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3 years ago

Which theorem or postulate justifies this statement? ∠6≅∠13

Mathematics

1 answer:

alexdok [17]3 years ago

5 0

Answer:

Theorem for alternate exterior angles.

Step-by-step explanation:

From the figure attached,

Two lines GN and FH are the parallel lines and a transversal JM is intersecting these lines at two distinct points.

Different pair of angles formed are between these parallel lines,

∠6 ≅ ∠10 [Corresponding angles]

∠8 ≅ ∠10 [Interior alternate angles]

∠6 ≅ ∠13 [Exterior alternate angles]

Therefore, theorem for alternate exterior angles justifies that ∠6 ≅ ∠13.

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Find y'' if y= 9csc x

sineoko [7]

Answer:

y" = csc(x)[9cot²(x) - csc²(x)]

Step-by-step explanation:

Step 1: Define

y = 9csc(x)

Step 2: Find 1st derivative

y' = -9csc(x)cot(x)

Step 3: Find 2nd derivative

y" = 9csc(x)cot(x)cot(x) + -csc(x)csc²(x)

y" = 9csc(x)cot²(x) - csc³(x)

y" = csc(x)[9cot²(x) - csc²(x)]

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3 years ago

1 5.2.3 Quiz: Completing the Square

Softa [21]

Answer:

x=5/2 or x=2.5

Step-by-step explanation:

x time 2 + 4x=15

6x=15

2x=15

2x=5

7 0

2 years ago

17u-8u=18<br> Can u explain how this works

Brilliant_brown [7]

U is 2
You collect like terms meaning you do 17-8= 9u
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8 0

2 years ago

For what value of the variable will the expression 8b-27 <br><br> -11

raketka [301]

Answer: 8b - 38

Step-by-step explanation:

8 0

2 years ago

Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for П ; height is 19 in; radius is 5 in. Round

Vera_Pavlovna [14]

Volume of Solids

The volume of the solid is 758.83 in³

Step-by-step explanation:

Given that the cone and half sphere is hollow

The volume of the cone = $1/3 \pi r^{2} h\\$

The Volume of the sphere = $4/3 \pi r^{3}$

So the Volume of the half sphere = $2/3\pi r^{3}$

The volume of solid = volume of cone + volume of the half sphere

$V = V_{1} + V_{2}$

Given

height h = 19 in

radius r = 5 in

$V_{1\\}$ = $1/3 \pi r^{2} h$

= 1/3 × 3.14 × 5 × 5 × 19

= 497.16 in³

$V_{2} = 2/3 \pi r^{3}$

= 2/3 × 3.14 × 5 × 5 × 5

= 261.67 in³

V = 497.16 in³ + 261.67 in³

= 758.83 in³

Hence the volume of the solid is 758.83 in³

3 0

3 years ago