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3 years ago

Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.

Mathematics

2 answers:

mars1129 [50]3 years ago

7 0

Given that :- 

Width of garden is 4 meters

Perimeter of garden is 26 meters

To Find :- 

Length of rectangular garden.

Solution :- 

→ Perimeter = 2( Length + breadth)

→ 26 = 2 ( Length+ 4 )

→ 26/2 = Length + 4

→ 13 = Length + 4

→ Length = 13 -4

→ Length = 9 meters. 

So the Length of Lisa's garden is 9 meters .

Amanda [17]3 years ago

6 0

Answer:

Step-by-step explanation:

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3 years ago

Using the method of completing the square, put each circle into the form

tatiyna

Answer:

Standard form: $(x-\frac{1}{2})^2 + (y-0)^2 = 15$

Center: $(\frac{1}{2}, 0)$

Radius: $r =\sqrt{15}$

Step-by-step explanation:

The equation of a circle in the standard form is

$(x-h)^{2} + (y-k)^{2} = r^{2}$

Where the point (h, k) is the center of the circle

To transform this equation $4x^{2} -4x + 4y^{2} - 59 = 0$ this equation in the standard form we use the method of square.

First, we group similar variables

$(4x^{2} -4x) + (4y^{2}) - 59 = 0$

Divide both sides of equality by 4

$(x^{2} -x) + (y^{2}) - 14.75 = 0$

Now we complete square for variable x.

Take the coefficient "b" that accompanies the variable x and divide by 2. Then, elevate the result to the square:

$b =-1\\\\\frac{b}{2}= \frac{-1}{2}= -\frac{1}{2}\\\\(\frac{b}{2})^2= (-\frac{1}{2})^2 = \frac{1}{4}$

Now add $(\frac{b}{2})^2$ on both sides of the equality

$(x^{2} -x +\frac{1}{4}) + (y^{2}) - 14.75 = (\frac{1}{4})$

Factor the expression and simplify the independent terms

$(x-\frac{1}{2})^2 + (y^{2}) = 15$

$(x-\frac{1}{2})^2 + (y-0)^2 = 15$

Then

$h =\frac{1}{2}\\\\k=0$

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radius $r =\sqrt{15}$

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3 years ago

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3 years ago

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Solution:

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If the starting point of the inequality is half shaded, the sign will be < or >.
If the starting point of the inequality is fully shaded, the sign will be ≤ or ≥.

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The inequality will either have an < or > sign.
The blue line tells us that the value of x must be greater than -1.

This clearly tells us that the inequality is x > -1

In conclusion:

Option C is correct.

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2 years ago

Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximati

pochemuha

Answer: 8 (Pi - sqrt(3))

Discussion:

The area of the shaded region is that of the semicircle minus the area of the triangle..

Area of semicircle = 1/2 * Pi * R^2

Where R^2 is the square of the radius of the circle. In our case, R ( = OC)

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(1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi

Area of triangle.

First of all, angle ACB is a right angle ( i.e. 90 degrees).

* This is the Theorem of Thales from elementary Plane Geometry. *

so by Pythagoras

AC^2 + BC^2 = AB^2

But CB = 4 (given) and AB = 4*2 = 8 ( the diameter is twice the radius).

Substituting these in Pythagoras gives

AC^2 + 4^2 = 8^2 or

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Hence AC = sqrt(48) = sqrt (16*3) = 4 * sqrt(3)

We are almost done! The area of the triangle is given by

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3 years ago