Find the area of the trapezoid with bases 5cm and 2cm and height 1/5 cm.

(Simplify your answer)

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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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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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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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

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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Answer: -9 1/4

Step-by-step explanation:

Answer:

1:10

Step-by-step explanation:

30 boxes = 180 eggs

3 boxes = 18 eggs

18:180 = 1:10

The solutions to sin(θ) = -√3/2 in the interval 0 ≤ θ ≤ 2π are approximately θ = 5π/3 and θ = 4π/3.

What is an interval?

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbers.

The equation sin(θ) = -√3/2 has two solutions in the interval 0 ≤ θ ≤ 2π.

Since the sine function has a range [-1, 1], the value of -√3/2 lies in the range of the sine function, so there are solutions in the specified interval.

Using the unit circle, we can find the values of θ that satisfy the equation. In the unit circle, the sine of an angle is equal to the y-coordinate of the point on the circle that corresponds to that angle.

The point (-√3/2, -1/2) lies on the unit circle and has an angle θ that satisfies the equation.

The other solution can be found by adding π to θ, since the sine function has a period 2π.

Hence, the solutions to sin(θ) = -√3/2 in the interval 0 ≤ θ ≤ 2π are approximately θ = 5π/3 and θ = 4π/3.

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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

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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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 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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The answer is 21/6720

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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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 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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Answer: your answer is 16!

Step-by-step explanation:

Answer:

5 pens

Step-by-step explanation:

$10 - 6$ = $4

$4/$0.80

she can afford 5 pens

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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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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Point M has the coordinates (-3, -1.5) which are written as decimals.

What is the midpoint of the line segment?

The midpoint of a line segment is the point that is exactly in the middle of the line segment. It is the point that divides the line segment into two equal parts.

To find the midpoint of a line segment, you can use the formula:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Where x1, y1 and x2, y2 are the coordinates of the two endpoints of the line segment.

In this case, the endpoints of the line segment are B(2, 1) and C(–8, –4).

So we can substitute the coordinates of B and C in the midpoint formula:

Midpoint = ( (2 + -8) / 2 , (1 + -4) / 2 )

Midpoint = ( -3 , -1.5)

The midpoint of the line segment is (-3, -1.5).

Hence, point M has the coordinates (-3, -1.5) which are written as decimals.

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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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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

The domain of the given function f(x) = (x + 4)/x² + x - 12 is given by {x|x ≠ 3, 4}.

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. In Mathematics, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By critically observing the graph of this function f(x) = (x + 4)/x² + x - 12 shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = (-∞, 4) U (-4, 3) U (3, ∞); {x|x ≠ 3, 4}.

Range = (-∞, -1/7) U (-1/7, 0) U (0, ∞); {y|y ≠ 0, -1/7}.

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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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Answer:

x=6x okay that should help

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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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%