After a discount, the marked price of an article is 48$. Calculate the original price if a 20% discount was given

The algebraic expression of the statement is 5 + 3y ≤ z + 14

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

5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14

When represented as expression, we have

5 + 3y is less than or equal to z + 14

As an inequality, we have

5 + 3y ≤ z + 14

hence, the expresion si 5 + 3y ≤ z + 14

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Quadrilateral MNOP is similar to quadrilateral QRST. The measure of side RS is approximately 39.2 units.

If two quadrilaterals are similar, their corresponding sides are in proportion. Therefore, we can set up a proportion between the corresponding sides of quadrilaterals MNOP and QRST as follows:

MN / QR = NO / ST = OP / RS

We are given the lengths of MN, NO, and OP, but we need to find the length of RS. We can solve for RS by rearranging the proportion as follows:

OP / RS = MN / QR

RS = OP / (MN / QR)

We can substitute the given values to get:

RS = 58 / (19 / 13)

Simplifying this expression gives:

RS = 58 * (13 / 19) = 39.241 ≈ 39.2

Therefore, the measure of side RS is approximately 39.2 units.

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____The given question is incomplete, the complete question is given below:

Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale. QT =58, PM= 19 ON=13.

Answer:

Step-by-step explanation:

3*6=18

Answer:

6x-5 ≤ 29

Step-by-step explanation:

Let translate each part of the sentence into an equation or expression.

1.  "five subtracted from the product of 6 and a number"

2.  "is less than or equal to 29"

3.  Assemble the two expression into an equation

    Combine parts 1 and 2 into an equation.

       6x-5 ≤ 29

=============

Extra

6x-5 ≤ 29 can be simplified:

6x ≤ 29+5

6x ≤ 36

x ≤ 6

The exponent is 81.m⁴.n²⁰

Here we have to determine the sign for exponential or radical expression

[tex](-3mn^5)^4[/tex]

Now using the exponent power rule (aˣ)ⁿ = aˣⁿ =. We get

= 81.m⁴.n²⁰

Therefore the exponent as a product of power is 81.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the phrase "2 to the 3rd" (written as 23) means:

2 x 2 x 2 = 8.

23 and 2 x 3 = 6 are not equivalent.

Keep in mind that any number is itself when raised to the power of 1.

The outcome is always a fraction when the exponent is negative. A numerator and a denominator make up fractions. The numerator in this case is always 1. Assuming the negative exponent is positive, raise the number to that power to determine the denominator

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The solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

What is a differential equation?

Any equation involving the derivatives of one dependent variable with respect to another independent variable is referred to as a differential equation. Differential equations are widely used in mathematics, but they also play an important role in the sciences of medicine, chemistry, physics, and engineering.

To solve this differential equation, we need to find a function y(x) that satisfies the equation. Here's how to do it:

First, we can divide both sides of the equation by D³ + 1 to get:

y = (eˣ+1)² / (D³+1)

Next, we can take the derivative of both sides with respect to x:

dy/dx = d/dx[(eˣ+1)² / (D³+1)]

Using the quotient rule of differentiation, we get:

dy/dx = [(D³+1)(2eˣ)(eˣ+1) - (eˣ+1)²(3D²)] / (D³+1)²

Simplifying the numerator, we get:

[tex]dy/dx = [2e^{(2x)} + 2e^x - 3D^{2}(e^x+1)^2] / (D^3+1)^2[/tex]

Therefore, the solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

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The total number of miles that Parker would have to run is given as follows:

88.41 miles.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

As the number of miles increases by 5% each week, the common ratio is obtained as follows:

100% + 5% = 105% = 1.05.

Hence the number of miles each week is given as follows:

Then the total number of miles is given as follows:

16 + 16.8 + 17.64 + 18.52 + 19.45 = 88.41 miles.

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Answer:

Step-by-step explanation:

I cant see

On converting the length , 151 centimeter is equivalent to 4.954 feet .

The Units of measuring the length are used to measure the distance between two points of an object. There are several units of measuring length , which are : meter , centimeter , kilometer , feet .

We have to convert 151 cm to feet,

So , we use the conversion factor of 0.03281 feet per centimeter  , which means that there are approximately 0.03281 feet in 1 centimeter.

So , to convert 151 cm to feet, we multiply the number of centimeters by this conversion factor ;

Using this method, we get ;

⇒ 151 cm × 0.03281 feet/cm = 4.954 feet ;

Therefore, 151 cm is equal to approximately 4.954 feet.

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The number of $56 dollar tickets to center section was 200 and the number of tickets costing $38 to the left and right sections were 200.

Let us consider the number of tickets to the center section be x and right and left sections be y.

Here the total number of tickets sold are 540.

So,  x+ y = 540  ---------> i

The cost of tickets cost $56 will be 56x

The cost of tickets cost $38 will be 38y.

The total cost was given as $24120

So, 56x+ 38y = 24120 -----------> ii

Multiplying equation i with 56,

56x + 56y = 30240  ------------> iii

Subtracting equation ii from equation iii

   56x+ 56y = 30240

-   56x + 38y = 24120

So 18y = 6120

      y = 6120/18 = 340

Since x+ y = 540

          x+ 340 = 540

          x = 540- 340 = 200

So the number of $56 ticket sold is 200 and the number of $38 ticket sold is 340.

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The Coordinates after dilation of 1.5 about the origin is

F'(1.5, -1.5)

G'(0, 3)

H'(1.5, 3)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

Given:

We have the Coordinates F(1, -1), G(0, 2), H(1, 2).

As, the Dilation Rule for point (x, y) about origin with scale factor h

h(x, y)------>(hx, hy)

Applying the Dilation Rule we get

F(1, -1)-----> 1.5 F'(1, -1)-----> F'(1.5, -1.5)

G(0, 2)-----> 1.5 G'(0, 2)-----> G'(0, 3)

H(1, 2) -----> 1.5 H'(1, 2)-----> H'(1.5, 3)

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The volume of the solid generated when r is revolved about the​ y-axis is 3.2π.

Volume of Solid:

The volume of a solid is a measure of the space occupied by an object. This article explains how to calculate the volume of solids and the volume of regular and irregular solids.

According to the Question:

We know that:

A ( y ) = π × (f₁ (y)² - f₂ (y)²)

where,

f₁ (y) is the function further away from y axis

f₂ (y) is the function closer to y axis

f₁ (y) = 2

f₂ (y) = 2y²

A ( y ) = π × [2² - (2y)²]

A (y) = π × (4 - 4y²)

A (y) = 4π (1 - y²)

Now,

Computing V (y)

[tex]V =\int\limits^1_0 {A(y)} \, dy[/tex]

[tex]V = 4\pi \int\limits^1_0 {(1-y^2)} \, dx[/tex]

V = 4π (1 - 0.2)

V = 3.2π

Therefore, The volume of the solid generated when r is revolved about the​ y-axis is 3.2π.

Complete Question:

Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the​ y-axis. y= square root of (x/2) , y=0 , x=2

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Answer:

Step-by-step explanation:

w is the independent

b is the dependent

Think of it this way: the number of birdhouses depends on the amount of wood available.

The equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3

The cost of using a computer at the internet cafe can be represented by a linear equation, where C is the total cost and t is the number of minutes used. The equation can be written as C = 0.80t + 3, where 0.80 is the cost per minute and 3 is the initial charge.

To make a table of values, we can plug in different values of t into the equation and solve for C
 
   Number of Minutes (t)  Total Cost to Use Computer (C)
            0                            C = 0.80(0) + 3 = 3
            1                             C = 0.80(1) + 3 = 3.80
           2                             C = 0.80(2) + 3 = 4.60
           3                             C = 0.80(3) + 3 = 5.40
 
So the equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3.

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The  single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.

To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.

First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:

ln 2 - ln 4 = ln(2/4) = ln(1/2)

Now, we can rewrite the expression as:

4 + ln(1/2)

We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:

4 + ln(2^(-1))

Simplifying further:

4 - ln(2)

Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:

ln(2^2 / 2) = ln(2)

So, the answer is (a) ln 2.

In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.

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The inequality that represents the number of push-up, is p ≥ 33. The minimum number of push-ups Dean must do on each remaining day to reach his goal is 33.

A mathematical statement describing how one linear expression is either less than or greater than another is known as a linear inequality. A real number that, when used as the variable in a linear inequality, results in a true assertion is the solution. There are either an endless number of solutions to linear inequalities or none at all. If there are an unlimited number of solutions, plot the solution set on a number line or use interval notation to express the solution.

Given that, Dean has done 230 push ups.

The remaining number of push ups to reach his goal is:

R = 900 - 230

R = 670

The number of pushups he needs to do in the next 20 days to reach his goal is:

p = 670/20

p ≥ 33

Hence, the inequality that represents the number of push-up, Dean must do on each remaining day to reach his goal is p ≥ 33.

The minimum number of push-ups Dean must do on each remaining day to reach his goal is 33.

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The statement that must be true is option (f) "The equation Ax = b has a solution for all b precisely when it has more columns than rows".

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

This is because if the matrix has more columns than rows, then the system of equations cannot be underdetermined, meaning that there is a unique solution for the equation.

On the other hand, if the matrix has more rows than columns, then it is possible that the equation Ax = b could have no solutions, which would mean that it is an overdetermined system.

Furthermore, if the matrix is a square matrix, then it will have the same number of rows and columns, and it is possible that the equation Ax = b could have either one solution or no solutions.

Therefore, the statement "The equation Ax = b has a solution for all b precisely when it has more columns than rows" is the only one out of the six given that must be true

Hence the option (f) is correct.

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The value where the histogram balances when supported at that point is called the mode of the distribution.

The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.

For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.

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The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.

To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:

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

This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1)d

Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:

a₇ = (-3x+5) + (7 - 1)(5x - 2)

Simplifying the equation:

a₇ = -3x + 5 + 30x - 12

a₇ = 27x - 7

Therefore, the 7th term of the arithmetic sequence is 27x - 7.

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Answer:

Elimination , $1.79

Step-by-step explanation:

You were correct with elimination! Good job , now to find the cost of fries we have to put elimination in practice. Elimination is subtracting one equation from the other to get the equation of one variable.

4x + 5y = 24.11

-4x + 3y = 20.53

        2y = 3.58

     2y/2 = 3.58/2

           y = 1.79

The required solutions to the equation are x = 2 or x = -14.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Starting with the equation:

(x + 6)² = 64

Taking the square root of both sides, we get:

x + 6 = ±8

Solving for x, we have two cases:

Case 1:
x + 6 = 8

x = 8 - 6

x = 2

Case 2:
x + 6 = -8

x = -8 - 6

x = -14

Therefore, the solutions to the equation are x = 2 or x = -14.

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Answer:

Anything.

Step-by-step explanation:

The reason why I say " anything " is because the fraction, [tex]\frac{1}{1}[/tex] is bascially representing the number 1, nothing else so you can put whatever you want, tens, hundreds, thousands, millions, and so on.

So whatever number you want to put it will always equal, [tex]\frac{1}{1}[/tex], But just remember to always put the number that you choose on top or the numerator such as the following:

[tex]\frac{4}{1}[/tex].

Thus, you answer is, anything.

Transformations on a graph refer to changes made to the graph that affect its appearance or position without changing its underlying structure or properties.

Some common transformations on a graph include:

Translation: This involves shifting the entire graph horizontally or vertically without changing its size or shape. For example, if a point on the graph is originally located at (2,3), a translation by (4,-1) would move it to (6,2).

Scaling: This involves enlarging or shrinking the entire graph uniformly in all directions. For example, a scaling factor of 2 would double the distance between all points on the graph, while a scaling factor of 0.5 would halve it.

Reflection: This involves flipping the graph across an axis, such as the x-axis or y-axis. Reflections can also be performed across other lines, such as y = x or y = -x.

An overview on transformation was given as the information is incomplete.

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Answer:

c

Step-by-step explanation:

DO THE MATH!!!!!!!PLEASE

Answer: (x,y)=(1,-10)

Step-by-step explanation:

y=-7x-3

5x+4y=-35

substitute the value of y

5x+4(-7x-3)=-35

solve the equation

x=1

substitute the value of x

y=-7 x 1-3

solve the equation

y=-10

A possible solution is

(x,y)=(1,-10)

Check the solution

-10=-7 x 1-3

5 x 1+4 x (-10)=-35

simplify

-10=-10

-35=-35

The ordered pair is a solution

(x,y)=(1,-10)

On converting the weight of 140 lbs to Kilogram , we get that 140 lbs is equivalent to 63.49 Kg .

The Conversion Factors is used to convert the weight between pounds and kilograms. that means :  To convert 1 pound to kilograms , We multiply the number of pounds by 0.4535  .

In this case , we have to convert 140 pounds to kilograms ;

So , we multiply the given weight in pounds with 0.4535 .

On multiplying ,

We get ;

⇒ 140 pounds = 140 × 0.4535 Kg ;

⇒ 140 pounds = 63.49 Kg .

Therefore , 140 lbs is approximately equal to 63.49 Kg .

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There cannot be a point P on altitude BD that is equidistant from A and C, as this would mean that the two smaller triangles are congruent. This is because the altitude BD divides the triangle into two smaller triangles, ABD and CBD. If AB is unequal to BC, then these two smaller triangles cannot be congruent.

To prove this, let's assume that there is a point P on altitude BD that is equidistant from A and C. This would mean that AP = CP. However, since AB is unequal to BC, we know that AD is not equal to DC. Therefore, the triangles ABD and CBD are not congruent, and there cannot be a point P on altitude BD that is equidistant from A and C.

In conclusion, if AB is unequal to BC, then there does not exist a point P on altitude BD that is equidistant from A and C. This is because the altitude BD divides the triangle into two smaller triangles that cannot be congruent if AB is unequal to BC.

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To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.

Temperatures, across the worlequal td, are measured either in Fahrenheit(the US temperature scale) or Celsius(the metric scale), two of the most popular and widely used scales.Temperature Conversion – Degrees Celsius into Degrees Fahrenheit.

Celsius to Fahrenheit conversion formula is all about converting the temperature denoting in Celsius to Fahrenheit. As mentioned earlier, the temperature of boiling (hot) water in Celsius is 0 degrees and in Fahrenheit is 21 degrees, the formula to convert C to F is

F = C x (9/5) + 32To convert 39.5 degrees Celsius to Fahrenheit, you can use the formula:

°F = (°C × 9/5) + 32

Substituting 39.5 for °C, we get:

°F = (39.5 × 9/5) + 32

°F = (71.1) + 32

°F = 103.1

Therefore, 39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.

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Step-by-step explanation:

Principal (P)=$7869

Rate (R)= 13%

Time (T)= 5 years

Compound Interest (CI)=?

We know that,

CI = P { (1+R/100)^T -1}

= $7869 {(1+13/100)^5 -1}

= $7869 {(113/100)^5 -1}

= $7869 {(1.13)^5 -1}

= $7869 {1.84-1}

= $7869 × 0.84

= $6609.96

Compound Amount= CI+p

= $6609.96+7869

= $14478.96

Therefore, he will have $14478.96 after 5 years.