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3 years ago

Which of the following sets is NOT closed under addition.

Mathematics

1 answer:

Veronika [31]3 years ago

7 0

Answer:

Step-by-step explanation:

The odd numbers.

Suppose you have 31 and 27 when you add these two together, you get 58 which is not an odd number.

If you need a more mathematical proof, you could do it this way.

2x+1

2x is even. Anything multiplied by 2 is even. When you add 1 you get an odd number

So continue on

2y + 1 is the other number.

2x + 1 + 2y + 1 = 2(x + y) + 2

2 (x + y ) is even. When you add 2 to it, nothing changes. The result is still even.

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In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

6 0

2 years ago

Need help with work g

Nonamiya [84]

Answer:

21 meters

Step-by-step explanation:

First find the circumference of the tire:

c = πd

c = 3.14(670)

c = 2103.8

Multiply by 10 to find the distance the bike has travelled:

2103.8*10 = 21,038

Convert millimeters to meters:

21,038 millimeters ≈ 21 meters

8 0

2 years ago

Read 2 more answers

What is the solution to the equation?

stiv31 [10]

Answer:

x = - 71

Step-by-step explanation:

x - 12 = - 83

+12 +12 (adding 12 to both sides)

x = - 71

7 0

2 years ago

Use a net to find the surface area of the right triangular prism shown:

vazorg [7]

The surface area of the right triangular prism is 270 sq ft

<h3>Total surface ara of the prism</h3>

The total surface area of the prism is the sum of all the area of its faces

For the two triangles

A = 2(0.5bh)

A = bh

A = 7 * 12 = 84 sq.ft

For the two rectangles

A = 2lw

A = 2(6*12)

A = 2 * 72 = 144 sq.ft

For the third triangle;
Area 6ft * 7ft

Area = 42 sq.feet

Taking the sum of the areas

TSA = 84 + 144 + 42

TSA = 270 sq ft

Hence the surface area of the right triangular prism is 270 sq ft

Learn more on surface area of prism here; brainly.com/question/1297098

3 0

2 years ago

What is 5/12 times 6 in multiply fractions with whole numbers

KiRa [710]

5/12*6 =5/12*6/1 crosscancle you get 5/2 the you get 2 1/2

3 0

3 years ago