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alexira [117]
3 years ago
5

Factor completely 4x2 - 121

Mathematics
2 answers:
zepelin [54]3 years ago
5 0

Answer:-113

Step-by-step explanation:

You do 4x2 = 8 and then take 121 away from 8 which is -113

anzhelika [568]3 years ago
4 0

Answer:

(2x+11)x (2x-11)

Step-by-step explanation:

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Pretty Pavers company is installing a driveway. Below is a diagram of the driveway they are
prohojiy [21]

Answer:

The most correct option is;

(B) 958.2 ft.²

Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

The dimension of the diameter of the small semicircle = 10·√3

Radius of the small semicircle = Diameter/2 = 10·√3/2 = 5·√3

Area of the small semicircle = (π·r²)/2 = (π×(5·√3)²)/2 = 117.81 ft.²

Similarly;

The dimension of the diameter of the large semicircle = 10·√3 + 2 × 6 × √3

∴ The dimension of the diameter of the large semicircle = 22·√3

Radius of the large semicircle = Diameter/2 = 22·√3/2 = 11·√3

Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

Area of rectangle = 11·√3 × 17·√3 = 561

Area, A of large semicircle cutting into the rectangle is found as follows;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2

Where:

\theta = 2\times tan^{-1}( \frac{The \, number \, of  \, vertical  \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle}{The \, number \, of  \, horizontal \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle} )

\therefore \theta = 2\times tan^{-1}( \frac{10\cdot \sqrt{3} }{5\cdot \sqrt{3}} ) = 2.214

Hence;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (2.214 - sin2.214) \times (11\cdot\sqrt{3} )^2 = 128.3 \, ft^2

Therefore; t

The area covered by the pavers = 561 - 128.3 + 570.2 - 117.81 = 885.19 ft²

Therefor, the most correct option is (B) 958.2 ft.².

4 0
2 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= root 2 cm.
Nata [24]

Given CD is an altitude such that AD=BC , AB=3 cm and CD= √2 cm.

Let AD=x, Since given AB=3

                                     AD+DB=3

                                       x+DB = 3

                                        DB = 3-x

Since ΔBCD is rght angle triangle, let's apply Pythagoras theorem

BC^{2} = DB^{2} +CD^{2}

BC^{2} = (3-x)^{2} +(\sqrt{2} )^{2}

BC^{2} =(3-x)^{2} +2

Since given AD=BC,let us plugin BC=x in above step.

x^{2} =(3-x)^{2} +2

x^{2} =9-6x+x^{2} +2

6x=11

x=\frac{11}{6}

Now we know AD=x=\frac{11}{6} and given CD=√2.

Let us apply Pythagoras theorem for ΔACD

AC^{2} =AD^{2} +DC^{2}

AC^{2} = (\frac{11}{6} )^{2} +(\sqrt{2} )^{2}

AC^{2} =\frac{193}{36}

AC=\sqrt{\frac{193}{36} } = 2.315cm

3 0
3 years ago
Draw the image of ∆ABC under the dilation with scale factor 4 and center of dilation (-3, -4).
castortr0y [4]

Answer:

ABC

Step-by-step explanation:

7 0
3 years ago
Work out the value of x.
Alona [7]
2x+3x=180
5x=180
x=180/5
x=36
3 0
3 years ago
The equation x+53=15 can be solved by performing two operations on both sides.
Wewaii [24]
Hey!


You're right! This equation can definitely be solved by performing two operations on both sides. Let me show you how it's done.

First, let's write out our equation.

<span><em>Original Equation :</em>
</span>x + 53 = 15

Now that that's done, we'll be performing two operations on both sides. The operation we'll want to do is subtracting both sides of the equation by 53. We do this to get x on its own.

<em>Original Equation :</em>
x + 53 = 15

<em>New Equation {Added Subtract 53 to Both Sides} :</em>
x + 53 - 53 = 15 - 53

Now we have to solve the equation. Let's do the left side first.

<em>Left Side of the Equation :</em>
x + 53 - 53 

<em>Left Side of the Equation {Solved} :</em>
x

Now, we'll solve the right side of the equation.

<em>Right Side of the Equation :</em>
15 - 53

<em>Right Side of the Equation {Solved} :</em>
-38

Now we can put both solutions to both sides of the equation together.

<em>New Equation :</em>
x = -38

Since this cannot be simplified any farther, this is our final answer. And that's it!

<em>So, now we know that in the equation x + 53 = 15,</em>  x = -38

Hope this helps!


- Lindsey Frazier ♥
3 0
2 years ago
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