Juice wa packed in individual juice boxe of 1/2-cup each. A carton of 64 juice boxe wa hrink-wrapped and hipped to a tore. How many gallon of juice were in the hrink-wrapped carton?

The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions is

4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions shown below

Explanation in detail:

Two expressions are shown here.

Expression 1 : 2x/x-1

Expression II for 5x/2x+4.

The product of expressions I and II must be calculated.

(2x / x-1 ) ÷ (5x / 2x+4)

applying the upcoming regulation

a ÷ b = a× 1/b

(2x/x-1)×( 2x+4 / 5x)

(2x) (2x+4) / (x-1)(5x) (5x)

(2) (2) (x+2) / (x-1)(5) (5)

The solution to the previous question is 4(x+2) / 5(x-1).

The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

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The quadratic polynomial whose sum and the product of zeroes is x^2 - √2x + 1.

A degree two polynomial is a quadratic polynomial. The formula for a univariate quadratic polynomial is f(x)=a 2x2+a 1x+a 0. A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution known as the quadratic formula.

A quadratic polynomial's general formula is represented as f(x)=ax2 + bx + ca. A parabola is the name of the quadratic polynomial's curve. A quadratic polynomial is one that has the formula ax2 + bx + c, where a, b, and c are all real values and an is 0.

Only a few quadratic polynomials are amenable to the factorization technique. The quadratic polynomial formula, however, can be used for any quadratic problem.

In addition, the discriminant's value can be used to examine the characteristics of a quadratic polynomial's roots.

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The area will be 1/4 of the original.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

The area of all shapes is determined by their dimensions and attributes. Different shapes have various areas. The perimeter of a shape is defined as the total distance around the shape.

Given that,

[scale factor]=1/2

[dilated area of circle]=[original area of circle]*[scale factor]²

so

[dilated area of circle]=[original area of circle]*[1/2]²

[dilated area of circle]=[original area of circle]*[1/4]

Thus, The area will be 1/4 of the original.

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Answer: 76.92%

Step-by-step explanation:

To find the percent decrease is simple. First let's find the difference: 65 - 15 which gives you 50. 50/65 * 100 = 76.92%.  Have a good day ;)

After solving, we check that [tex]x^2[/tex] - 1 cannot be the quotient of p(x).

In the given question, we have to check whether the quotient is [tex]x^2[/tex] - 1.

The given polynomial is [tex]x^6 + 2x^3[/tex] + x - 1 is divided by a polynomial in x of degree 5.

Given a polynomial p(x) and a non-zero polynomial g(x), the division algorithm asserts that there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

5th degree polynomial because the power of the dividend should equal the degree of the product of the quotient and the divisor.

Degree 1 will result from the division of a degree of polynomial 6 by a degree of polynomials 5 and 6.

From the given question,

P(x) = [tex]x^6 + 2x^3[/tex] + x - 1

g(x) = x in degree of 5

q(x) = x² - 1

So,

[tex]x^6 + 2x^3[/tex] + x - 1 = (x in degree of 5)([tex]x^2[/tex] - 1) + r(x)

[tex]x^6 + 2x^3[/tex] + x - 1 = x in degree of 7

Hence, [tex]x^2[/tex] - 1 cannot be the quotient of p(x).

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The complete question is:

Can [tex]x^2[/tex] - 1 be the quotient on division of [tex]x^6 + 2x^3[/tex] + x - 1 by a polynomial in x of degree 5?

There are several methods for finding the solution to a system of equations, which include:

1. Graphing: This method involves plotting the equations on a coordinate plane and finding the point(s) of intersection. This method is useful when the system has a small number of variables and the equations are in the form of y = mx + b.

2. Substitution: This method involves solving one of the equations for one variable and then substituting that expression into the other equation. This method is useful when one equation is easier to solve than the other or when one equation is a simpler form than the other.

3. Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. This method is useful when the variables are in similar forms and the coefficients are easy to add or subtract.

4. Matrix method: This method involves solving the system of equations in matrix form using matrix algebra techniques such as Gaussian elimination, Gauss-Jordan elimination and Cramer's rule. This method is useful when the system of equations have a large number of variables and when you want to solve system of equations in a more efficient and less time-consuming way.

5. Numerical methods: This method involves using numerical techniques such as Newton-Raphson method, Iterative methods to approximate the solution of a system of equations.

It is important to note that in some cases, a system may have no solution or infinitely many solutions. A system has no solution when the equations are inconsistent, meaning they cannot be true at the same time. A system has infinitely many solutions when the equations are dependent, meaning one equation can be derived from the other equation

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The steps to evaluate an exponential expression include:

First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.

Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.

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The angle e between vectors u and v to the nearest tenth of a degree is

≈ 3.14°.

An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.

When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]

u·v = (5)(4) + (2)(-3)

       = 20 - 6

        = 14

llull = √[(5)2 + (2)2]

= √29    

llvll = √[(4)2+(-3)2]

= √25

So, cosθ = 14 / [√725]

            = 0.51

θ = cosθ-(0.51) ≈ 3.14°

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The scenario is best represented by a discrete or continuous domain is

a. discrete

b. continuous

c. discrete

d. continuous

e. discrete

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A horizontal straight line at the -7 point.

A straight line can be formed between two points also but both ends extend to infinity.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.

A straight line does not have any curve in it. It can be horizontal, vertical, or slanted. If we draw an angle between any two points on a straight line, we will always get a 180-degree.

With no other values other than -7, the only value possible must be -7. Thus, we get a straight line.

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Answer: 1/8

Step-by-step explanation:

16x - 4y = 12

4x - y = 3

4x = 3+y

x= 3+y/4

for y = 1

x= 3+1/4 = 1

y = 2

x=3+2/4 = 5/4 = 1.25

y = 3

x = 3+3/4 = 6/4 = 1.5

Answer:

15 nickels and 8 dimes

Step-by-step explanation:

Let N = number of nickels and D = number of dimes

N - D = 7   (the number of nickels exceeds the number of dimes by 7.)

or

N = D + 7

Total value of N nickels = 5N

Total value of D nickels = 10D

Combined total value => 5N + 10D = 155

Substitute for N in terms of D
==> 5(D + 7) + 10D = 155

5D + 35 + 10D = 155

15D + 35 = 155

15D = 155 - 35

15D = 120

D = 120/15

D = 8

N = D + 7 = 8 + 7 = 15

15 nickels and 8 dimes

Lance and Alberto cycled along the same 75 km route. Speed of Alberto is 30 km/ hr

Since, Lance takes 3 hours to complete 75km, his speed will be

v= [tex]\frac{75}{3}[/tex]

v= 25 km/hr

The amount of time taken by Lance to complete 10 km is

t= 10/25

t =0.4 hr

t= 0,4×60 min

t=24 min.

Since Alberto started 4 min late and  time taken by Alberto to complete 10 km is

t= 24-4

t=20 min.

Hence, speed of Alberto is v=10/0.33

v=30 km/hr.

A measure of how quickly something is moving is speed. The distance an object travels in a single time unit is its speed. The speed formula is: Distance times speed. Meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph) are the most common units of speed.

Speed is calculated by dividing distance by time. You must be familiar with the distance and time units in order to determine the units of speed. The units will be measured in meters per second (m/s) because distance is measured in meters (m) and time is measured in seconds (s).

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Based on the price of the hats and the new price after the discount, the percent discount is 15%.

What is the Percentage discount?

Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and its par value.

Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

To find the discount, use the formula:

= (Difference between price before discount and price after discount) / Initial price of hat x 100%

According to the given values,

Solving gives:

= (34.99 - 29.99) / 34.99 x 100%

= 15%

In conclusion, the approximate percent discount is 15%.

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Answer:

p is the dependant variable and w is the dependent variable

Step-by-step explanation:

The number of plots is dependent because the number of plots doesnt change. The amount of wheat depends on the amount of plots you have.

Answer: Law of Sines: When we divide side a by the sine of angle A

it is equal to side b divided by the sine of angle B. It's also equal to side c divided by the sine of angle C.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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The vertex of the equation y = x² + 2x -3 is (-1, -4).

The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

Here we have the expression y = x² + 2x -3

As we all know that the given equation of parabola is written as,

=> y = ax² + bx + c

As we all know that the vertex of the parabola is given by (h, k).

Here we have calculated the value of the x coordinate of vertex as ,

=> h = -b/2a

And the value of y coordinate of vertex k by using the formula,

=> k  = y(h)

Through the given equation we have identified the value of a = 1, b = 2 and c = -3

Then the value of x coordinate is calculated as,

=> h = -2/(2 × 1)

Therefore, the value of h is -1

Then the value of y coordinate is calculated as,

=> k = y (-1)

Here we have to substitute -1 in the equation, then we get

=> k = (-1)2 + 2(-1) - 3

=> k = 1 - 5 = -4

Hence the coordinate of the vertex is (-1, -4).

Complete Question:

Where is the vertex of the parabola of the equation y = x² + 2x -3?

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The measure of angle B is 50 degrees and angle C is 80 degrees.

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.

In the given triangle, we can use the concept of triangle angle sum to find the unknown measures.

We know that the sum of the angles in a triangle is always 180 degrees.

Therefore, if we know two angles in a triangle, we can find the third angle by subtracting the sum of those angles from 180.

We are given that angle A is 50 degrees. We are also given that angles B and C are unknown. Therefore,

we can use the following equation to find the measure of angles B and C:

A + B + C = 180

50 + B + C = 180

B + C = 180 - 50

B + C = 130

So the sum of angles B and C is 130 degrees. Therefore, we can't find individual measures of angles B and C.

Alternatively, we can use the property of the angle pair which states that if two parallel lines are intersected by a transversal, the alternate interior angles are congruent.

If we know that angle A and angle B are congruent, we can find the measure of angle B as 50 degrees. As a result, angle C will be 180 - 50 - B = 130-50 = 80 degrees.

Hence, the measure of angle B is 50 degrees and angle C is 80 degrees.

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The solution of the system by using elementary row operations on the equations or on the augmented matrix following systemic elimination procedure is x1 = −8 and x2 = 3.

The complexity of the algebra required to solve a linear system rises as the number of equations and unknowns grows. By streamlining the nomenclature and standardizing processes, the necessary computations may be made easier to handle.

The procedures listed below should be followed in order to solve a system of linear equations using the row operations:

1. As a matrix equation, write the equations as AX = B.

2. Create an augmented matrix by converting the matrix equation to the following form: [A | B] (the word "augmented" refers to the vertical line we create to remind us where the equals sign belongs).

3. Reduce the augmented matrix using row operations to arrive at the answer.

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The solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.

In the given question, we have to solve 3x + 4y = -12 for y.

The given equation is 3x + 4y = -12.

To solve this equation for y, we have to isolate the y.

Now solving the given equation.

3x + 4y = -12

Subtract 3x on both side, we get

4y = -12 - 3x

Divide by 4 on both side, we get

y = [tex]\frac{1}{4}[/tex](-12 - 3x)

Now simplifying the expression.

y = -12/4 - 3/4 x

y = -3 - 3/4 x

Hence, the solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.

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The complete question is:

How do you solve 3x + 4y = -12 for y?

Answer:3 symmetrical lines

Step-by-step explanation: just look in the middle and draw a line

The two triangles in this problem are not similar, as they do not have congruent angle measures.

Similar triangles are triangle that share these following two features:

The angle measures for each triangle are given as follows:

As the triangles have different angle measures, they are not similar.

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The vehicle with best mileage per gallon is Minivan vehicle .The maximum milage value is 19 miles/gallon.

We have, a table as present in above figure. The table contains 4-column and 3 rows. Column 1 is labeled different Vehicles, Column 2 is labeled Miles Traveled and Column 3 is labeled Gasoline Used (gallon). We have determine the vehicle gets the best mileage per gallon. Milage of a vehicle means how many distance vehicle going to run per quantity of fuel. In this cas milage of vehicle is miles going to run per gallons of fuel.

The formula to calculate gas mileage is

Milage = Miles Traveled/ Gasoline used (gal).

Now, we consider each row one by one.

Milage for Sedan = 630/35 = 18 miles/gallon

Milage for Minivan = 798/42 = 19 miles/gallon

Milage for Truck = 864/54 = 16 miles/gallon

Hence, the required vehicle is Minivan with milage of 19 miles/gallon.

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Complete question:

Which vehicle gets the best mileage per gallon? The above table complete the question. A 4-column table with 3 rows. Column 1 is labeled Vehicle with entries Sedan, Minivan, Truck. Column 2 is labeled Miles Traveled with entries 630, 798, 864. Column 3 is labeled Gasoline Used (gallon) with entries 35, 42, 54. Column 4 is labeled Unit Rate with entries 18, 19, 16.

For math equation, To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them.

Determine the set of solutions to the following system of equations using the elimination method, if x and y are variables in the set of real numbers.

Completion:

1. x + y = 1 and x + 5y = 5

To eliminate the y variable, remember that the coefficients of y must be the same, so the equation x + y = 1 times 5 and the equation x + 5y = 5 times 1, then:

x + y = 1     │× 5 => 5x + 5y = 5

x + 5y = 5   │× 1 => x + 5y = 5

5x + 5y = 5

x + 5y = 5

--------------- –

4x + 0 = 0

x = 0

Same as step I, there is no need to equate the coefficients to eliminate variable x because the coefficients are the same, then:

x + y = 1

x + 5y = 5

--------------- –

0 + –4y = –4

y = 1

So, the solution set is {(0, 1)}.

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Five rays from common endpoints or vertex form 10 distinct angles.

Angles are constructed when two lines intersect at a point. The measurement of the 'opening' between these two rays is called an 'angle'. The symbol represents it ∠. Angles are usually measured in degrees and radians, which is a measurement of circularity or rotation.

In geometry, an angle is constructed when two rays are joined at their endpoints. These rays are named the sides or arms of the angle.

The arms and the vertex are two primary parts of an angle.

The two rays which converge at a common point to create the angle are called the arms of the angle.

Vertex is a common endpoint that is shared by the two sides.

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Answer:

AB + CD → AD + CB

Explanation:

The double-replacement reaction generally takes the form of AB + CD → AD + CB where A and C are positively-charged cations, while B and D are negatively-charged anions.