, is the practice of adding interest to the principal amount of a loan or deposit. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. Thus, we can infer that the interest the bank charges is compound interest rather than simple interest.

Given,

Principal amount P = $263,000

Rate of interest r = 4.075%

Time period t = 6 months = 0.5 years

Final amount =  [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

where n = 365

A = [tex]P(1 + \frac{r}{n})^{nt} =263000(1 + \frac{0.04075}{365})^{365*0.5}[/tex]  = $269,320.60

Therefore the balance amount when compounded daily at a rate of 4.075% is  $269,320.60.

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The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of each packet is given as,

v = 16 x 9 x 4

v = 576 cubic cm

The volume of the cubical box is given as,

V = (1.2 x 100) x (1.2 x 100) x (1.2 x 100)

V = 120 x 120 x 120

V = 1,728,000 cubic cm

Then the number of packets is given as,

n = V / v

n = 1,728,000 / 576

n = 3,000

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

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Answer:

I think its

Step-by-step explanation:

2^(n+1) is the explicit form

thus, a = -39 is the solution to the equation -a = 4b-7 when (a, -8) is a solution

An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of two sides, with an equal sign between them. Equations are used to describe connections between variables, and to break problems in colorful fields, including mathematics, wisdom, engineering, and economics.

Given by the question.

the equation given is -a = 4b - 7.

We are also told that (a, -8) is a solution to this equation. This means that if we substitute a for x and -8 for y, the equation will be true.

Substituting the given values, we get:

a = 4b - 7 (Given equation)

a = 4(-8) - 7 (Substituting b = -8, since (a, -8) is a solution)

a = -32 - 7 (Simplifying)

a = -39 (Final answer)

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Answer:

To add different quantities of liquids with different units of measurements, we need to convert them all to the same unit of measurement. In this case, let's convert everything to quarts since that is what we want the final answer to be in.

2 gallons = 8 quarts (since 1 gallon = 4 quarts)

5 quarts of pineapple juice = 5 quarts (no conversion needed)

4 pints of cranberry juice = 8 cups = 2 quarts (since 1 pint = 2 cups and 1 quart = 4 cups)

6 cups of apple juice = 1.5 quarts (since 1 cup = 0.25 quarts)

Now we can add up all the quantities:

2 + 5 + 2 + 1.5 = 10.5

Maya made 10.5 quarts of fruit punch in all

The actual train is 957 inches long.

A ratio indicates the number of times one number contains another. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the model train to the actual train is 1 : 87.

The model train is 11 inches long, therefore,

1=11

Then, the value of 87 is:

87 = 87×11

   = 957

Hence, the actual train is 957 inches long.

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