solve the equation a^2x^2 = abx + 2b^2 using completing the square method​

Distributive property is illustrated by the statement given as 4[3+2]=4[3]+4[2]

The distributive property is defined as an expression of the form A(B + C). This property is known by distributive law and applies to subtraction also. This can be solved by a multiplication over addition operation that is written as:

A(B + C) = AB + AC

Distributive property is the sum of two numbers times a third number is equal to the sum of each add end times the third number.

Since the general rule is that:

a(b + c) = ab + ac

Then, 4[3+2]=4[3]+4[2]

Therefore, the given statement elaborates the Distributive property.

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The percent markup of the supplied statement is equal to 50% after the problem is solved.

There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Cost price of game=$25

Selling price of game=$37.50

Profit =  selling price - cost price

Profit =  37.50 - 25

Profit / markup percentage = (profit /cost price ) * 100

= (12.50/25) * 100

= 50%

The percent markup of the supplied statement is equal to 50% after the problem is solved.

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Answer:

I would say (option A)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that our x-values can be any number. Therefore, we have all real numbers as our domain:

→ A) x < 2.

Hope this helps!

The amount of flour needed for soft pretzel is c = 1/8 and the amount of flour needed for the loaf of bread is b = 3.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given system of equations,

b = 24 c and

[tex]\frac{1}{4}[/tex] b + 4c = [tex]\frac{5}{4}[/tex]

Substitute b = 24 c in the second equation.

[tex]\frac{1}{4}[/tex] (24 c) + 4c = [tex]\frac{5}{4}[/tex]

6c + 4c = [tex]\frac{5}{4}[/tex]

10 c = [tex]\frac{5}{4}[/tex]

c = [tex]\frac{5}{4}[/tex] × [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{8}[/tex]

b = 24c = 24 / 8 = 3

Hence c = 1/8 and b = 3 in cups.

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Hello there!

Answer:

[tex](9, +\infty)[/tex]

Step-by-step explanation:

It has no real roots only if

[tex] \sqrt{b {}^{2} - 4ac } [/tex]

has no roots. That means that b² - 4ac is smaller than 0:

[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]

we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]

Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.

The process of expressing a specific element in mathematics in the most typical way is known as standard form. Every element of mathematics, including big and small numbers, equations and lines, is designated in a standard form.

A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of rules. The standard form is used to clearly represent extremely large or extremely small numbers.

To write an equation in standard form passing through the (-1,-1) and parallel to y = - x - 5, we need to find y-intercept form first

We know that parallel lines have same slope, so

y - y1 = m(x - x1)

y -(-1) = -1(x -(-1)

y + 1 = -x - 1

y = -x - 2

y + x = -2

Thus, Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.

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(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that the side of the square must be equal to the width of the rectangle, x feet.

The length of the rectangle must be 50 feet longer than its width

The field the farmer wants to build the two fenced sections in has an area of y square feet.

The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet

the sum of the fenced areas must be less than the area of the field.

y≥x²+1000

y>2x²+50x

(20, 2,200) and (5, 3,000) are the viable solutions

Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.

[tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex] are the coordinates of a triangle's vertices [tex](x_3,y_3)[/tex]. The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.

When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.

First do the first transformation, the translation.

J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).

After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).

We Utilize those new coordinates to do the reflection in the y axis.

J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).

After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).

Those exists the vertices after the transformations.

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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.

[tex](x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})[/tex]  are the coordinates of a triangle's vertices . The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.

When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.

First do the first transformation, the translation.

J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).

After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).

We Utilize those new coordinates to do the reflection in the y axis.

J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).

After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).

Those exists the vertices after the transformations.

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Step-by-step explanation:

Why can't I plus x² to each side of the inequality x²+4x > -x² ?

(Note: one adds things; one does not plus them.)

You can easily add x² to both sides here:

(x² + 4x) + x² > (-x²) + x², or

2x² + 4x > 0, or

x² + 2x > 0, or

x(x + 2) > 0.

For this to be true, x > 0 and x+2 > 0; or else x < 0 and x+2 < 0.

Case 1: x > 0 and x+2 > 0.

Rewrite this as x > 0 and x > -2.

This is true for all x > 0.

Case 2: x < 0 and x+2 < 0.

Rewrite this as x < 0 and x < -2.

This is true for all x < -2.

The solution set for the inequality, in interval notation, is then (-∞,-2) ∪ (0,∞).

done its a good question btw ....

The point shown on the graph is

(4, -5, 6)

An ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.

Each axis also has an orientation, and the length of all three axes is equal.

In ordered triplet, the order of the axis is (x, y, z)

z is vertical up positive and down negative

y is horizontal right is positive and left is negative

x is the axis pointing to us which is positive pointing away is negative

Using this information, to trace the point shows that the point marked by a dot is  (4, -5, 6).

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The fraction of the entire bulletin board decorated by each classmate is N/20.

Fraction is a mathematical expression which is made up of denominator and a numerator. So that fractions may generally be categorized into 3 types. These are: proper fraction, improper fraction, and mixed fraction.

Considering the given question, let the size of the bulletin board be represented by N.

The section of the bulletin board to be decorated = 1/5 * N

                                                                       = N/ 5

There are 4 classmates that has been selected to divide the section to be decorated equally among themselves. So.

Fraction of the board to be decorated by each student = (N/ 5)/ 4

                                                                             = 1/20 N

The fraction of the board to be decorated by each student is N/20.

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An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

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Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.

By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

With regard to the inequality expression

-3m + 5 > 14

5 from each side is subtracted.

-3m + 5 - 5 > 14 - 5

-3m > 9

Subtract -3 from both sides.

-3m/-3 < 9/-3

m < -3

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Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.

Here,

Given : -4.9t² + 2.94t + 25.48

Then,

To find the When does the object strike the ground :

We get :

=> -4.9t² + 2.94t + 25.48 = 0

Using discriminant formula

We find the value of t:

=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] /  2(-4.9)

=> t =-2 or 6

So we neglect -2

So solution for t = 6 seconds

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

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Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.

The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.

Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.

Thus, total possibility = 10.

probability of getting 100 = 1/10

There are 5 volumes which are  less than 100 here,  [95, 99]. Thus, the probability = 5/10 = 1/2.

There are 5 values between 98 and 102 including these two values.

Hence, probability of getting these range  = 5/10 = 1/2.

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the true statements for 8u + 5 + 3v are:

1.) 8u+3v+5 is written as a sum of three terms.

4.)5 is a constant.

The word "constant" in mathematics has several different connotations. When used as a noun, it can have either of the following two meanings: Non-variance (i.e., not changing in relation to some other value) or Variance.

an unchanging number or other non-changing mathematical object that is fixed and well-defined. Sometimes, to distinguish between these two meanings, the terms mathematical constant or physical constant are used.

a function with a constant value (i.e., a constant function).

These constants are frequently represented by a variable that is independent of the main variable or variables in question.

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Answer:

11/10

Step-by-step explanation:

33/10 - 22/10

The initial amount that was invested in the account was $49.

We know that we can be able to obtain the principal by the use of the formula for the simple interest and by that formula we would now have that;

I = PRT/100

I = interest

P = principal

R = rate

T = time

Then we are going to have that;

R = 2.7

P = ?

I = 6.62

T = 5

Then;

6.62 = P * 2.7 * 5/100

6.62 * 100 =  P * 2.7 * 5

P = 6.62 * 100/2.7 * 5

P = 662/13.5

P = 49

Thus we have but in at the beginning about $49

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Answer:

wouldn't it be 1/25 black??

Answer:

  -6

Step-by-step explanation:

You seem to want the value of q₃ in the matrix Q⁻¹.

The inverse matrix, Q⁻¹, is the transpose of the cofactor matrix, divided by the determinant. That makes q₃ = -q₂₁/det(Q):

  q₃ = -(-2/3)/((-1(-1/9) -(-2/3)(-1/3))

  q₃ = (2/3)/(1/9 -2/9) = (6/9)/(-1/9)

  q₃ = -6

__

Additional comment

The transpose of the cofactor matrix of a 2×2 matrix is the original with the diagonal terms swapped, and the off-diagonal terms negated. Basically, the only math involved in computing the inverse is finding the determinant, and dividing by it.

Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.

If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.

Step-by-step explanation:

The trigonometric ratios for the angle x in the triangle are given as follows:

The three trigonometric ratios are defined as follows:

In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:

These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.

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20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.

In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.

The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.

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The area of the square having the same length of the base of the triangle is 7245 square inches.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.

So,

Base = {√(87² - 18²)}.

Base = √(7245) inches.

Base = 85.11 inches.

Now, We also know that the area of a square is (side)².

Therefore it is (87.11)² which is the same as 7245 sq inches.

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Answer:

  see below

Step-by-step explanation:

You want the ingredient quantities for several different multiples of the basic recipe.

To fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.

  [tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]

The inverse of the function is y = 3/(x + 2) - 1

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

y=3/(x+1) -2

Rewrite as

y = 3/(x + 1) - 2

Swap the positions of x and y

So, we have the following representation

x = 3/(y + 1) - 2

Next, we make y the subject of the formula

This gives

3/(y + 1) = x + 2

Take the inverse of both sides

(y + 1)/3 = 1/(x + 2_

So, we have

y = 3/(x + 2) - 1

Hence, the inverse is y = 3/(x + 2) - 1

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You can hire around 173 employees. Here's the calculation: $1,900 / ($11/hour * 40 hours/week) = 173.333..., which rounds down to 173.

Answer: Both Rick and Jenny could be correct because we do not know what "x" is.

Step-by-step explanation:

The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.

I hope this helps :)