Jessie paid $43.75 for 5 movie tickets. Each ticket cost the same amount. What was the cost of each movie ticket in dollars and cents?

The error in the given solution was adding the numerators while ignoring the Denominators.

Solve the expression:$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$

$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{3x+2}{(x+2)(x-6)} + \frac{2x-1}{(x+3)(x-4)}$$$$= \frac{(3x+2)(x+3)}{(x+2)(x-6)(x+3)} + \frac{(2x-1)(x+2)}{(x+3)(x-4)(x+2)}$$

Using the least common denominator and adding, we get$$\frac{(3x+2)(x+3)}{(x+2)(x-6)(x+3)} + \frac{(2x-1)(x+2)}{(x+3)(x-4)(x+2)}$$$$= \frac{(3x+2)(x+3) + (2x-1)(x+2)}{(x+2)(x-6)(x+3)}$$$$= \frac{3x^2 + 11x + 4}{(x+2)(x-6)(x+3)}$$

Correct Answer:$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{(3x+2)(x-4) + (2x-1)(x+3)}{(x-6)(x+3)(x-4)}$$$$= \frac{3x^2 - 10x - 5}{(x-6)(x+3)(x-4)}$$

Error Analysis:The given problem was solved using the correct approach to add or subtract rational expressions. However, the calculations made were incorrect.

The error made in the solution was the addition of the numerators while ignoring the denominators, which is not allowed. The correct method to add or subtract rational expressions is to find the least common denominator (LCD) of the given expressions.

The LCD of the given expressions is $(x+2)(x-6)(x+3)(x-4)$.After finding the LCD, we rewrite each term with the same denominator, and then add or subtract the numerators.

In this problem, the correct solution would be$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{(3x+2)(x-4) + (2x-1)(x+3)}{(x-6)(x+3)(x-4)}$$$$= \frac{3x^2 - 10x - 5}{(x-6)(x+3)(x-4)}$$

Therefore, the error in the given solution was adding the numerators while ignoring the denominators.

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Using the chain rule dz/dt = -e⁻t/ (e²t + 6\(e^t\)+ 1). As We have:

z = tan⁻¹(y/x), x = \(e^t\\\), y = 3 - \(e^{(-t)\).

To find dz/dt, we need to apply the chain rule:

dz/dt = dz/dy * dy/dx * dx/dt

First, let's find dz/dy:

dz/dy = 1 / (1 + (y/x)²)

Using x = \(e^t\) and y = 3 - e^(-t), we get:

dz/dy = 1 / (1 + (3\(e^t\) - 1)²)

Next, let's find dy/dx:

dy/dt = \(-e^{(-t)\)

dy/dx = dy/dt * dt/dx = \(-e^{(-t)\)/ \(e^t\) = -e^(-2t)

Finally, let's find dx/dt:

dx/dt = d/dt(\(e^t\)) = \(e^t\)

Putting it all together, we get:

dz/dt = dz/dy * dy/dx * dx/dt

= [1 / (1 + (3\(e^t\) - 1)²)] * [-e(-2t)] * [\(e^t\)]

= \(-e^{(-t) }\)/ (\(e^{(2t)}\) + 6\(e^t\)+ 1)

Therefore, dz/dt = -e⁻t/ (e²t + 6\(e^t\)+ 1).

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The derivative dz/dt is:

dz/dt = \(e^{(1-t)}\) [et/(3 − e−t − e−t) − e−2t/(3 − e−t)]

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

To find dz/dt, we first need to find ∂z/∂x and ∂z/∂y, and then use the chain rule as follows:

dz/dt = (∂z/∂x) (dx/dt) + (∂z/∂y) (dy/dt)

We have:

x = et

dx/dt = e

y = 3 − e−t

dy/dt = e−t

Using the formula for arctan and the chain rule, we have:

z = tan − 1(y/x)

= tan−1[(3 − e−t)/et]

∂z/∂x = 1/[1 + (y/x)²] (−y/x²)

     = −y/[x² (1 + (y/x)²)]

∂z/∂y = 1/[1 + (y/x)²] (1/x)

       = x/[y (1 + (x/y)²)]

Substituting x and y and simplifying, we get:

∂z/∂x = −(3 − e−t)/(et)² [e−t/(3 − e−t)²]

= −e−2t/(3 − e−t)

∂z/∂y = et/[3 − e−t (1 + e−2t)] = et/(3 − e−t − e−t)

Finally, we can compute dz/dt using the chain rule:

dz/dt = (∂z/∂x) (dx/dt) + (∂z/∂y) (dy/dt)

= −e−2t/(3 − e−t) (e) + et/(3 − e−t − e−t) (e−t)

= \(e^{(1-t)}\) [et/(3 − e−t − e−t) − e−2t/(3 − e−t)]

Therefore, the derivative dz/dt is:

dz/dt = \(e^{(1-t)}\) [et/(3 − e−t − e−t) − e−2t/(3 − e−t)]

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The cοrrect answer tο this questiοn is x = 89°.Tο sοlve this questiοn, we must first calculate the sum οf the interiοr angles οf a clοsed figure, which is always equal tο 360°.

Interiοr angles are angles inside a clοsed shape such as a triangle, quadrilateral, pentagοn, hexagοn οr any οther pοlygοn. These angles are fοrmed by twο lines that intersect inside the shape.

Sum of Interior angle of polygons is given by:

(n − 2) × 180°

Here, n is number of sides = 6

So,

(6 − 2) × 180°

720°

That gives us

149° + 161° + 135° + 59° +127 + x = 720°

631 + x = 720°

x = 720° - 631

x = 89°

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The volume of the composite figure is 3532.5 cubic inches

From the given figure, we have the following dimensions:

The volume of a cylinder is

V = πr^2h

So, the volume of the composite figure is

V = πR^2h - πr^2h

Substitute the known values in the above equation

V = 3.14 * 10^2 * 15 - 3.14 * 5^2 * 15

Evaluate the product

V = 3532.5

Hence, the volume of the composite figure is 3532.5 cubic inches

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James needs to make a cut that is 18 inches long along the median to cut the tiles in half and create two congruent triangles. The correct answer is: D. 18 inches

To cut the tiles along the median, James needs to make a cut that divides the trapezoid into two congruent triangles. The median of a trapezoid is the line segment that connects the midpoints of the non-parallel bases.

In this case, the top base of the trapezoid is 15 inches, and the bottom base is 21 inches. To find the length of the median, we can take the average of the lengths of the top and bottom bases.

Median = (15 + 21) / 2

Median = 36 / 2

Median = 18 inches

The correct answer is: D. 18 inches

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Answer:

1) 10x

2)360-(5x+20)-10x-(7x-8) (I think?)

3) 7x-8

4) 5x+20

Step-by-step explanation:

Answer:

x=15.8degrees

Step-by-step explanation:

10x+5x+7x+20-8=360

22x+12=360

=22x=360- 12

22x=348

x=15.8 degrees

Answer:

negative correlation

Step-by-step explanation:

Asked my teacher

The median decreases from 777.5 to 724.

(a) What happens to the median?

(a) The median is the middle value when the data is arranged in order. With the original salaries, the median is the average of the two middle values:

median = (744 + 811)/2 = 777.5

If the $872 salary changes to $680, the new ordered list of salaries is:

564, 675, 678, 680, 704, 744, 811, 816

The median is now the average of the two middle values, which are 704 and 744:

median = (704 + 744)/2 = 724

Therefore, the median decreases from 777.5 to 724.

(b) The mean is the average of all the salaries:

mean = (564 + 675 + 678 + 704 + 744 + 811 + 816 + 872)/8 = 738.5

If the $872 salary changes to $680, the new sum of salaries is:

564 + 675 + 678 + 704 + 744 + 811 + 816 + 680 = 6032

The new mean is the new sum divided by the number of salaries (which is still 8):

mean = 6032/8 = 754

Therefore, the mean increases from 738.5 to 754.

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Answer:

\( \boxed{c = -17} \)

Step-by-step explanation:

\( = > 3 - 7c - 20c = 7( - 7c - 19) + 14c \\ \\ = > 3 - 27c = ( - 7c \times 7) - (7 \times 19) + 14c \\ \\ = > 3 - 27c = - 49c - 133 + 14c \\ \\ = > 3 - 27c = - 35c - 133 \\ \\ = > 3 - 27c + 35c = - 133 \\ \\ = > 3 + 8c = - 133 \\ \\ = > 8c = - 133 - 3 \\ \\ = > 8c = - 136 \\ \\ = > c = - \frac{136}{8} \\ \\ = > c = - 17\)

Answer:

c = -17

Step-by-step explanation:

→Distribute the 7 to (-7c - 19):

3 - 7c - 20c = -49c - 133 + 14c

→Add like terms (-7c and -20c, -49c and 14c):

3 - 27c = -35c - 133

→Add 35c to both sides:

3 + 8c = -133

→Subtract 3 from both sides:

8c = -136

→Divide both sides by 8:

c = -17

W satisfies both conditions and is closed under addition and scalar multiplication.

In mathematics, a vector space is a fundamental concept in linear algebra.

It is a mathematical structure that consists of a set of objects called vectors, along with operations for vector addition and scalar multiplication.

These operations follow certain axioms, which define the properties of a vector space.

The statement "W is the set of all nonnegative functions in C(−∞, ∞)" does not specify the vector space C(−∞, ∞) correctly.

To determine if W is a subspace of a given vector space, we need to define the vector space correctly.

However, assuming C(−∞, ∞) refers to the set of all continuous functions defined on the interval (−∞, ∞), we can analyze whether W is a subspace of this vector space.

To be a subspace, W must satisfy two conditions:

W must be closed under addition.

W must be closed under scalar multiplication.

Let's evaluate these conditions for W, the set of all nonnegative functions in C(−∞, ∞):

W is closed under addition:

If we take two nonnegative functions from W, their sum will also be nonnegative.

Thus, the sum of any two functions from W will remain in W. Therefore, W is closed under addition.

W is closed under scalar multiplication:

If we multiply a nonnegative function from W by a positive scalar, the result will still be a nonnegative function.

Thus, scalar multiplication by a positive scalar preserves the nonnegativity of the function.

Therefore, W is closed under scalar multiplication.

Based on the above analysis, W satisfies both conditions and is closed under addition and scalar multiplication.

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Answer: c or a

Step-by-step explanation:

The area of Vanessa's patio is represented by the expression 3x⁴ - 4x³ - 13x² + 35x + 10, which is obtained by multiplying the expressions representing the length and width.

To find the area of Vanessa's patio, we need to multiply the expressions representing the length and width.

Length = 3x² + 5x + 10

Width = x² - 3x - 1

Area = Length x Width

Area = (3x² + 5x + 10)(x² - 3x - 1)

To multiply these expressions, we can use the distributive property and then simplify

Area = 3x⁴ - 4x³ - 13x² + 35x + 10

Therefore, the expression that represents the area of Vanessa's patio is 3x⁴ - 4x³ - 13x² + 35x + 10.

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In 30 minutes, the woman will travel 12.5 miles.

This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.

The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).

In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.

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Given:

There are given the equation:

Explanation:

According to the question:

We need to find the solution to the given quadratic.

Then,

To find the solution, we will use the quadratic equation formula.

Then,

From the equation:

Where,

Then,

Put all the value into the formula:

Then,

Then,

Therefore, the solution of the given quadratic equation:

Final answer:

Hence, the correct options are B and E.

Answer:

the nominator could be any number here

Step-by-step explanation:

what do you need ? the equation itself is true, if you put the same number in both places above 21.

any number is possible there, it will not change the equation.

so, again, I am not sure, what you need here.

let's write it with a variable to make my statements clearer :

9 + 1 x/21 = 10 x/21

that is true, because we can combine the whole numbers first giving us 9 + 1 = 10.

and then we add the fraction again (x/21).

again, you can put any number instead of x, and it will always be true.

example

9 + 1 4/21 = 10 4/21

The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Answer:

$342.23

Step-by-step explanation:

35/100 x $390 = $136.50

Price of couch after 35% discount

= $390 - $136.50

= $253.50

35/100 x $253.50 = $88.725

Price of couch after the 35% increase

= $253.50 + $88.725

= $342.225

= $342.23 (round off to nearest cents)

The y-component of the force vector is 84.45 N.

The y-component of the force vector can be found by multiplying the magnitude of the force by the sine of the angle between the force vector and the y-axis.

Since the angle given is with respect to the positive x-axis, we need to first determine the angle between the force vector and the y-axis, which is 90 - 21.21 = 68.79 degrees.

Then, we can calculate the y-component of the force vector using:

y-component = F * sin(68.79 degrees)

y-component = 91.52 N * sin(68.79 degrees)

y-component ≈ 84.45 N

Note that the y-component of the force is positive because the angle between the force vector and the y-axis is in the first quadrant.

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The value of \(y\) after \(x\) units of time can be calculated using the equation \(y = 17x - 76\). So after 5 units of time, \(y\) would be 9.

To model the quantity \(y\) after \(x\) units of time, we can use the equation \(y = mx + b\), where \(m\) represents the rate of change and \(b\) represents the initial value.

In this scenario, the quantity \(y\) starts at -76 and increases at a rate of 17 per minute. Therefore, the equation becomes \(y = 17x - 76\).

To calculate the value of \(y\) after a certain amount of time \(x\), we can use the equation \(y = 17x - 76\).

For example, if we want to find the value of \(y\) after 5 units of time (\(x = 5\)), we substitute the value into the equation:

\(y = 17(5) - 76\)

\(y = 85 - 76\)

\(y = 9\)

So, after 5 units of time, \(y\) would be 9.

Similarly, you can calculate the value of \(y\) for any other given value of \(x\) by substituting it into the equation and performing the necessary calculations.

It's important to note that the equation assumes a linear relationship between \(x\) (time) and \(y\) (quantity), with a constant rate of change of 17 per unit of time, and an initial value of -76.

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The algebraic expression that represents the total cost of buying one carton of strawberry ice cream and one carton of chocolate ice cream is 4.00 + 4.00 = 8.00.

Let's break down the given information step by step. The grocery store is offering a sale on ice cream, and each carton of any flavor costs 4.00. Cecy wants to buy one carton of strawberry ice cream and one carton of chocolate ice cream.

To represent the total cost algebraically, we need to add the cost of the strawberry ice cream to the cost of the chocolate ice cream. Since each carton costs 4.00, we can write the expression as 4.00 + 4.00.

By adding the two terms, we get 8.00, which represents the total cost of buying one carton of strawberry ice cream and one carton of chocolate ice cream.

Therefore, the algebraic expression 4.00 + 4.00 = 8.00 represents the total cost of buying the ice cream.

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(a) Divergence at the indicated point is positive. (b) Divergence at the indicated point is zero. (c) Divergence at the indicated point is negative.

To find the divergence of each vector field at the indicated point, we will first calculate the divergence of each field and then evaluate it at the given point.
(a) The vector field is given as F = xi + yj.
The divergence of a 2D vector field F = P(x,y)i + Q(x,y)j is calculated as:
div(F) = (∂P/∂x) + (∂Q/∂y)
For this vector field, P(x,y) = x and Q(x,y) = y. So:
div(F) = (∂x/∂x) + (∂y/∂y) = 1 + 1 = 2
The divergence at the indicated point is positive.
(b) The vector field is given as F = yi.
For this vector field, P(x,y) = y and Q(x,y) = 0. So:
div(F) = (∂y/∂x) + (∂0/∂y) = 0 + 0 = 0
The divergence at the indicated point is zero.
(c) The vector field is given as F = yi - yj.
For this vector field, P(x,y) = y and Q(x,y) = -y. So:
div(F) = (∂y/∂x) + (∂(-y)/∂y) = 0 - 1 = -1
The divergence at the indicated point is negative.

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Answer:

y=3x+2

Step-by-step explanation:

The area of the trepezium will be 80 sq. unit.

What precisely is a trepezium?

Trapezoids are made up of two parallel and two oblique sides. A Trapezium is another name for it. A trapezoid is a closed four-sided shape or figure with a space-filling perimeter. It is a 2D figurine rather than a 3D figure. A trapezoid's bases are the sides that are parallel to one another. Legs are non-parallel sides, often known as lateral sides. The space between its parallel sides determines its height.

A trepezium's area is equal to 1/2*(a+b)*h.

where h is the height or distance between two parallel lines

The lines a and b are parallel.

Now,

Given A rectangle with a length of 17 and a height of 4 has two right triangles on each side of it with long leg lengths of 5

then parallel sides of trepezium will be 17 and 17+3+3=23

because for the triangle base will be =√5²-4²

=3

and height of trepezium=4 unit

So, area of trepezium will be=1/2(23+17)*4

=40*2

=80 sq. unit

hence,

           The area of the trepezium will be 80 sq. unit.

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Answer:

5 and 6 is slope of two/three

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Yes, I can find the slope of a line and type the correct code. The SLOPE function will return the slope of the linear regression line that best fits the data.

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula for finding the slope of a line is (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.

The slope is a measure of how steep the line is. It can be positive, negative, zero, or undefined. The code for finding the slope of a line in ALL CAPS with no spaces is SLOPE.

To use this function in Excel, you need to provide the range of x-values and the range of y-values.

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so whats the question to me its feels like your tell us