The length of a rectangular vegetable garden i 4ft more than it' width. After a 2 foot boarder i placed around the garden, the area of the garden and boarder i 320ft^2. Find the original dimenion of the garden

The dimensions of the region bounded by the curve, y² = x, the lines,  x = 1 and x = 4, and the x-axis exists the dimensions ABCD

Thus area of ABCD = [tex]\int_1^4 \mathrm{ydx} \\[/tex]

[tex]& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\[/tex]

[tex]$& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\[/tex]

[tex]$& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right][/tex]

simplifying,

[tex]$& =\frac{2}{3}[8-1] \\[/tex]

Then we get,

[tex]$& =\frac{14}{3} \text { units }[/tex]

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Chunking is a good way to introduce your child to some of the more basic concepts of division, and once they have come to terms with this they can then move onto the short method of division.

Now, According to the teaching Ideas:

We have four basic arithmetic operations i.e., addition, subtraction, multiplication, and division. Amongst these four operations, the division is one of the major operations we use in our daily activities. It is the process of splitting a large group into equal smaller groups. For example, divide 25 by 5. Division fact for this example will be, 25 ÷ 5 = 5.

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Answer: 7

Step-by-step explanation:

the -9 coordinate is the same, so to get the distance you do 10 - 3 which is 7

The distance between points A and B is 7units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9,10).

A point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10)

The coordinate of point A is (-9, 3)

The coordinate of point B is (-9, 10)

The distance formula can be given as:

d=[tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

d=[tex]\sqrt{((-9)+9)^2 + (10-3)^2}[/tex]

d=[tex]\sqrt{7^2}[/tex]

d=7

The distance is 8 units.

Therefore, the distance between points A and B is 7 units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10).

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To determine their ages, the substitution approach is used.

Joy's age and her brother's age are differed by 10 years.

What is linear system?

It is an system of equation where the maximum power of the variable is consistently 1. a single-dimensional object with no breadth. It consists of an endless number of dots placed side by side.

Given

The combined ages of Joy and her brother total 24.

Joy's older brother is three years older than  twice his age she is.

To locate

Joy's age as compared to that of her brother.

Assume that Joy is x years old and her brother is y.

then in line with the first circumstance.

x + y = 24 ...(1)

And according to the second condition.

2x + 3 = y ...(2)

On solving equations 1 and 2. We get

x + 2x + 3 = 24

            x = 7

Then

y = 2x + 3

y = 17

Then, the difference between Joy's age and her brother's age.

y - x = 17 - 7 = 10

Thus, the difference between Joy's age and her brother's age is 10.

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The multiplicative inverse of 3/7 will be 7/3. Thus, correct option is B).

The word "inverse" refers to something that has an opposite impact. A number's multiplicative inverse is a number that, when multiplied by the inputted number, produces the result 1, or 1. It is the reciprocal of an integer, as defined by the multiplicative inverse.

1/N or N-1 is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. To put it another way, it is a technique for dividing a number by itself to produce identity 1.

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Note that the correct question is:

What is the multiplicative inverse of 3/7 ?

A) - 3/7

B) 7/3

C) - 7/3

D) 1

55/24 will be the simplified form of the expression 43/8 + 25/12 -31/6.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

given an expression 43/8 + 25/12 -31/6

Simplify given data

=> 43/8 + 25/12 -31/6

=> 5 + 3/8 + 2 + 1/12 - 5 - 1/6

=> 2 + 3/8 + 1/12 - 2/12

=> 2 + 3/8 -1/12

=> 2 + 9/24 -2/24

=> 2 + 7/24

=> 55/24

therefore, The simplified form of the given equation will be 55/24.

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Without the price floor, the equilibrium price is $0.15, and the equilibrium quantity is 200 billion pounds of milk.

Consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the price they actually pay. With an equilibrium price of $0.15, the consumer surplus can be calculated by calculating the area between the demand curve and the price line at $0.15.

The producer surplus can be calculated using an equilibrium price of $0.15 by calculating the area between the supply curve and the price line at $0.15. The producer surplus is the triangular area between the two prices and the supply curve, which intersects the price axis at $0.05.

The sum of the consumer and producer surpluses is the total surplus. Without the price floor, the consumer and producer surpluses would be different than they are now. The total surplus would also differ, reflecting changes in consumer and producer behavior.

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Answer:

12.5%

Step-by-step explanation:

12.5% of 120 is 15 so if you take 15 divided by 120 you would get 0.125 and turned into a percentage is the 12.5%

Answer:

78 Tigers

Step-by-step explanation:

1440=270+15x

1170=15x

78=x

Answer:

Step-by-step explanation:25

Parallelogram II and IV have the same area.

A parallelogram with the same base and height has the same area, regardless of shape. The product of base and height is equal. 

The following is a list of the characteristics of a parallelogram:

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The value of x is 16.2degrees

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given;

(x+14), (9x-4)

Now,

According to supplementary angles;

(x+14)+ (9x-4)=180

10x+18=180

10x= 180-18

10x= 162

x= 16.2

Therefore, in these angles the value of x will be 16.2degree

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A circle not 100 degrees because 360 is a highly composite number, when a circle is drawn it completes a whole loop making it a 360 degrees.

As you surely well know, we modern people like to divide a circle into 360 wedges that resemble pies. We define the angle at the vertex of each of these wedges as being one degree in size. As you presumably well know, we can measure angles in other ways other in degrees. Angles are also measured in radians and, on a very rare occasion, in the enigmatic gradians used by the military (thus the presence of "deg rad grad" buttons on many calculators).

While the reason the 360 degree convention was chosen is unknown to us, we do know roughly when and where it all began (more on that in a moment). We at least know that it originated a very, very long time ago—around 4,000–5,000 years ago with the Babylonians, the Greeks, and possibly other much older peoples.

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Answer:

10 seconds

Step-by-step explanation:

create a proportion

450 copies over 15 seconds = 300 copies over 't' seconds

cross-multiply to get:

450t = 4500

t = 10

it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report if they maintain the same printing rate.

What are arithmetic operations?

Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, division, and others.

Periodical Express printed 450 copies of The Informer in 15 seconds, which means they printed 450/15 = 30 copies per second.

To find out how long it would take to print 300 copies of the Sports Report, we just need to divide the number of copies by the rate of printing.

So, the calculation is 300 / 30 = 10 seconds

Therefore, it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report, if they maintain the same printing rate.

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The square root function is translated so that the endpoint is located at (-7,7), [tex]g(x)= \sqrt{x+7} +7[/tex]  and this can be determined by using the transformation.

The square root parent function is translated so that the endpoint is located at (-7,1).

The following steps can be used to determine the equation that represents this new function:

                       [tex]f(x) =\sqrt{x}[/tex]

[tex]g(x)= \sqrt{x+7} +7[/tex]

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We are aware that x+y=15 (the total number of mugs he buys).The man then purchased 5 large cups and 10 mini mugs .

Let x represent how many little cups he buys.

Let y represent how many large mugs he purchases.

We are aware that x+y=15 (the total number of mugs he buys)

We are also aware of the mugs' costs.

The total price (69) can therefore be deduced to equal 3.50x + 6.80y.

To find x, use the first equation.

x = 15 - y

You can now enter that x-value into the other equation.

69 = 3.50(15 - y ) + 6.80y

Solve for y now.

69 = 52.5 -3.50y + 6.80y

69= 52.5 + 3.3y

16.5 = 3.3y\sy = 5

So, we are aware that the man purchased 5 huge cups.

You can re-insert the y value into x+y=15.

x+5=15\sx+10

The man then purchased 5 large cups and 10 mini mugs!

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Answer:

268268268 + 424424424 = 692692692

So there are 692692692 cans of food

692692692 - 242424 × x = 0

x = Amount of boxes used

x = 2857.36021186...

The rounded answer is 2857.

The area of this triangle in the coordinate plane with coordinates A( 4,5) , B(1,2) and C( 6,2) is equals to the 15 unit². So, option (d) is correct.

The basic formula for the area of a triangle is (1/2) × base × altitude. But we have to calculate the area of a triangle in coordinate geometry. Coordinate geometry is defined as the study of geometry using coordinate points. If coordinates of the triangle are(x₁, y₁), (x₂, y₂), and (x₃, y₃) then the area of the triangle is defined as Area = 1/2[ x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃(y₁ - y₂) ]

We have a triangle ABC in coordinate plane in above figure. The coordinates of triangle are A( 4,5) , B(1,2) and C( 6,2). Here, x₁ = 4 , y₁ = 5 , x₂ = 1 , y₂ = 2 ,x₃ = 6 , y₃ = 2. So, Area of ∆ABC

= 1/2[ 4( 2 - 2)+ 1( 2 - 5) + 6(5 - 2)

= 0 + (-3) + 18 = 15

Hence, the required area is 15 unit².

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Complete question:

What is the area of this triangle in the coordinate plane? See the above figure.

a)25. 0 units²

b) 27. 5 units²

c) 50. 0 units²

d) 15. 0 units²

The rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

What is rectangle ?

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle.

To find the rectangular coordinates for a point in a plane given its polar coordinates, use the following formula:

x = r * cos(θ)

y = r * sin(θ)

Where (r, θ) are the polar coordinates and (x, y) are the rectangular coordinates.

For the point (4.5, -30 degrees), have:

r = 4.5

θ = -30 degrees = -30 * (π / 180) radians

x = r * cos(θ) = 4.5 * cos(-30 * (π / 180)) = 3.9

y = r * sin(θ) = 4.5 * sin(-30 * (π / 180)) = -2.3

So, the rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

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The rectangular coordinates for (4. 5, -30 degrees) are (3.9, -2.3).

The rectangular coordinates for (4.5, -30 degrees) can be found using the following formula:

x = r * cos(θ)

y = r * sin(θ)

where r is the magnitude (or distance from the origin) and θ is the angle in radians.

In this case, r = 4.5 and θ = -30 degrees = -30 * (π/180) radians.

So:

x = 4.5 * cos(-30 * (π/180)) = 4.5 * cos(-π/6) = 4.5 * sqrt(3)/2

y = 4.5 * sin(-30 * (π/180)) = 4.5 * sin(-π/6) = -4.5 / 2

Therefore, the rectangular coordinates are (x, y) = (4.5 * sqrt(3)/2, -4.5 / 2), which is approximately (3.9, -2.3).

Option B (3.9, -2.3) is the right response as a result.

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In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. You will find the formulas, rules, characteristics, charts, deviations, exponentially series, and examples of exponential functions in this article.

Depending on the exponential function, an exponential curve might increase or decrease. A quantity should have either exponential growth or exponential decay if it regularly increases or decreases by a predetermined percentage.

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To solve the equation 2x + 3y = 10 we need to plot the graph for the equation by calculating the intercepts for the same.

Here we see that we are given the equation

2x + 3y = 10

Since we do not have any other equation we will solve this by plotting it on a graph by the intercepts.

Intercepts of both the x and y axes are obtained by equating the other to 0.

Hence to get the x-intercept, we need to equate y to 0

Hence we get

2x = 10

or, x = 5

Hence for the y-intercept, we equate x to 0 to get

3y = 10

or, y = 10/3

By plotting these points and drawing a line through them we will get the graph for the equation.

Now to obtain a unique solution, we need to follow similar steps for the other equation and the intersecting point will give us the solution.

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Complete Question

How to solve 2x + 3y = 10?

Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.

What exactly is a math graph?

A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.

This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.

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Answer:

To find the amount of money after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt)

Where:

A = the amount of money after 10 years

P = the initial investment (24000 birr)

r = the interest rate (4%)

n = the number of times the interest is compounded per year

t = the number of years

In this case, since the interest is compounded annually, n = 1.

So,

A = 24000(1 + 0.04)^(1*10)

A = 24000(1.04)^10

A = 24000(1.46) = 24000*1.46 =35,040 birr

So, after 10 years the total amount of money will be 35,040 birr.

If the area of the triangle is 120 cm^2, the value of x is equal to 6.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = 1/2 × b × h

Where:

According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]

Where:

s = (a + b + c)/2

s = (x + x + 1 + 2x - 1)/2

s = 4x/2

s = 2x

Substituting the parameters into Hero's Formula formula, we have the following;

x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]

x√10 = x√2(x − 1)

√10 = √2(x − 1)

Taking the square of both sides, we have:

10 = 2(x - 1)

10 = 2x - 2

2x = 12

x = 12/2

x = 6.

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The process to graph an absolute value piecewise function is explained below .

Let us consider the Absolute value function as :

y = | x -2 | ;

this absolute function can be written in piecewise wise form as :

⇒ [tex]y =\begin{array}{cc} \{ & \begin{array}{cc} -x+2 & x < 2 \\ x-2 & x\geq 2 \end{array}\end{array}[/tex]  ;

this piecewise function means that the main function divides into two pieces ,

for any input value that is less than 2 , the function"-x+2" will be used , and

for any input value greater than or equal to 2, the function "x-2" , will be used ;

for example : if x = 3 , then ⇒ y = 3 - 2 = 1  ;

and is x = 1 , then ⇒ y = -1 +2 = 1 ;

the points to be plotted are (3,1) and (1,1) .

The graph of this absolute value piecewise function is shown below .

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Answer: 4x -30 > 25 would be your answer

Step-by-step explanation: I hope this helps!

Answer:

C

Step-by-step explanation:

Rectangle Area = Length x Breadth

6.12 = Length x 1.8

Therefore, Length = 3.4m

We can find no solution by the condition; if (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.

A linear equation in two variables is a type of equation in the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. A linear equation with no solution is named an inconsistent pair of linear equations.

Suppose the pair of linear equations is in two variables, x and y.

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers.

Note that, a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.

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The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)

= (2x)2(6x2 + 4x − 3)(5x + 6)

= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)

= 60x4 + 48x3 − 45x2 − 36x

So it will take 945 sec to solve 21 math problem.

As per the data given in the above question are as bellow,

The details provided are as bellow,

Moria solve 15 math question in 20 minutes,

We have to determine how long will it take her to solve 21 math problem?

First taking how much time its take to solve one question ,

So, Total number of question divide the total time we get,

Substitute the value in above equation we get,

=15* 60 =900 Sec

=900/20

=45 sec

So the time taken to solve 21 question will be,

=45*21

=945 sec

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