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larisa [96]
3 years ago
15

The hexagon is made from a rectangle and two identical triangles.

Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0

Answer:

The area of the hexagon is 108 cm².

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure we get

Length of rectangle = 12 cm

width of rectangle = 5 cm

It is given both triangles are identical.

Base of each triangle = 12cm

Height of each triangle = (13-5)/2 = 4 cm

Area of rectangle is

Area=length\times width=12\times 5=60

Area of rectangle is

Area=\frac{1}{2}\times base\times height

Area=\frac{1}{2}\times 12\times 4=24

Area of one triangle 24 cm². So, area of both triangle is

2\times 24=48

Area of hexagon = Area of rectangle + Area of both triangles

                            = 60+48

                            = 108

Therefore, the area of the hexagon is 108 cm².

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3 years ago
What are the coordinates of the focus of the parabola?
Dima020 [189]
This is a tough one.  the general form of a parabola is (x-h) ^{2} =4p(y-k), where h and k are the coordinates of the vertex and p is the distance from the vertex to the focus.  In order to get our parabola into this form and solve for p (which will give us our focal point), we have to complete the square.  Set the parabola equal to 0, then move over the constant to get this equation: - \frac{1}{16}  x^{2} -x=-2.  In order to complete the square, the leading coefficient on the squared term has to be a +1.  Ours is a - \frac{1}{16}, so we have to factor that out of the x terms.  When you do that you end up with - \frac{1}{16} ( x^{2} +16x)=-2.  Now we can complete the square by taking half the linear term, squaring it, and adding it to both sides.  Our linear term is 16, so half of 16 is 8 annd 8 squared is 64.  HOWEVER, on the left side, that - \frac{1}{16} is still hanging out in front, which means that when we add in 64, we are actually adding in - \frac{1}{16} *64 which is -4.  Now here's what we have: - \frac{1}{16} ( x^{2} +16x+64)=-2-4which simplifies to - \frac{1}{16}( x^{2} +16x+64)=-6.  Creating the perfect square binomial on the left was the point of this (to give us our vertex), so when we do that we have - \frac{1}{16} (x+8) ^{2} =-6.  Now just for simplicity, we will take baby steps.  Move the -6 back over by addition and set it back equal to y: - \frac{1}{16}(x+8) ^{2}+6=y.  Now we will work on getting into standard form.  Move the 6 back over by the y (baby steps, remember) to get - \frac{1}{16} (x+8) ^{2} =y-6.  Multiply both sides by -16 to get our "p" on the right: (x+8) ^{2} =-16(y-6).  We need to use our "4p" part of the standard form to find the p, which is the distance from the vertex to the focus. 4p=-16, and p = -4.  That means that the focus is 4 units below the vertex.  Let's figure out what the vertex is.  From our equation, the vertex is ( -8, 6), and since this is an upside-down opening parabola, the focus will be aligned with the x-coordinate of the vertex.  So our focus lies 4 units below 6 (6 is the y coordinate of the vertex which indicates up and down movement), so our focus has coordinates of (-8, 2), the first choice above.  Told you it was a tough one!  These conics are quite challenging!
7 0
3 years ago
The line 2x + 3y - k = 0 bisects the line segment joining the points A(4, -3) and B(-2, 5). Find the value of k.​
lisabon 2012 [21]

Answer:

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3 0
2 years ago
What two numbers multiply to 44 and add up to 12?
djverab [1.8K]
This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.      x*y = 44 ..........(a)

Add up to 12.      x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44   

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.       

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.   

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0,  a = 1, b = -12, c = 44 

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a


x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)    

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number.  Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2      or     (12 - √-32 )/ 2   

x = (12 + 4i√2 )/ 2              (12 - 4i√2 )/ 2 

x = 12/2 + (4i√2)/2                12/2 - (4i√2)/2

x = 6 + 2i√2            or         6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2,  y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2,  y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2


x = 6 + 2i√2,  y = 6 - 2i√2

x = 6 - 2i√2,  y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2
8 0
3 years ago
Read 2 more answers
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