Describe the transformation

Step-by-step explanation:

[tex]area \: of \: rectangle \: = 60 \: {yards}^{2} \\ \therefore \: (w + 4) \times \: w = 60\\ \\ \therefore \: {w}^{2} + 4w -60 = 0 \\ \\ \therefore \: {w}^{2} + 10w - 6w -60 = 0 \\ \\ \therefore \: w({w} + 10) - 6(w + 10)= 0 \\ \\ \therefore \: ({w} + 10) (w- 6)= 0 \\ \therefore \: {w} + 10 = 0 \: or \: w- 6 = 0 \\ \therefore \: {w} = - 10 \: or \: w = 6 \\ \because \: sides \: of \: rectangle \: cant \: be \: negative \\ \therefore \: w \neq \: - 10 \\ \\ \therefore \: w = 6 \\ \\ \therefore \: w + 4 = 6 + 4 = 10 \\ \\ length \: of \: rectangle \: = 10 \: yards.[/tex]

The length of a rectangle is 10 yards, and its width is 6 yards. The rectangle's area is 60 square yards. The length is 4 yards more than the width.

Let's call the width of the rectangle "W" in yards. According to the information given, the length of the rectangle is 4 more than the width, so the length can be represented as "W + 4" yards.

The formula for the area (A) of a rectangle is:

A = Length × Width

In this case, we know that the area is 60 square yards, so we can set up the equation:

60 = (W + 4) × W

Now, we can solve for the width (W). First, expand the equation:

60 = W^2 + 4W

Next, rearrange the equation to set it equal to zero:

W^2 + 4W - 60 = 0

Now, we can solve this quadratic equation for W. You can do this by factoring, completing the square, or using the quadratic formula. In this case, I'll use the quadratic formula:

W = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = 4, and c = -60. Plug these values into the formula:

W = (-4 ± √(4^2 - 4 * 1 * (-60))) / (2 * 1)

W = (-4 ± √(16 + 240)) / 2

W = (-4 ± √256) / 2

W = (-4 ± 16) / 2

Now, you have two potential solutions for W:

1. W = (-4 + 16) / 2 = 12/2 = 6

2. W = (-4 - 16) / 2 = -20/2 = -10

Since the width of the rectangle cannot be negative, we take the positive value, which is W = 6 yards.

Now that we know the width, we can find the length, which is W + 4:

Length = 6 + 4 = 10 yards

So, the length of the rectangle is 10 yards.

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Answer: 48 vegetables

Step-by-step explanation:

30 vegetables

Increase is by 60% = 0.6 x 30= 18

30+18= 48 vegetables

Answer:

48

Step-by-step explanation:

30 x 60% (.60) = 18.

30 + 18 = 48

Answer:

True

Step-by-step explanation:

Answer: True

Step-by-step explanation:

In electromagnetic waves, the more the work, the greater the energy expended.

Answer: 42 nickles 19 quarters

hope this was helpful

Camille has 42nickels and 19 quarters.

The price depends on how much amount of product one has/consumes.

Let, Camille has 'y' no. of nickels.

Therefore, she has (61-y) no. of quarters.

We know that,

1 nickel = 5cents

1 quarter =25 cents

$6.85 = 685cents (as 1 dollar = 100cents)

now,

5*y+25*(61-y)=685

or,5y-25y=685-1525

or, 20y = 840

or, y= 42

Therefore, Camille has 42 nickels and (62-41)=19 quarters.

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Answer:

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Step-by-step explanation:

The following are the formulas used to find the area and the perimeter of a rectangle:

Area = L · W

Perimeter = L + L + W + W

If you group common variables, you can simplify the formula used to find the perimeter down to:

Perimeter = L + L + W + W

Perimeter = 2L + 2W (Since you're adding 2 of each)

Using these formulas, we can insert our values into them. We know that the rectangle has an area of 56 square inches meaning:

L · W = 56

We know that the rectangle has a perimeter of 36 inches meaning:

2L + 2W = 36

Answer:

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Step-by-step explanation:

Answer:

1/26

Step-by-step explanation:

the probably is 1/26 becasue there is 26 letter in the alphabet

Answer:

y = 7/3 x + 2

Step-by-step explanation:

y = mx+b is the slope intercept form of a line

where m is the slope and b is the y intercept

Substituting in what we know

y = 7/3 x + 2

Answer:

Step-by-step explanation:

i. y = 60 ÷5

The correct expression would be 5y = 60, so 12  sheets of paper do Andre's notebooks contain.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Each notebook contains 60 sheets of paper. Andre has 5 notebooks.

We need to find the number of sheets of paper do Andre's notebooks contain.

Therefore, using unitary method

60 sheets of paper = 5 notebooks.

y  sheets of paper = 5y/ 60 notebooks.

= 60/5 = 12

The answer is 5y = 60

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Answer:

Option D, 7xy^5 + 2y^2 - 10

Step-by-step explanation:

Step 1:  Pull out 3xy from all of the top

[tex]\frac{3xy(7xy^5+2y^2-10)}{3xy}[/tex]

The 3xy on top and the 3xy cancel to make:  7xy^5 + 2y^2 - 10

Answer:  Option D, 7xy^5 + 2y^2 - 10

Answer:

y = 6,x = 2

Step-by-step explanation:

Answer:y = 6,x = 2

Step-by-step explanation:Geometric figure: Straight Line

 Slope = -6.000/2.000 = -3.000

 x-intercept = 6/3 = 2

 y-intercept = 6/1 = 6.00000

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    12*x+4*y-(24)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  12x + 4y - 24  =   4 • (3x + y - 6)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   3x+y-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x+y-6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 6/1 so this line "cuts" the y axis at y= 6.00000

 y-intercept = 6/1  =  6.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000

 x-intercept = 6/3  =  2

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 6.000 and for x=2.000, the value of y is -0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.000 - 6.000 = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -6.000/2.000 = -3.000

Geometric figure: Straight Line

 Slope = -6.000/2.000 = -3.000

 x-intercept = 6/3 = 2

 y-intercept = 6/1 = 6.00000

Answer:

40°  

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

Sam

Step-by-step explanation:

Sam: Longest ski trail >3x    x = shortest ski trail

Eli: Longest ski train< 3x

Sam is correct because the longest ski trail has to be greater than the shortest and it can't be less than.

Answer:

[tex]946.4\ m[/tex]

Step-by-step explanation:

Let

h(t) ---> the height of an object in meters

t ----> the time in seconds

we have

[tex]h(t)=-2.6t^2+40t+800[/tex]

For t=6 sec

substitute in the quadratic equation  the value of t and solve for h

[tex]h(6)=-2.6(6)^2+40(6)+800[/tex]

[tex]h(6)=946.4\ m[/tex]

Answer:

Perimeter: 16 centimeters

Area: 15 square centimeters

I hope this helps! :)

Answer:

Step-by-step explanation:

so, the perimeter is 5+5+3+3 which is 16

and  the area is 5 x 3 so it is 15

Answer: x=46

Step-by-step explanation:

Answer:

46 degrees

Step-by-step explanation:

There are 180 degrees in a straight angle. Take 134 and subtract it from 180 to get your answer of 46 degrees.

Answer:

18 square feet

Step-by-step explanation:

the table was most likely 6 by 6 before getting cut. that is an area of 36 you could half that making 18 or make one of the 6s a 3 so it is 3 by 6 after the table is cut.

Answer:

2q+y+5

Step-by-step explanation:

Simplify the expression

Answer:

x=4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helps!!! Brainliest is appreciated.

x−3=−x+5

Add x to both sides.

x−3+x=−x+5+x

2x−3=5

Add 3 to both sides.

2x−3+3=5+3

2x=8

Divide both sides by 2.

2x /2 = 8 /2

x= 4

Answer:

x-22

Step-by-step explanation:

The expression representing the value 22 less than x is x - 22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given statement is that 22 is less than x. The expression will be written as below,

E = 22 less than x

E = x - 22

Therefore, the expression representing the value 22 less than x is x - 22.

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Answer: 2

x+x=8-2

2x=4

Divide:

4/2=2

x=2

Answer: 5 and 3

Step-by-step explanation:

From the question,

Let the first number be x

And the second be y

x + y= 8

x- y= 2

Add the equations

x + y + x - y = 8 + 2

2x= 10

x=5

Slot the value of x into any of the equations: x +y = 8

5+ y= 8

y= 8 - 5

y = 3

Answer:

12

Step-by-step explanation:

3X4=12

Answer:

8 tablespoons

Step-by-step explanation:

its is 8 because 4 teaspoons per dozen and there are 6 dozens so 4 times 6 is 24, then 24 divided by 3 because thats how many teaspoons are in 1 tablespoon so its 8 tablespoons

Answer:

Step-by-step explanation:

Let's say we have 2x-y=4, and 4x-3=5y. So, elimination is basically what the name is. You eliminate one variable by subtracting and then plug in that variable to find the other one. So,

4x-3=5y

2x-y=4

Multiply 2x-y=4 by 2, to make it equal to the x value in the top.

4x-3=5y

-

4x-2y=8

Now, you can subtract the equations. You Eliminate the 4x, then you get

-3-2y=5y-8

Then you solve for y

y=7/5

then you plug y into the equation

4x-3 = (7/5)5

4x-3=7

4x=10

x=5/2

And you have your solution ----> (5/2, 7/5) is where the lines intersect.

Hope that helps!

arc ABC = 4π[tex]\frac{134}{180}[/tex]

Step-by-step explanation:

Given,

∠BOA = 51° and ∠AOC=83°

We take O as the center

So, ∠BOC = 51°+83° = 134°

To find the arc ABC

Formula,

The relation between arc and radius is, s = rθ where s be the arc and θ be the angle measured in radian]

θ degree = θΠ×[tex]\frac{1}{180}[/tex] in radian

Hence,

arc ABC = 4π[tex]\frac{134}{180}[/tex]

Answer:

-4 +3x = -2

Step-by-step explanation:

the equation will give x = 2/3

3x = -2 +4

3x = 2

x = 2/3

brainliest please :)

When x is replaced by 2/3.in the equation, it satisfies the equation, making 2/3 the solution that satisfies the equation x - (2/3) =0

To create a subtraction equation with one variable that has a solution of  2/3 , follow these steps:

Step 1: Define a variable. Let's use x as the variable.

Step 2: Formulate the equation using subtraction. The equation should represent a situation where when 2/3  is subtracted from a number, the result is zero.

Mathematically, the equation can be written as:

x - (2/3) =0

Step 3: To verify that x - (2/3) is the solution, solve the equation by isolating the variable x.

x=2/3

This equation represents a subtraction scenario where 2/3 is subtracted from x resulting in zero. When x is replaced by 2/3.in the equation, it satisfies the equation, making 2/3 the solution that satisfies the equation x - (2/3) =0

Complete Question:

Write the equations described below.a subtraction equation with one variable that has a solution of 2/3.

Answer:

2000

Step-by-step explanation:

2000 is closer than 3000.

Final answer:

The Sears Tower has 110 stories. We found this by setting up an equation with the given information and solving for the number of stories in the Sears Tower.

Explanation:

To find out how many stories the Sears Tower has, we need to set up an equation using the information provided.

We know that Hong Kong's tallest building (International) is 88 stories tall, and the combined height of all the buildings stacked on top of each other is 300 stories. Let's assign the variable S to represent the number of stories in the Sears Tower and E to represent the number of stories in the Empire State Building. According to the question, the Sears Tower is eight stories taller than the Empire State Building, so we can express this relationship as S = E + 8.

Now, let's add up the stories of all three buildings: Hong Kong's International + Sears Tower + Empire State Building = 300. Substituting the given information and our variable S, we get the equation 88 + S + (S - 8) = 300.

Let's solve this equation:

Therefore, the Sears Tower has 110 stories.

Answer: 9

Step-by-step explanation:

1/2 * -12= -6

5*-3= -15

-15- (-6)=  -9

Answer:

The numbers are 12 and 32.

Step-by-step explanation:

x = One number

x - 20 = Another number

3x - (x - 20) = 84 (If the lesser number is subtracted from three times the greater number, the difference is 84)

Let's solve for x, this way:

3x - (x - 20) = 84

3x - x + 20 = 84

2x = 84 - 20 (Subtracting 20 at both sides)

2x = 64

x = 64/2

x = 32 ⇒ x - 20 = 12

For the given problem, by denoting the lesser number as 'x', we can form and solve an algebraic equation to find 'x=12' and 'x+20=32', which are the lesser and the greater numbers respectively.

This problem involves the concepts of algebraic equations. Let's denote the lesser number as 'x'. Therefore, the greater number becomes 'x+20' because it is 20 more than the lesser number. The problem states that three times the greater number subtracted by the lesser number is 84. So, we can translate that into the equation: 3*(x+20) - x = 84.

Solving this equation we get: 3x + 60 - x = 84, which simplifies further to 2x + 60 = 84. Deducting 60 from both sides gives 2x = 24. Finally, dividing by 2 gives x = 12 which is the lesser number. So the greater number becomes x + 20 = 12 + 20 = 32.

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