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Kitty [74]
3 years ago
7

1. find the sum of the measures of exterior angles, one at each vertex, of an octagon.

Mathematics
2 answers:
love history [14]3 years ago
5 0
For #1, C. 1080, For #2, B. 7, For #10, I think its because of the reflexive property (honestly, Google it just to be safe) , And for #11, A Rhombus, Having trouble remembering why but I know its not a rectangle or square.

QveST [7]3 years ago
4 0

Answer: First question: b. 360°

Second question : b. 7

Third question: Yes, it is a parallelogram.

Fourth question:  It is a rhombus.

Step-by-step explanation:

1. Since,  The sum of exterior angles in a polygon is always equal to 360 degrees.

And, an octagon is also a polygon.

Therefore the sum of the all exterior angle of an octagon = 360°

2. Since, the sum of the interior angles of a polygon of n sides is (n-2)×180°

But here (n-2)×180°=900

⇒ n-2 = 5 ( After dividing both sides by 180° )

⇒ n = 5 + 2 = 7

Thus,  If the sum of the interior angles of a polygon is 900° then the polygon has 7 sides.

10. Since, In triangles XNY and WNZ,

XN≅NZ (Given)

NY≅NW ( Given)

∠XNY≅∠WNZ ( vertically opposite angles)

Thus, By SAS postulate of congruence,

ΔXNY≅ΔWNZ,

By CPCTC, XY≅WZ

Similarly, Δ XNW≅ Δ YNZ,

By CPCTC, XW≅YZ

Therefore, In quadrilateral XYZW, Opposite sides are equal.

⇒ XYZW is a parallelogram.

11. Let ABCD is a parallelogram,

In which AC is a diagonal.

Also, AB = CD and AD= BC ( By the property of parallelogram)

And, It is given that ∠DAC=∠DCA = 72°

Therefore ADC is an isosceles triangle ( By the property of isosceles triangle)

Thus, AD=DC

Similarly, ABC is an isosceles triangle.

Thus, AB= BC

Thus, AB=BC=CD=DA.

Also, ∠ADC=∠ABC  ( By the property of parallelogram)

Therefore, In ABCD all sides are equal and Opposite angles are equal.

⇒ ABCD is a rhombus. ( The diagram is shown below)



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Select the two binomials that are factors of 64x^2 – 36.
lara [203]
64x² - 36 factors to be (8x + 6)(8x - 6)

Option C is your answer. 

HOWEVER, I cannot tell what the operation is supposed to be performed because of the way it is showing up above (see attached pic). So I can also just simplify it.

64x² - 36 becomes 4(16x² - 9) or 4(4x - 3)(4x + 3)

64x² + 36 becomes 4(16x² + 9)

7 0
3 years ago
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A pound is approximately 0.45 kilogram. A person weighs 86 kilograms. what is the person's weight, in pounds, when rounded to th
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Answer:

C. 193 lb

Step-by-step explanation:

To find their weight in pounds, divide their weight in kilograms by 0.45:

86/0.45

= 191.11

This is closest to answer choice C, so C is the correct answer.

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3 years ago
consider the cube shown below identify the two dimensioal shape of the cross section if the cube is sliced horizontally
AnnyKZ [126]
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2 years ago
The 16th term of an A.P. is 40 and the sum of the first 5 terms is 5. Find the sum of the first 50 terms.
KiRa [710]

Answer:

The sum of first 50 terms is 3425.

Step-by-step explanation:

Let the first tem of A.P be 'a' and it's common difference be 'd'

Thus the 16th term of the A.P is given by

T_n=a+(n-1)d\\\\40=a+15d..........(i)

Now we know that the sum of first 'n' terms of the A.P is given by

S_n=\frac{n}{2}[2a+(n-1)d]\\\\5=\frac{5}{2}[2a+4d]\\\\1=a+2d..........(ii)

Solving equation 'i' and 'ii' simultaneously we get

40=1-2d+15d\\\\13d=39\\\\\therefore d=3

Thus a=1-2\times 3=-5

Thus the sum of first 50 terms euals

S_{50}=\frac{50}{2}[2\times -5+(50-1)3]\\\\S_{50}=3425.

7 0
3 years ago
Read 2 more answers
Solve the problem. If s is a distance given by s(t) = + + 40 + 10. find the acceleration, alt). Q ald) = 10 ald) = 2t + 4 O alt)
QveST [7]

Answer:

C

Step-by-step explanation:

Remember that if s(t) is a position function then:

v(t)=s'(t) is the velocity function and

a(t)=s''(t) is the acceleration function.

So, to find the acceleration, we need to solve for the second derivative of our original function. Our original function is:

s(t)=t^2+4t+10

So, let's take the first derivative first with respect to t:

\frac{d}{dt}[s(t)]=\frac{d}{dt}[t^2+4t+10]

Expand on the right:

s'(t)=\frac{d}{dt}[t^2]+\frac{d}{dt}[4t]+\frac{d}{dt}[10]

Use the power rule. Remember that the derivative of a constant is 0. So, our derivative is:

v(t)=s'(t)=2t+4

This is also our velocity function.

To find acceleration, we want to second derivative. So, let's take the derivative of both sides again:

\frac{d}{dt}[s'(t)]=\frac{d}{dt}[2t+4]

Again, expand the right:

s''(t)=\frac{d}{dt}[2t]+\frac{d}{dt}[4]

Power rule. This yields:

a(t)=s''(t)=2

So, our answer is C.

And we're done!

6 0
3 years ago
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