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2 years ago

What is the measure of EGF? What is the measure of CGF?

Mathematics

1 answer:

noname [10]2 years ago

8 0

Answer:

65 degree, 15 degree

Step-by-step explanation:

In triangle GEF,

∠E = ∠G (Given)

Let's say,

∠E = ∠G = x

∠E + ∠G + ∠F = 180 (Angle sum property of Triangle)

=>x + x + ∠F = 180

=>2x + ∠F = 180

=>2x + 50 = 180

=>2x = 180-50

=> 2x =130

=> x = 130/2

=> x = 65

=>∠E = ∠G = 65

=>∠GEF = ∠EGF = 65 Degree

∠EGF + ∠CGF = 180

=>65 + ∠CGF =180

=>∠CGF = 180 - 65

=> ∠CGF = 15

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)

notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A mathematical induction consists in only 2 steps:

First step: Show the proposition is true for the first one valid integer number.

Second step: Show that if any one is true then the next one is true

Finally, if first step and second step are true, then the complete proposition is true.

So, given $2*n^3+3*n^2+n$

First step: using and replacing n=2 (the first valid integer number >1)

$2*(2)^3 +3*(2)^2+2=30$

$\frac{30}{6} =5$

As the result is an integer number, so the first step is true.

Second step: using any next number, $n+1$ , let it replace

$2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)$

As the First step is true, we know that

$2*n^3+3*n^2+n$ $=6*k$ ,

So let it replace in the previous expression

$6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]$

Finally

$\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)$

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0

3 years ago

Can someone help me pls

Artist 52 [7]

Answer:

PΔJKL=66

Step-by-step explanation:

so we are given the line segments JK, KL, and LJ which are tangent to k(O), and also that JA=9, AL=10, and CK=14

JL=JA+AL (parts whole postulate)

JL=9+10=19 (substitution, algebra)

JA=JB=9 (tangent segments from the same point are congruent)

CK=KB=14 (tangent segments from the same point are congruent)

JK=JB+KB (parts whole postulate)

JK=9+14=23 (substitution, algebra)

LA=LC=10 (tangent segments from the same point are congruent)

LK=LC+CK (parts whole postulate)

LK=10+14=24 (substitution, algebra)

Perimeter of ΔJKL=LK+KL+LJ (perimeter formula for triangles)

Perimeter of ΔJKL=23+24+19=66 (substitution, algebra)

3 0

2 years ago

Help please:) i’m trying to get all of this work completed but i just don’t understand it

leva [86]

$\pi r^{2} =\\3,14*4^{2} \\3,14*16\\=50.24$

8 0

2 years ago

Read 2 more answers

What value of x makes the equation true? -1=1 – 4(-5+4x) – 4x

cluponka [151]

Answer:

x = 11/10

Step-by-step explanation:

we have from statement:

-1=1 - 4(-5+4x) – 4x

we apply distributive property:

-1 = 1 -4*(-5) -4*(4x) -4x

so we have:

-1= 1+20 -16x -4x

-1 = 21 -20x

-22=-20x

so we have:

x=22/20

x=11/10

we can substitute the x value found:

-1 = 1 - 4(-5+4*(11/10)) – 4*(11/10)

-1 = 1+20 -17.6 -4.4

-1 =21 -22

so we have:

-1 = -1

4 0

3 years ago

Alex needs to buy compressed air to fill empty cylindrical tanks for his tire store. Each tank is 12 feet deep and has a radius

agasfer [191]

---------------------------------------
Formula
---------------------------------------
Volume = πr²h

---------------------------------------
Find Volume of one tank
---------------------------------------
Volume of 1 tank = πr²h
Volume of 1 tank = 3.14 x 6² x 12
Volume of 1 tank = 678.24 ft³

---------------------------------------
Find Volume of 5 tanks
---------------------------------------
Volume of 1 tank = 678.24
Volume of 5 tanks = 678.24 x 5
Volume of 5 tanks = 3391.2 ft³

---------------------------------------
Answer: 3391.2 ft³
---------------------------------------

4 0

3 years ago