There were some fiction and non fiction books in a second hand bookstore. The number of fiction bookw was 3/5 of non fiction bookw. After an equal number of fiction and non fiction books were sold,the ratio of the number of fiction books to the number of non fiction books left was 5:9. There were 240 books altogether at first. How many books were sold altogether?

The equivalent expression to 4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³  

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.

In general, something is considered equal if two of them are the same. Similar to this, similar expressions in mathematics are those that hold true even when they appear to be different.

However, both forms provide the same outcome when the values are entered into the equation.

Here we have  

4y²(6x³ + 4xy + 3y)  

Simplify the given expression as follows

=> 24x³y² + 16xy³ + 12y³  

Therefore,

The equivalent expression to  4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³  

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By substitution; x = 4 and y = -31

An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.

y=-6x-7 --- 1

7x+y=-3 --- 2

Substituting y as 6x - 7 in equation 2

7x + (-6x - 7) = -3

7x - 6x - 7 = -3

x - 7 = -3

x = -3 + 7

x = 4

Substitute x as 4 in equation 1

y = -6x - 7

y = -6(4) - 7

y = -24 - 7

y = -31

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Ellie needs 5050 grams extra fertilizer and total cost of fertilizer = 22.81-pound sterling.

Multiplication is the product of two or more numerical terms. Division is the process of dividing any numbers into equal parts.

Cost of 750 grams fertilizer = 2.95-pound sterling,

the area of the lawn = 145 square meters.

Ellie uses 40 grams fertilizer for every square meter of lawn.

So, fertilizer needed for the 145 square meters of land = (145 × 40)

                                                                                        = 5800 grams

it stated earlier that 750-gram fertilizer was bought but Ellie needs 5800 grams fertilizer.

the extra amount of fertilizer that Ellie needs = (5800 - 750) = 5050 grams.

cost of 750 gram fertilizer = 2.95-pound sterling

cost of 5050-gram fertilizer = (2.95 × 5050) / 750 = 19.86-pound sterling

cost of extra fertilizer = 19.86-pound sterling.

Total cost of fertilizer = (2.95 + 19.86) pound sterling

                                   = 22.81-pound sterling

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The product of the expression is 8x²-10x

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given that, an expression 8x(x-5/4x) we are asked to find its product,

8x(x-5/4x)

= 8x²-10x

Hence, the product of the expression is 8x²-10x

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For the polynomial functions f(x) = 3x - 2 and g(x) = x² + 1, then function (f + g)(x) is calculated to be

A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation or the cubic equation.

The equation in the problem has integers as below

f(x) = 3x - 2: integer value here is 1

g(x) = x² + 1 integer value here is 2

In both conditions, the integer values are positive hence both are polynomial functions

(f + g)(x) is addition of the two polynomials

f(x) = 3x - 2 + g(x) = x² + 1

= 3x - 2 + x² + 1

= x² + 3x - 1

hence (f + g)(x) = x² + 3x - 1

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Hi Bixby can you help me with this Mr. CV is making an area to display 9 pictures for for each pair of different functions there are 2 Irish he can we how many different areas can Mr. Semi make is in the number of a rice old number odd or even

Answer: -9 1/4

Step-by-step explanation:

Answer: your answer is 16!

Step-by-step explanation:

Answer:

y = 3x

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,6), we see that the y increase by 6 and the x increase by 2, so our slope is

m = 6/2 = 3

Y-intercept is when the x = 0, we see that the y-intercept is located at (0,0)

So, our equation is

y = 3x

Answer:

1:10

Step-by-step explanation:

30 boxes = 180 eggs

3 boxes = 18 eggs

18:180 = 1:10

The length of A'B' after undergoing the dilation is; A'B' = 2√2

The scale factor in the dilation of an object tells us how much larger or smaller the image will be when compared to the original object. Thus, the coordinates will be multiplied by the scale of dilation to get the new coordinates.

We are given the coordinates of Polygon ABCD as A(0, 4), B(-4, 8), C(3, 3), and D(4, -2). With a scale of dilation of ½, we will have the new coordinates as;

A'(0, 2), B'(-2, 4), C'(1.5, 1.5), and D'(2, -1)

The formula to find the distance between two coordinates is;

Distance = √[(y₂ - y₁)² + (x₂- x₁)²]

Thus;

A'B' = √[(4 - 2)² + (-2 - 0)²]

A'B' = √8

A'B' = 2√2

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When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or probability that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as a percentage form 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.

given

There are six possible methods to select two coins (sequence is irrelevant): 1, 5, 1, 10, 1, 25, 5, 10, and 1, 25. (10,25).

Three of these add up to at least 25, thus 3/6 or 1/2 of them.

Alternatively, there are 4 ways to choose 2 coins from 4, or 4 C 2 = 6.

You then select one of the three remaining coins and the quarter (required to reach at least 25) as follows: 3 C 1= 3 ways.

When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.

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Answer:

D) 50%

Step-by-step explanation:

There are 5 weekdays, Monday through Friday.

In each of the 5 weekdays she runs 2.6 miles.

In a week, she runs 5 × 2.6 miles = 13 miles by running only on weekdays.

Now we need to find out what percent of 26 miles is 13 miles.

percent = part/whole × 100%

percent = 13/26 × 100%

percent = 0.5 × 100%

percent = 50%

Answer: D) 50%

The inequality that represents this sentence is 6 + 2 < 9 + 3

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

Six plus two is less than nine plus three

Express as numbers

So, we have

6 plus 2 is less than 9 plus 3

Introduce the operators

6 + 2 < 9 + 3

Hence, the inequality is 6 + 2 < 9 + 3

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Answer:

x=6x okay that should help

The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given as,

- (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7)

Simplify the equation, then we have

- (3/2) x (4/7) = x - (2/3) x (7/4)

- 6/7 = x - 7 / 6

x = 7/6 - 6/7

x = (49 - 36)/42

x = 13 / 42

The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.

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Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality.

The nine basic characteristics of equality are addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root. Real number-based algebraic problems can be resolved with the aid of the addition, subtraction, multiplication, and division properties of equality.

When you add the same amount to both sides of an equation that has two equal expressions, the equation will stay equal. Finding the value of the variable that makes an equation true is the process of solving an equation.

The Subtraction Property of Equality asserts that when an equal value is subtracted from or removed from two equal objects, a new equal quantity is created. A mathematical statement with two equivalent sides is denoted by an equal sign. The formula for the subtraction property is if a = b, then a - c = b - c.

According to the equality's multiplication property, an equation's two sides stay equal when multiplied by the same amount.

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The retailer's selling price per sweater should be $45.60 if she wants to make a profit of 20% of her cost price (markup) of $38.

The selling price is the marked-up cost.

The markup is the percentage added to the cost price to achieve a target profit percentage.

Cost price per unit = $38

Target profit = 20%

Selling price = $45.60 ($38 x 1.2)

Thus, for the retailer to make a profit of 20% of her cost, she must sell each sweater for $45.60.

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x = 27

y = 50

Step-by-step explanation:

ABC=FDE

We need x first.

AC=EF

108=2x-y

54=x -1 . . . . . divide by2

27=x

x=27

Now, we can find y.

∠B = ∠F

2X-Y=48

Y=48+2X=50

Y=50

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Answer:

5 pens

Step-by-step explanation:

$10 - 6$ = $4

$4/$0.80

she can afford 5 pens

The features of the cosine function are given as follows:

The equation of the cosine function is given as follows:

y = 1/3cos(2(x - π/3)).

The cosine function is defined as follows:

g(x) = acos(b((x+c))+d.

The coefficients have these following roles:

The function oscillates between -1/3 and 1/3, hence the amplitude is of:

a = 1/3.

The period is of 2π/3 - (-π/3) = π, hence:

2π/B = π.

B = 2.

The horizontal shift is of -π/3, hence the equation is given as follows:

y = 1/3cos(2(x - π/3)).

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The answer is 21/6720

Answer:

Y = 4

Step-by-step explanation:

5x-y=54

50-y=54

circle y and subtract 50 from itself then subtract 50 from 54.

after subtracting you should have y=4

Answer: yes, you did

Step-by-step explanation:

21 divided by 25 is 0.84

the you times 0.84 with 100 and you would get 84%

On solving the provided question, we can say that the equation that can be formed are  4x+5y=38.50 and 3x+9y=47.25

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation that can be formed are

Sandwiches are $5.25 Bowls are $3.50

4x+5y=38.50

3x+9y=47.25

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The solution to the quadratic equation are x = 1 and -5/2

We have the quadratic function;

2x² + 7x + 5

Using the factorization method of solving quadratic equation. We need to multiply the coefficient of x² and the constant 5.

Then find the pair factors and substitute the values into the function.

Substitute the values, we have;

2x² + 2x + 5x + 5

Factor the expression in pairs

(2x² + 2x) + (5x + 5)

Factor the common terms, we get;

2x(x + 1) + 5( x+ 1)

We have the equations;

2x + 5 = 0

x = -5/2

And

x + 1 = 0

x = -1

Thus, the values are x = -5/2 and -1

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Answer:

ρ= 5 g/cm³

Step-by-step explanation:

density= mass/volume

ρ= m/v

As all  side of the cube is equal so the formula for volume is a³ 3³

which gives us volume 27.

ρ= 135g/27cm³

ρ= 5 g/cm³

The equation for a tangent to the graph of y = arcsin(x/2) at the origin is y = x.

To find the equation for a tangent to a graph at a certain point, we need to find the slope of the tangent at that point. To do this, we can use the derivative of the function. In this case, the function is y = arcsin(x/2). Using the chain rule, we can find the derivative of this function:

y' = d/dx(arcsin(x/2))

= d/dx(sin^-1(x/2))

= 1/√(1 - (x/2)^2)

Now, to find the slope of the tangent at the origin (0,0), we can plug x = 0 into this derivative:

y'(0) = 1/√(1 - (0/2)^2) = 1

So the slope of the tangent at the origin is 1. To find the equation of the tangent, we can use the point-slope form of a line:

y - y1 = m(x - x1) where,

Plugging in the values for the origin and the slope we found above:

y - 0 = 1(x - 0)

or, y = x

So the equation for the tangent is y = x. But the options are incorrect.

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The value of x = -3 in the given quadratic equation.

In mathematics, a quadratic equation is defined as an equation of degree 2, which means that the highest exponent of this function is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are numbers and a cannot be 0.

Quadratic equations are unique in that they can have up to two real solutions. Solutions are found where the quadratic equals 0. Real solutions are those that are not fictitious and have real numbers.

8 to the power of X over 2 divided by 4 to the power of X over 3 = 2 to the power of -5 over 2.

In equation it will be written as

[tex]$ 8^{x/2} \div 4^{x/3} = 2^{-5/2}[/tex]

[tex]$ (2^3)^{x/2} \div (2^2)^{x/3} = 2^{-5/2}[/tex]

[tex]$ (2)^{3x/2} \div (2)^{2x/3} = 2^{-5/2}[/tex]

[tex]$ (2)^{\frac{ 3x}{2} -\frac{ 2x}{3} } = 2^{-5/2}[/tex]

[tex]$ (2)^{\frac{ 5x}{6} } = 2^{-5/2}[/tex]

By solving this

x = -3

Thus, the value of x = -3 in the given quadratic equation.

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The graph of y = -(2/3)x + 2 is shown, having a slope of -2/3 and y intercept of 2

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

The equation y = -(2/3)x + 2 have a negative slope of -2/3 and y intercept of 2

The graph of y = -(2/3)x + 2 is shown

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