using the rule of 78 find the amount of unearned interest with finance charge 747 total payments 24 with remaining number of payments, when paid in full 8

The solution of the quadratic equation (x - 3)² - 24 = 25 is x = 10, -4.

Given that the quadratic equation is (x - 3)² - 24 = 25

Expanding the left side of the equation, we get:

(x - 3)² - 24 = 25

Simplifying the above equation, we get:

x² - 6x + 9 - 24 = 25

Solving by combining like terms, we get:

x²  - 6x - 40 = 0

We can solve for x by factoring the quadratic equation:

(x - 10)(x + 4) = 0

Therefore, x can be equal to 10 or -4.

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Answer:

Step-by-step explanation:

[tex]\frac{2}{\sqrt{40} }[/tex]

=[tex]\frac{2}{\sqrt{40} }*\frac{\sqrt{40} }{\sqrt{40} }[/tex]            multiply root on top and bottom

=[tex]\frac{2\sqrt{40} }{40}[/tex]                    reduce fraction outside of root

=[tex]\frac{\sqrt{40} }{20}[/tex]                     break up 40 under root

=[tex]\frac{\sqrt{4*10} }{20}[/tex]                  break up roots to see better

=[tex]\frac{\sqrt{4}\sqrt{10} }{20}[/tex]                 √4 = 2

=[tex]\frac{2\sqrt{10} }{20}[/tex]                   reduce fraction outside of root

=[tex]\frac{\sqrt{10} }{10}[/tex]                    answer

The total number of beads which Lola use to make 13 bracelets and 8 necklaces is 1340 beads.

An expression will consists of one or more numbers along with one more operation. X + 1 is an example of an expression.

We will use this expression to calculate the number of beads. The number of beads will be: (number of bracelets x beads per bracelet) + (number of necklaces x beads per necklace)

Substituting the values, we get:

= (13 x 44) + (8 x 96)

= 572 + 768

= 1340 beads

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The equation is filled as;

366 · (673 + 518) = 366 · 673 + 366 · 518

PEDMAS is described as a mathematical acronym that is used to represent the different mathematical operations in their order of application.

PEDMAS represents the following;

From the information given, we have that;

366 · (673 + 518)

Using the first rule, expand the parentheses

We have;

366(673) + 336(518)

This is also represented as;

366. 673 + 366. 518

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The shipping container shaped like a cuboid is 9.5 feet tall.

Let's call the height of the shipping container "h".

As per the given information, the shipping container can be described as a cuboid.

We are aware that the container's volume is given by the formula:

V = lwh,

where l stands for length, w for width, and h for height.

Substituting the values provided yields:

3040 = 8 x 40 x h

Simplifying, we get:

3040 = 320h

Dividing both sides by 320, we get:

h = 9.5

Therefore, the height of the shipping container is 9.5 feet.

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The solution for the given inequality is x ≥ - 7.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

- 3 - 3x ≤ 18

Adding 3 on both sides, we get -

- 3 - 3x + 3 ≤ 18 + 3

- 3x ≤ 21

Divide by -1 on both sides, we get -

3x ≥ - 21

x ≥ - 7

Therefore, the solution for the given inequality is x ≥ - 7.

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The surface area of the box formed by the pattern is given as follows:

72 cm².

The surface area of a figure is calculated as the sum of the areas of all the components of a figure.

The components of the figure in this problem can be defined as follows:

The area of the large rectangle is given as follows:

6 x 10 = 60 cm².

The combined area of the smaller rectangles is given as follows:

2 x 3 x 2 = 12 cm².

Hence the surface area of the figure is given as follows:

60 + 12 = 72 cm².

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The rational function r(x) with the given features is r(x) = 4(x + 9)(x - 4)²/(x - 3)(x + 5)(x + 2)

We use the given parameters to determine the possible function

So, we have

crosses the x-axis at -9

Factor = (x + 9)

touches the x-axis at 4

Factor = (x + 9)(x - 4)²

Vertical asymptote at x = 3 and at x = -5

Denominator = (x - 3)(x + 5)

A hole at x = -2

This means that the function is undefined at x = -2

So, we have

Denominator = (x - 3)(x + 5)(x + 2)

Horizontal asymptote at y = 4

So, the function becomes

r(x) = 4(x + 9)(x - 4)²/(x - 3)(x + 5)(x + 2)

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To calculate the number of gallons of gas a family will save over one year by replacing their old car with a new car, you will need to know the following information:

The current mileage of the old car: this will help you determine how many miles the car is driven in a year.

The miles per gallon (MPG) rating of the old car: this will tell you how many gallons of gas the car uses per mile.

The MPG rating of the new car: this will tell you how many gallons of gas the new car uses per mile.

The price of gasoline: this will allow you to determine the total cost of the gasoline used over the course of a year.

To calculate the number of gallons of gas saved, you will need to first determine the total number of miles driven in a year. Then, divide that number by the MPG rating of the old car to determine the number of gallons of gas used. Repeat the process using the MPG rating of the new car to determine the number of gallons of gas the new car would use over the same distance. Finally, subtract the number of gallons used by the new car from the number used by the old car to determine the total number of gallons of gas saved.

For example, if the old car gets 25 MPG and is driven 15,000 miles per year, it will use 600 gallons of gas (15,000 miles / 25 MPG = 600 gallons). If the new car gets 35 MPG, it will use 428.57 gallons of gas over the same distance (15,000 miles / 35 MPG = 428.57 gallons). The family would save 171.43 gallons of gas per year by replacing the old car with the new one (600 gallons - 428.57 gallons = 171.43 gallons).

Since the question was not complete, the answer is general. However, the solution is given with an example to make it simpler for you to solve.

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complete question:

Paula father thinks replacing their old car will save the most gas because the new car gets more miles per gallon than the new van calculate the number of gallons of gas family will save over one year by replacing their old car with the new car

Answer:

Step-by-step explanation:

It has a center at (3,5)  and r=4

Draw your center then go out 4 up, down, left, and right

Domain = [(3-4),(3+4)] = [-1, 7]    this is where the function exists for x

Range = [(5-4), (5+4)] = [1, 9]    this is where the function exists for y

Answer:

Let's assume that the two numbers are x and y, where x is greater than y.

From the given information, we can write two equations:

x^2 + y^2 = 85 (Equation 1)

x - y = 1 (Equation 2)

We can solve Equation 2 for x and substitute into Equation 1:

x = y + 1

(x = y + 1) into (Equation 1)

(y + 1)^2 + y^2 = 85

Simplifying this equation, we get:

2y^2 + 2y - 84 = 0

Dividing both sides by 2, we get:

y^2 + y - 42 = 0

Factoring this equation, we get:

(y + 7)(y - 6) = 0

Therefore, y = -7 or y = 6. Since x is greater than y, we can ignore the negative value.

So, y = 6 and x = y + 1 = 7.

Therefore, the two numbers are 6 and 7.

The answer is that the the equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n comma such that n is an integer is, 2 coscec 2x.

Since, Cosecant is one of the trigonometric ratios .

It is calculated as the ratio of the hypotenuse to the perpendicular of a right triangle.

It is also calculated as the reciprocal of the sine function.

Now, here if the vertical asymptotes is x = pi/2 + pi/2 (n).

This is not defined when n=0.

so, when x= pi/2,

sin 2x = sin x = 0

which means w =0 .

and we get the equation for cosecant function to be,

⇒ f(x) = 2 cosec 2x

since cosec x = 1/ sin x.

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The perimeter of the sector in terms of π is (7π+18) cm.

A sector is a shape that is bounded by an arc and two radius.

To calculate the perimeter of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The equation of the ellipse graphed in the image is given as ((x-4)²/16) + ((y-6)²/4) = 1.

The standard form equation of an ellipse with center (h,k), horizontal axis of length 2a, and vertical axis of length 2b is,

((x-h)²/a²) + ((y-k)²/b²) = 1

Since the center is given as (4, 6), we have h = 4 and k = 6. The vertex is given as (0, 6) which means the horizontal distance from the center to the vertex is a = 4. Also, the co-vertex is given as (8, 6) which means the vertical distance from the center to the co-vertex is b = 2. Therefore, substituting these values in the equation of an ellipse, we get,

((x-4)²/4²) + ((y-6)²/2²) = 1

Simplifying, we get the equation of the ellipse,

((x-4)²/16) + ((y-6)²/4) = 1

Thus, the equation of the ellipse with center (4, 6), vertex at (0, 6), and co-vertex at (8, 6) is ((x-4)²/16) + ((y-6)²/4) = 1.

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The coordinates of the vectors are, respectively:

Vector A: P = (7, π / 4)

Vector B: P = (7, 3π/ 4)

Vector C: P = (7, 5π / 4)

Vector D: P = (7, 7π / 4)

In this question we have the need of representing four vectors described in the figure given. Each description must be done in polar form:

P = (r, θ)

Where:

Now we proceed to determine the coordinates for each vectors:

Vector A

P = (7, π / 4)

Vector B

P = (7, 3π/ 4)

Vector C

P = (7, 5π / 4)

Vector D

P = (7, 7π / 4)

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The ultimate reason that the Bergen-Belsen camp was surrendered to British forces was C. The Nazis worried that if the prisoners escaped, typhus would spread.

One of the last camps to be liberated during World War II was Bergen-Belsen, a concentration camp in Nazi Germany. The camp was overcrowded and in appalling condition by April 1945. There was a possibility of a typhus epidemic, and the convicts were ill and malnourished.

To stop the typhus from spreading, the German army was on the run. The SS leaders agreed to hand over the camp to the British soldiers as a result. When British troops invaded Bergen-Belsen on April 15, 1945, they discovered some 60,000 captives there, the majority of whom were sick and dying.

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The cost of the 28 inches and 36 inches diagonal Smart TVs, based on the quadratic cost function are;

28 - inch diagonal; $134

36 - inch diagonal; $165

A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The cost of the Smart TV as a function of the diagonal length is C(d) = 0.322·d² - 16.776·d + 351.444

The above function indicates that the cost of a Smart TV that is 28 inches long is; C(28) = 0.322 × 28² - 16.776 × 28 + 351.444 ≈ 134

The cost of a Smart TV with a diagonal of 36 inches is therefore;

C(36) = 0.322 × 36² - 16.776 × 36 + 351.444 ≈ 165

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Answer:

Step-by-step explanation:

I) In the scatter graph question, D is the most suitable line of best fit for the data. Reason: the line diligently follow the points as they move upwards. Also, the points outside the line(i.e besides the line) are equally divided, on the up and down part of the line unlike in F

II) Here, you trace the values provided on the graph on one axis to get the corresponding value on the other axis.

Therefore, From the graph 600umbrellas = corresponds to 160 days.

III) Same rule in II) applies here.

28 lions = corresponds to 20 hyenas

IV) 50 cm = corresponds to 20kg weight

Answer: 3200, less

Step-by-step explanation:

The rate at which the space explorers fly in miles per hour is the slope.

Space explorer B flies at a rate of 6400 miles per hour. This is because

y=mx+b, where m is the slope.

Space explorer A flies at a rate of (32000-16000)/(10-5) = 3200 miles per hour.   Slope is (y2 - y1) / (x2 - x1) where the coordinates are (x1,y1) and (x2,y2).

Space explorer B - Space Explorer A = 6400 - 3200 = 3200.

Therefore space explorer A travels 3200 miles per hour less than explorer B.

Answer:

Step-by-step explanation:

From the graph A find slope = (32000-16000)/(10/5)=3200

So for the equation y=3200x  plug 1 in you get 3200

For B if you plug in 1 you get 6400 miles per hour

6400-3200=3200

A travels 3200 miles per hour slower than B

y = a(x + 4)^2 + 12

where "a" is a constant that determines the shape of the parabola. To find the value of "a", we can use the y-intercept (0,-36):

-36 = a(0 + 4)^2 + 12

-36 = 16a + 12

-48 = 16a

a = -3

Therefore, the equation of the parabola is:

y = -3(x + 4)^2 + 12

To find the x-intercepts, we can set y = 0 and solve for x:

0 = -3(x + 4)^2 + 12

3(x + 4)^2 = 12

(x + 4)^2 = 4

x + 4 = ±2

x = -4 ± 2

So the x-intercepts are (-6,0) and (-2,0). Therefore, the answer is:

(-6,0), (-2,0)

Therefore, we can estimate that approximately 34.1% of values in this distribution fall between 28 and 30 and approximately 99.7% of values in this distribution fall between 24 and 36.

Percent is a unit of measurement that expresses a part-to-whole ratio as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express changes, proportions, and rates in many fields such as mathematics, science, economics, and finance. They are often used to compare values of different sizes and scales, and to convey information in a clear and concise way.

Here,

(a) To find the percentage of values in the distribution between 28 and 30, we need to determine the z-scores corresponding to these values and use the empirical rule to estimate the proportion of values that fall between these z-scores.

First, we calculate the z-score for a value of 28 as:

z = (28 - 30) / 2

= -1

Next, we calculate the z-score for a value of 30 as:

z = (30 - 30) / 2

= 0

According to the empirical rule for a normal distribution, approximately 34.1% of values fall between a z-score of -1 and 0. Therefore, we can estimate that approximately 34.1% of values in this distribution fall between 28 and 30.

(b) To find the percentage of values in the distribution falling between 24 and 36, we need to determine the z-scores corresponding to these values and use the empirical rule to estimate the proportion of values that fall between these z-scores.

First, we calculate the z-score for a value of 24 as:

z = (24 - 30) / 2

= -3

Next, we calculate the z-score for a value of 36 as:

z = (36 - 30) / 2

= 3

According to the empirical rule for a normal distribution, approximately 99.7% of values fall between a z-score of -3 and 3. Therefore, we can estimate that approximately 99.7% of values in this distribution fall between 24 and 36.

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Complete question:

A normal distribution has a mean of 30 and a standard deviation of 2 Use the 68-95-99.7 rule to find (a) the percentage of values in the distribution between 28 and 30 % (b) the percentage of values in the distribution falling between 24 and 36 %.

The statement as a function of Jessica earnings is f(x) = 10x + 15

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

Represent the number of hours worked with x

So, we have

f(x) = babysitting * x + bonus

This gives

f(x) = 10x + 15

Hence, the function is f(x) = 10x + 15

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The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.

To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:

1(1!)+2(2!) +3(3!) +4(4!) +3(3!)

= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)

= 1 + 4 + 18 + 96 + 18

= 137

Therefore, the value of the summation when m = 3 is 137.

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Since you cannot make a fraction of a round trip, you will need to make 5 round trips (back and forth) between Seattle and Miami to earn a free flight.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Each round trip between Seattle and Miami covers a distance of 2 x 2,724 = 5,448 miles (round-trip distance). To accumulate 25,000 miles, you need to make 25,000 / 5,448 = 4.59 round trips.

Since you cannot make a fraction of a round trip, you will need to make 5 round trips (back and forth) between Seattle and Miami to earn a free flight.

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Answer:

The rectangle is 7 cm x 18 cm

Step-by-step explanation:

w = width

l = length

(1)  A = wl = 126 cm²

(2) P = 2w + 2l = 50 cm

Solve equation (2) for w:

2w = 50 - 2l

w = (50 - 2l) / 2 = 25 - l         plug this in to equation (1)

(25 - l)(l) = 126

-l² + 25l - 126

Use quadratic formula to find the 2 roots of l:  a = -1, b = 25. c = -126

l = 7, 18

Since l > w, then l = 18

Solve for w:

w = 126/18 = 7

The second pair of numbers with a highest common factor (HCF) of 4 and lowest common multiple (LCM) of 40, other than 4 and 40, could be 8 and 20. Their sum is 28.

The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. It is also known as the greatest common divisor (GCD). On the other hand, the lowest common multiple (LCM) is the smallest common multiple of two numbers.

For the numbers 4 and 40, the HCF is indeed 4, and the LCM is 40. Let's denote our second pair of numbers as 'a' and 'b'. Given that these two numbers share the same HCF (4) and LCM (40), we could set up these equations:

Given these constraints, the possible pairs ('a', 'b') could be (4, 40) or (8, 20). Since 4 and 40 have been provided as examples, we'll take the second pair. Therefore, the sum 'a' + 'b' = 8 + 20 = 28.

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The solution to the equation 2(x+1) = -8 is x = -5.

Given information:

The equation is 2(x+1)=-8.

In order to solve the equation 2(x+1)=-8, follow the process given below.

1. Distribute the 2 to the parentheses:

2x + 2 = -8

2. Subtract 2 from both sides to isolate the x term:

2x = -10

3. Divide both sides by 2 to solve for x:

x = -5

Therefore, the solution is x = -5.

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The number of tons of cream chees  ordered by each supplier are 20 tones

The given parameters are

x = tons of CCC **AND** BBF (can use same variable for both since these amounts [CCC & BBF] are the same)

y = t

2x+y = 100                         <== tonnage

80x + 65x + 50y = 5900       <== cost

  2x +     y = 100   <== multiply all by -50

145x + 50y =  5900

-100x - 50y = -5000

145x + 50y = 5900

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

  45x  +   0   = 900

Making x the subject of the relation we have

x = 810/45 = 20 tones

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To find f+g, we need to add f(x) and g(x):

f(x) + g(x) = (2x^(2) +5) + (1/2x)

f+g = 2x^(2) + (1/2)x + 5

To find f-g, we need to subtract g(x) from f(x):

f(x) - g(x) = (2x^(2) +5) - (1/2x)

f-g = 2x^(2) - (1/2)x + 5

To find fg, we need to multiply f(x) and g(x):

f(x) * g(x) = (2x^(2) +5) * (1/2x)

fg = x + (5/2)x^(-1)

To find f/g, we need to divide f(x) by g(x):

f(x) / g(x) = (2x^(2) +5) / (1/2x)

f/g = 4x + 10x^(-1)