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4 years ago

What is the sum of the angle measures in a 22-gon? 360° 2,200° 3,600° 3,960°

Mathematics

1 answer:

Elina [12.6K]4 years ago

4 0

Answer:

Option 3rd is correct

the sum of the interior angles measures in a 22-gon is, 3600°

Step-by-step explanation:

Sum of the interior angles of a polygon of n -sides is given by:

$\tetx{Sum} = (n-2) \times 180^{\circ}$ ....[1]

As per the statement:

Given that:

n = 22-gon

Substitute in [1] we have;

$\text{Sum} = (22-2) \times 180^{\circ}$

⇒ $\text{Sum} = 20 \times 180^{\circ}$

⇒ $\text{Sum} =3600^{\circ}$

Therefore, the sum of the interior angles measures in a 22-gon is, 3600°

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Point B is on line AC so that AB : BC = 2 : 1. Point D is on line AB so that AD : DB = 3 : 2. Find AD : DC

Leya [2.2K]

Firstly, we will draw figure

Let's assume

length of AC=x

we have

AB : BC = 2 : 1

so,

$AB=\frac{2}{3} x$

$BC=\frac{1}{3} x$

Point D is on line AB

and

$AB=\frac{2}{3} x$

AD : DB = 3 : 2

so, we get

$AD=\frac{3}{5} *\frac{2}{3} x$

$AD=\frac{2}{5} x$

$DB=\frac{2}{5} *\frac{2}{3} x$

$DB=\frac{4}{15} x$

now, we can locate these values

Firstly, we will find DC

DC=DB+BC

now, we can plug values

$DC=\frac{4}{15} x+\frac{1}{3} x$

$DC=\frac{3x}{5}$

we have got

$AD=\frac{2}{5} x$

now, we can find ratio

$\frac{AD}{DC} =\frac{\frac{2}{5} x}{\frac{3x}{5}}$

now, we can simplify it

$\frac{AD}{DC} =\frac{2}{3}$

so,

AD:DC=2:3...........Answer

5 0

3 years ago

Answer this question

ra1l [238]

First solve for x:
2x-3>12+x
x>15
And if this makes the statement true, than the statement would be false when x≤15

So then I guess G H and J are all answers

8 0

3 years ago

I think its b?

AfilCa [17]

Yes it is b because a positive multiplied by a negative is a negative.

4 0

4 years ago

Read 2 more answers

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea

Alex787 [66]

Answer:

The quantity of fuel bought at $4 is 40.84 gallons

The quantity of fuel bought at $3 is 116.699 gallons

The quantity of fuel bought at $5 is 17.505 gallons

Step-by-step explanation:

Here we have

Gas used on East coast = X gallons

Gas consumed in the mid-US = Y gallons

Gas consumed in the West coast = Z gallons

Where Y = 2×(X + Z)..........(1)

4·X + 3·Y + 5·Z = 515.........(2)

X + Y + Z = 150..................(3)

Therefore substituting for Y in equation (3) we have

X + 2×(X + Z) + Z = 150

3·X + 3·Z = 150

X = (150 - 3·Z)/3 = 50 - Z

Therefore, equation (2) becomes;

4·(50 - Z) + 3·(2×((50 - Z) + Z)) + 5·Z = 515

200 - 4·Z + 300 -6·Z + 6·Z + 5·Z = 515

500 + 2·Z = 515

Z = 15

X = 50 - Z = 50 - 15 = 35

Y = 2×(X + Z) = 2×(35 + 15) = 2 × 50 = 100

(b) Whereby the bought 174 gallons based on the same ratio as in part (a), we have;

Ratio in part (a) is given as follows;

Proportion of Z gallons = 15/150 = 1/10

Proportion of X gallons = 35/150 = 7/30

Proportion of Y gallons = 100/150 = 2/3

Therefore the proportion of 174 gallons that was consumed in the East coast, X gallons = (7/30)×174 = 203/5 gallons = 40.6 gallons

The proportion of 174 gallons that was consumed in the mid-US, Y gallons = (2/3)×174 = 116 gallons

The proportion of 174 gallons that was consumed in the West coast, Z gallons = (1/10)×174 = 87/5 gallons = 17.4 gallons

Based on price of per gallon, we have

The proportion of $515 that was consumed in the East coast on X gallons = $4 ×35 = $140

Proportion = 140/515= 28/103

The proportion of $515 that was consumed in the mid-US on Y gallons = $3 ×100= $300

Proportion = 300/515= 60/103

The proportion of $515 that was consumed in the West coast on Z gallons = $5 ×15= $75

Proportion = 75/515= 15/103

Therefore, the quantity of fuel bought at $4 = ((28/103) × 601)/4 = 40.84 gallons

The quantity of fuel bought at $3 = ((60/103) × 601)/3 = 116.699 gallons

The quantity of fuel bought at $5 = ((15/103) × 601)/5 = 17.505 gallons.

5 0

3 years ago

2х5y-3z-=14 x-2y+=-12 -x+ Зу-2z =13

lukranit [14]

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14 let's call this equation 1.

x-2y=-12 let's call this equation 2.

-x+Зу-2z =13 let's call this equation 3.

USING EQUATION 1 AND EQUATION 3.

2х+5y-3z-=14 (EQUATION 1)

-x+Зу-2z =13 (EQUATION 3)

LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.

2х+5y-3z-=14 (EQUATION 1) * 2

-x+Зу-2z =13 (EQUATION 3) * 3

4х+10y-6z-=28 let's call this equation 4.

-3x+9у-6z =39 let's call this equation 5.

TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).

4х+10y-6z-=28 (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11 let's call this equation 6.

USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.

x-2y=-12 (EQUATION 2)

x + y = -11 (EQUATION 6)

x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.

We will subtract equation 6 from equation 2. Take note of the signs.

x-2y=-12 (EQUATION 2)

- (x + y = -11) (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

Divide both sides by -3.

-3y/-3 = -1/-3

y = 1/3

LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.

x-2y=-12 (EQUATION 2)

x-2(1/3)=-12

x -2/3 = -12

Add 2/3 to both sides.

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.

2х+5y-3z-=14 (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

Add 21 to both sides.

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

Divide both sides by -3.

-3z/-3 = 35/-3

z = -35/3 or

Therefore, x = -34/3, y = 1/3, and z = -35/3

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6 0

3 years ago