v. Use elementary row operation to transfer the augmented matrix to echelon form. Solve by back substitution also explain the type of solution. 3x + 2x, +4x4 – x4 =13 -2x + x + 5 x =5

If the discount net price is $7,800 and Net Price Factor, trade discount are to be calculated, then trade discount is equal to $1,170 and Net Price Factor is equal to 0.9216.

The formula used for Trade Discount is given as product of List Price and Trade Discount Rate. The value of list price is given as $7,800.00 and that of Trade Discount Rate is 0.15. Putting the given values in the formula, we get the following result:

Trade Discount = $7,800.00 x 0.15 = $1,170.00

Cash Discount 2 = 4% of (Net Price - Cash Discount 1)

∵ Net Price Factor = (100% - 4%) x (100% - 4%) / 100%

⇒ Net Price Factor = 0.9216

Single Equivalent Discount = (1 - Net Price Factor) x 100%

∴ Single Equivalent Discount = (1 - .9216) x 100%

Single Equivalent Discount = 7.84%.

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Refer to complete question below:

Complete the following table by finding the net price factor, single equivalent discount, trade discount (in dollars), and net price in dollars). Round the net price factor and single equivalent discount to five decimal places, and the trade discount and net price to the nearest cent, when necessary. List Price Trade Discount Rate Net Price Factor Single Equivalent Discount Trade Discount Net Price $7,800.00 15/4/4

The inverse of AB is B−1A−1

1. True. Every square matrix with ones down the main diagonal has an inverse, since the diagonal elements are all non-zero.
2. False. Generally, the determinant of B does not necessarily equal the determinant of A, even when B is a product of A and other matrices.
3. True. If a matrix A satisfies the equation A2=A, then its determinant is 0, since A=A2 implies detA=det(A2)=detA×detA=detA2=0.
4. True. If A and B are both invertible n×n matrices, then AB is also invertible, and the inverse of AB is B−1A−1.

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The value of x is 23°

A line is a straight, one-dimensional figure that extends infinitely in both directions. It is often represented graphically as a straight line on a coordinate plane, with an equation that describes its position.

A line can be defined by any two points on it, and every point on the line can be expressed as a linear combination of those two points.

Line j and k are parallel and another line crossing it means transversal line, then the corresponding angles are equal which is,

(5x+9)° = (4x+32)°

5x-4x = 32-9

x = 23°

Therefore, the value of x is 23°

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Answer:

whats the equation

Step-by-step explanation:

Answer:

To simplify the expression, we need to distribute the negative sign to all the terms inside the parentheses, and then combine like terms.

Starting with:

(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)

Distribute the negative sign inside the parentheses:

5x^4 - 4x^3 - 2x^2 + x - 19 - x^4 - 5x^3 - 8x^2 - x - 5

Now we can combine like terms:

(5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5)

Simplifying further:

4x^4 - 9x^3 - 10x^2 - 24

Therefore, the simplified expression is:

4x^4 - 9x^3 - 10x^2 - 24.

So the probabilities of the given events are:

P(X = 5) = 1/9
P(2 ≤ X ≤ 6) = 5/12
P(X = 5 or X = 10) = 7/36

To find the probabilities of the given events, we need to consider all the possible outcomes of the two dice-throwing experiments and the number of favorable outcomes for each event.

There are 6 possible outcomes for each die, so the total number of possible outcomes for the two dice is 6 × 6 = 36.

For the event X = 5, the favorable outcomes are (1, 4), (2, 3), (3, 2), and (4, 1). So the probability of this event is P(X = 5) = 4/36 = 1/9.

For the event 2 ≤ X ≤ 6, the favorable outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), and (5, 1). So the probability of this event is P(2 ≤ X ≤ 6) = 15/36 = 5/12.

For the event X = 5 or X = 10, the favorable outcomes are (1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), and (6, 4). So the probability of this event is P(X = 5 or X = 10) = 7/36.

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Answer: 515,783

Step-by-step explanation:  f(x)= a(1+r)^x      450,000(1+0.023)^6

2 divided by 4 and 3 divided by 6 where these number can be any numbers that have the same ratio as 1:2 and under 0-6 and not repeating them.

A number is a fundamental building block of mathematics. For a range of tasks, including measuring, counting, and indexing, numbers are utilised. There are different types of numbers depending on their characteristics, such as natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc. The basic integer arithmetic operations can be used to calculate the outcome number.

In the given question, we need to find two sets of three distinct numbers between 0 and 6 that have the same ratio.

One possible solution is:

2 divided by 4.

= 3 divided by 6

Here:

The ratio of the first set is 2:4 or 1:2. When we divide 2 by 4, we get 0.5.

The ratio of the second set is 3:6 or 1:2. When we divide 3 by 6, we also get 0.5.

Therefore, we have:

2 divided by 4.

= 0.5

3 divided by 6.

= 0.5

So, we can say:

2 divided by 4

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.Similarly,

3 divided by 6

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.

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The values of m that will result in a repeated solution for 3x^(2)+4mx+m=0  are m = 0 and m = 3/4.

The given quadratic equation is 3x^(2)+4mx+m=0. In order to find the value(s) of m that will result in a repeated solution, we need to use the discriminant of the quadratic formula.

The discriminant of the quadratic formula is given by b^(2)-4ac, where a, b, and c are the coefficients of the quadratic equation.

In the given equation, a = 3, b = 4m, and c = m.

Plugging these values into the discriminant, we get:

(4m)^(2)-4(3)(m) = 16m^(2)-12m = 0

A repeated solution occurs when the discriminant is equal to 0. So, we need to solve the equation 16m^(2)-12m = 0 for m.

Factoring out a common factor of 4m, we get:

4m(4m-3) = 0

This gives us two possible values for m:

4m = 0 or 4m-3 = 0

Solving for m, we get:

m = 0 or m = 3/4

Therefore, the values of m that will result in a repeated solution for the given quadratic equation are m = 0 and m = 3/4.

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Answer:

The price of per ounce of strawberries is $ 0.25.

Step-by-step explanation:

Pounds to ounce conversion:

As we know that,

 One pound = 16 Ounce

Since, Jill bought a pound of strawberries for $4

It means that,

Price of 16 Ounces of strawberries = $ 4

So taht,  Price of one ounce of strawberries

Hence, the price of per ounce of strawberries is $ 0.25.

Answer:

0.25

Step-by-step explanation:

16 ounces = 1 pound

4.00 / 16 = 0.25

Answer:

Step-by-step explanation: g

The inequality is 3x + 2y ≥ 93 and the grade received is A for the test

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the number of multiply questions be x

Let the number of matching questions be y

Substituting the values in the equation , we get

3x + 2y ≥ 93

when x = 20 and y = 18

On simplifying the equation , we get

3 ( 20 ) + 2 ( 18 ) ≥ 93

60 + 36 ≥ 93

96 ≥ 93

Therefore , the student receives an A grade for the test

Hence , the inequality is true

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Answer:

27+X=42

X=15

Step-by-step explanation:

interior opposite angle are equal.

The sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.

What is the sequence of transformation?

In mathematics, a sequence of transformations refers to a series of geometric transformations performed on a shape to create a new shape. These transformations can include translations, rotations, reflections, and dilations.

The sequence of transformations is the order in which the transformations are performed. The order matters because different sequences of transformations can lead to different final shapes.

For example, to transform a triangle into a new position, we might first perform a translation to move the triangle to a new location, then perform a rotation to change its orientation, and finally perform a reflection to flip the triangle across a line. The sequence of transformations in this case is translation-rotation-reflection.

Sequences of transformations are used in geometry to analyze and describe shapes and to solve problems related to symmetry, congruence, and similarity. They are also used in computer graphics and animation to create 2D and 3D shapes that can be moved and transformed on a screen.

To map △RST to △R′S′T′, we need to perform a sequence of transformations that includes translations, rotations, reflections, and/or dilations. Here's one possible sequence of transformations:

Translation: We can translate △RST by 6 units to the right and 2 units down to get a new triangle that has R at (3, -3), S at (5, -3), and T at (2, -7).

Reflection: We can reflect the translated triangle across the y-axis to get a new triangle that has R′ at (-3, -3), S′ at (-5, -3), and T′ at (-2, -7).

Rotation: We can rotate the reflected triangle 90 degrees counterclockwise about the origin to get a new triangle that has R′ at (3, -3), S′ at (3, -1), and T′ at (-1, -4).

Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.

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Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify if we use the commutative property.

What is the commutative property, and how can it be used to simplify expressions?

The commutative property is a property of addition and multiplication that allows us to change the order of the numbers being added or multiplied without changing the result.

That is, [tex]a + b = b + a[/tex] and [tex]a \times b = b \times a[/tex].

To simplify expressions, we can use the commutative property to rearrange the order of the terms in a way that makes the arithmetic easier to perform.

Find the expression:

We are given the expression -1/3-10+7+2/3+5, and we want to know which option would be easier to simplify using the commutative property.

Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify using the commutative property because we can group the terms that have like terms together. Specifically, we can group the negative terms together and the positive terms together:

{5+(-1/3)+(-10)}+(2/3+7) = {(5)+[(-1/3)+(-10)]}+{(2/3)+7}

Now we can simplify each group separately. For the first group, we can add the terms inside the brackets using the commutative property:

{-1/3+(-10)} = -10 - 1/3 = -31/3

For the second group, we can add the terms directly:

{2/3+7} = 2/3 + 21/3 = 23/3

Substituting these results back into the original expression, we get:

-1/3-10+7+2/3+5 = -31/3 + 23/3 + 5

Now we can add the terms directly to get:

-31/3 + 23/3 + 5 = -8/3 + 5 = 7/3

Therefore, the expression simplifies to 7/3.

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a) The number of turning points of the function is 3.
b) The end behavior of the function is that as x approaches positive infinity.
c) The potential real zeros of the function are the factors of the constant term, 8. These are ±1, ±2, ±4, and ±8.
d) Using Descartes' Rule of Signs, there are 3 sign changes in the polynomial, so there can be 3 or 1 positive real zeros.
e) Using synthetic division and the potential real zeros, we can find that the rational zeros are -2 and 4.
f) The graph of the function is shown below with the turning points and zeros labeled.

The number of turning points of the function is 3. because the degree of the polynomial is 4 and the number of turning points is one less than the degree.

f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity. This is because the leading coefficient is positive and the degree is even.

There are 2 sign changes in the polynomial with the x values replaced with -x, so there can be 2 or 0 negative real zeros.

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The supplementary angles are ∠GDF and ∠EDG, ∠CED and ∠BEC. The correct options are C and D.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complementary angles is 90 degrees.

The sum of the two angles ∠GDF and ∠EDG is equal to 180°. So these angles are supplementary to each other.

The sum of the two angles ∠CED and ∠BEC is equal to 180°. So these angles are supplementary to each other.

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The probability that a person from the survey who has a tablet also has a laptop is 0.058, or approximately 5.8%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We are given that 62% of respondents have a tablet and 30% have a laptop.

Let T represent the event of having a tablet and L represent the event of having a laptop.

Then, we know -

P(T) = 0.62

P(L) = 0.30

We are also given that 12% of respondents who have a laptop also have a tablet.

In other words, the probability of having a tablet given that a person has a laptop is -

P(T|L) = 0.12

We can use this conditional probability to find the probability that a person who has a tablet also has a laptop, denoted by P(L|T).

By Bayes' theorem, we have -

P(L|T) = P(T|L) × P(L) / P(T)

Substituting the values we know, we get -

P(L|T) = 0.12 × 0.30 / 0.62

Simplifying this expression, we get -

P(L|T) = 0.058

Therefore, the probability value is 0.058, or 5.8%.

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Standard form of the number 3.5 × 10⁷ is 35000000.

In the United States and countries using US conventions, the standard form is the usual way of writing numbers in decimal notation.

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number.

Given number

3.5 × 10⁷

In standard form, digits are written left or right of decimal

number can be written as

= 35000000

Hence, 35000000 is standard form of the number 3.5 × 10⁷.

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b=7

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

The perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster will be 22 miles.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given, a coordinate system where 1 unit = 1 mile

Lets,

First, calculate the linear distance between adjacent points as displayed in the graph.

Distance between car to cabana = 4 units = 4 miles

Distance between cabana to beach = 6 units = 6 miles

Distance between beach to water slide = 5 units = 5 miles

Distance between water slide to roller coaster = 6 units = 6 miles

Distance between roller coaster to cabana =5 units = 5 miles

Thus,

1) the perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster:

Perimeter = 6 + 5 + 6 + 5

Perimeter = 22 miles

2) the total distance in miles from the car to the cabana and then from the cabana to the beach:

Distance = 4 + 6

Distance = 10 miles

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To determine the base of a parallelogram, we can use the formula for the area of a parallelogram, which is A = b*h, where A is the area, b is the base, and h is the height.

We are given the height (h) and the area (A), so we can rearrange the formula to solve for the base (b):
b = A/h

Substituting the given values for A and h:
b = 15/6

Simplifying:
b = 2.5

Therefore, the base of the parallelogram is 2.5 feet.

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The solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3.

To solve the trigonometric equation sin 2x=−√3/2 on the interval [0,2π), we need to find the values of x that satisfy the equation. We can do this by using the inverse sine function and the periodicity of the sine function.

First, let's find the general solution of the equation:
sin 2x=−√3/2
2x= sin⁻¹(−√3/2) + 2πn or 2x= π - sin⁻¹(−√3/2) + 2πn, where n is an integer
2x= -π/3 + 2πn or 2x= 4π/3 + 2πn
x= -π/6 + πn or x= 2π/3 + πn

Now, we need to find the values of x that are in the interval [0,2π). We can do this by plugging in different values of n until we find all the solutions in the interval.

For x= -π/6 + πn:
When n=0, x= -π/6 (not in the interval)
When n=1, x= 5π/6 (in the interval)
When n=2, x= 11π/6 (in the interval)
When n=3, x= 17π/6 (not in the interval)

For x= 2π/3 + πn:
When n=0, x= 2π/3 (in the interval)
When n=1, x= 5π/3 (in the interval)
When n=2, x= 8π/3 (not in the interval)

Therefore, the solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3. These are the exact form answers. If we want to round them to two decimal places, we get x= 2.62, 5.24, 1.05, and 3.14.

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The length of the tarp with an area of 200 square meters is 40 meters.

The area of a rectangle is expressed as;

Area = length × width

Given that;

When a rectangular tarp has an area of 200 square meters and a width of 5 meters, we can use the above formula to find the length of the tarp.

Plug these values into the formula and solve for the length:

Area = length × width

200 = Length x 5

To solve for Length, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5:

200/5 = Length

This simplifies to:

40 = L

L = 40

Therefore, the rectangular tarp is 5 meters wide and 40 meters long.

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The quadrilateral MNOP if MN=OP and MP=NO, then it must be square (option d).

First of all, since the opposite sides are equal in length (MN=OP and MP=NO), we know that MNOP is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

If we were given additional information about the angles of the quadrilateral, we could determine whether MNOP is a rectangle or a rhombus.

Lastly, it is worth noting that MNOP cannot be a square, because a square is a special type of quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.

In summary, based on the information given in the question, we can conclude that MNOP is a parallelogram, but we cannot determine whether it is a rectangle or a rhombus without additional information. We can also rule out the possibility that it is a square.

Hence the option (d) is correct.

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Complete Question:

Choose ALL answers that describe the quadrilateral MNOP if MN=OP and MP=NO?

a) Parallelogram

b) Rectangle

c) Rhombus

d) Square

e) Trapezoid

The simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

To rewrite the expression without parentheses and simplify it as much as possible, we need to distribute the term (-2a^(3)b) to each term inside the parentheses. This is done by multiplying the term outside the parentheses with each term inside the parentheses.

So, we have:
[tex](4a^2b^6-9b^4)(-2a^3b) = (4a^2b^6)(-2a^3b) - (9b^4)(-2a^3b)[/tex]

Next, we simplify the terms by combining like terms and using the rules of exponents:

[tex]= -8a^5b^7 + 18a^3b^5[/tex]

So, the simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

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The triangles which are right triangles as required to be determined in the task content are; Choice A; Triangle 1 and Choice D; Triangle 4.

Recall; the Pythagorean theorem only holds for right triangles.

Therefore, for a triangle to be a right triangle; the square of its longest side must be equal to the sum of squares of its two other sides.

Therefore;

Triangle 1 is a right triangle because; (√106)² = 9² + 5²; 106 = 106.

Triangle 2 is not a right triangle because; (√39)² ≠ 2² + 6²; 39 ≠ 40.

Triangle 3 is not a right triangle because; (√179)² ≠ 6² + 12²; 179 ≠ 180.

Triangle 4 is a right triangle because; (√73)² = 3² + 8²; 73 = 73.

Ultimately, the correct choices are; Choices A ana D.

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The tangent trigonometry ratio can be used to determine the measure of m∠F using the length shown. Option C is correct

The given figure is a right triangle.

According to the question, we are to determine the trigonometry ratio that can be used to find m∠F.

Given the following sides

Hypotenuse = EF

Opposite to m∠F = DE

Adjacent = DF

Since tan m∠;F = opposite/adjacent = DE/DF

tan m∠F can be used to determine m∠F.

The same goes with tan and sine since we can determine the value of the hypotenuse but only tangent can be used to find the measure given the length shown.

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