New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters.The new rectangular garden will have an area that is 25% more that the original square garden. Write an equation that could be used to determine the length of a side of the original square garden.
Determine the area, in square meters, of the new rectangular garden.
Answers
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= a² + 0.25·a²
= 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(a - 3)
1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
Therefore, the equation that could be used to determine the length of a side of the original square garden is:
2a² - 6a = 1.25a²
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
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Answer:
Step-by-step explanation:
Hello
I think I can help you with this
the area of a circle is given by.
where π is the relationship between the length of a circle and its diameter in Euclidean geometry, it is an irrational number and one of the most important mathematical constants.
Step one
Let
r=23 yd
π=3.14
Step two
put the values into the equation
I hope it helps , Have a great day.
The area of circle having radius 23yards is 1661.06 yd² .
Given,
Radius = 23 yard
Here,
Area of a circle = π × r²
r = radius of circle.
r=23 yd
So,
Substitute the values,
Area of circle = 3.14 × (23)²
Area of circle = 1661.06 yd²
Know more about area of circle,
#SPJ6
-56
76
88
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Answer: B) -56
Step-by-step explanation: In a quadratic equation, the discriminant helps tell you the number of real solutions and it is:
To calculate the discriminant of the given equation, we need to write it in the standard form (we equal it to zero):
here we can see that a=6; b=-4; and c=3
so the discriminant would be:
=
16-72=-56
The discriminant is found using
b²-4ac, after the quadratic is in standard form. First, we will add 6x² to both sides to write it in standard form:
3-4x=-6x²
3-4x+6x²=-6x²+6x²
6x²-4x+3=0
We can now see that b=-4, a=6 and c=3:
(-4)²-4(6)(3)
16-72
-56
Answers
Answer:
I believe it is 27
Step-by-step explanation:
Answer: x = 27
Step-by-step explanation:
To solve this, first insert 4 for y:
3x - 4 * 4 = 65
Next, multiply the numbers:
3x - 4 * 4 = 65
3x - 16 = 65
Next, move the constant to the right and change its sign:
3x - 16 = 65
3x = 65 + 15
Next, add the numbers:
3x = 65 + 16
3x = 81
Finally, divide both sides of the equation by 3:
3x = 81
3x ÷ 3 = 81 ÷ 3
(Any expression divided by itself equals 1)
3x ÷ 3 = 81 ÷ 3
x = 81 ÷ 3
x = 81 ÷ 3
x = 27
Answers
Answer:
5.1 IS less than 5.06
Step-by-step explanation:
5.1 is less than 5.06 because you can always add and take away the zero if you wanted to.
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