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The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

The following subsets of Z (with ordinary addition and multiplication) satisfy all but one of the

axioms for a ring. In each case, which axiom fails?

(a) The set S of odd integers.

• The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

Hence, Axiom 1 is violated.

(b) The set of nonnegative integers.

• If a is a positive integer, then there is no solution of a + x = 0 that is also positive. Hence, Axiom

5 is violated.

In general, to show that a subset S of a ring R, is a subring of R, it is sufficient to show that

(i) S is closed under addition in R

(ii) S is closed under multiplication in R;

(iii) 0R ∈ S;

(iv) when a ∈ S, the equation a + x = 0R has a solution in S.

Let a, b, c ∈ S ⊂ Z with a = rk, b = sk, c = tk.

(i) a + b = rk + sk = (r + s)k ∈ S

(ii) ab = (rk)(sk) = (rsk)k ∈ S

(iii) 0Z = 0 = 0 · k ∈ S

(iv) a = rs ∈ S ⇒ x = −rs ∈ S is a solution ofa + x = 0S

Thus, S is a subring of Z.

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Answer: Between 2 and 7

Answer:

2 to 5

Step-by-step explanation:

i don't know because of i don't this transmission may not have the completed Questionnaire

Answer:

-5

Step-by-step explanation:

2x+3y-4

Evaluate for x=1,y=−1

(2)(1)+(3)(−1)−4

(2)(1)+(3)(−1)−4

=−5

The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.

The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.

Now, given values :11.0, 24.2, -32.4, -0.6, 0.5

Arranging them in ascending order: -32.4, -0.6, 0.5, 11.0, 24.2Thus, The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.

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you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb

The maximum weight that your bag can have is 50 pounds.

The actual weight of your bag is 44.9 pounds, so if we define x as the weight you can add, then we can write the inequality:

44.9 lb + x ≤ 50lb

Solving the inequality for x, we get:

x ≤ 50lb - 44.9 lb

x ≤ 5.1 lb

Now, the weight of the items are:

hair dryer = 2.5 lb

souvenir = 1.3 lb

boots = 3.6 lb

So you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb

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The volume of the object which is made up of two different cylinders will be 383 cubic inches.

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,

V = π r²h cubic units

The object is made up of two cylinders. Then the volume of the object will be

V = π x (3)² x 8 + π x (5)² x 2

V = π(72 + 50)

V = 3.14 x 122

V = 383.08 ≈ 383 cubic inches

The volume of the object which is made up of two different cylinders will be 383 cubic inches.

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Step-by-step explanation:

23 + 10 - 2 + 14 + 2

33 - 2 + 16

31 + 16 = 47

Answer:

2yds 33 in

Step-by-step explanation:

Convert everything to the lowest unit(inches) perform the operation and convert back

1 yard = 3 feet
1 foot = 12 in
1 yard = 3feet x 12in = 36 in

19yd, 28in = 19 x 36 + 28 = 684 + 28 = 712 in

16yd, 31 in= 16 x 36 + 31 = 576 + 31 = 607 inches

19yd, 28in - 16yd, 31 in = 712 - 607 = 105 inches

Divide by 36 to get the whole number of yards as quotient
105/36  with remainder of 33

∴ 19yd, 28in - 16yd, 31 in = 105 inches = 2yds 33 inches

We can verify this by converting 2yds 11inches to inches and seeing the values agree

2 yds 33 in = 2 x 36 + 33 = 105

Answer:

Y+5=0

Step-by-step explanation:

Here,given eqn of line is 0.X+Y+1=0_____(i)

since required eqn is parallel to eqn (i)

0.X+Y+K=0____(ii)

passing point (-3,5)

putting the value of Y

5+K=0

.-.K=(-5)

r required eqn is Y-5=0

Answer:

a=17, R=101

Step-by-step explanation:

10:

We know that if all angles of a triangle are congruent, the angles must be as well. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

We also know that all interior angles of a triangle add up to 180 degrees. If they are all equal this only leaves us with the possibility of every angle equaling 60 degrees, otherwise they wouldn't add up to 180 AND be equal simultaneously.

To find the value of a set the equation equal to 60.

[tex]4a-8=60[/tex]

Solve for a:

[tex]4a-8=60\\4a=68\\a=17[/tex]

19:

We know in a parallelogram all interior angles sum to 360 degrees.

Remember the sum of angle pairs between parallel lines is 180 degrees. Meaning if we add angles T and S and set them equal to 180 degrees we can then find the value of angle S as we would have the value of variable x.

[tex](4x+1)+(3x+4)=180\\7x+5=180\\7x=175\\x=25[/tex]

Now substitute in the known value of x to find angle S:

[tex]3(25)+4\\75+4\\79[/tex]

Angle S measures 79 degrees.

Using our previous knowledge of two angles on a parallel line summing to 180 degrees, we can find the measure of angle R by subtracting 79 from 180.

[tex]180-79=x\\101=x[/tex]

R=101

Answer:

D.  

Theres no need for a explanation :)

The number of weeks it would take the workers to build 15 more floors is 5 weeks.

The number of weeks it would take to build 15 more floors can be determined by dividing the number of additional floors by the number of floors the workers can build in one week.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient.

Number of weeks = additional floors ÷ number of floors that can be built in a week

15 ÷ 3 = 5 weeks

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Answer:

(a)20π

(b)74π

Step-by-step explanation:

(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)

= 2π(10)

= 20π

(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π

=75π

Answer: P=20 cm    S=75 cm²

Step-by-step explanation:

We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm

[tex]\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ \frac{\pi D}{2}[/tex]

[tex]\displaystyle\\a)\\P=2*\frac{\pi d }{2} +\frac{\pi D}{2} \\\\P=\pi d+\frac{\pi D}{2} \\\\P=\pi *(d+\frac{D}{2} )\\P=\pi *(10+\frac{20}{3} )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\[/tex]

[tex]b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ \frac{\pi D^2}{4} \\The\ area\ of \ the\ semicircle \ is\ \frac{\pi D^2}{8}\\\\S=2*\frac{\pi d^2}{8} +\frac{\pi D^2}{8} \\\\S=\frac{2*\pi *10^2}8} +\frac{\pi *20^2}{8} \\\\S=\frac{2*\pi*100 }{8} +\frac{\pi *400}{8} \\\\S=\frac{200\pi }{8}+\frac{400\pi }{8} \\\\S=\frac{600\pi }{8} \\\\S=75\pi \ cm^2[/tex]

If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters, is the "if-then" form of A side of a square measures 3 decimeters if the side's measure is 30 centimeters.

A statement with an assumption and a conclusion is known as a conditional statement (also known as an if-then statement). The hypothesis is the initial clause, or "if," part of a conditional statement which is followed by the second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.

Thus, option B is correct which is, if the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.

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The tree in Naomi's backyard lost 120 leaves in 12 days. Therefore, the required expression is A. 120÷12

Hope this helps :)

Answer:

Here SOLUTION: −5x + 4y = 20. 10x − 8y = −40.

Step-by-step explanation:

First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity.

Answer: x=-3.25

y=7/12

Step-by-step explanation:

2x + 6y = -3

12y = 4x + 20

6y = -3-2x

6y=20-(-3)+4x-(-2x)

6y=20+3+4x+2x

6y=23+6x

23+6x=-3-2x

23=-3-8x

-8x=26

x=-13/4

x=-3.25

12y = 4(-3.25) + 20

12y=-13+20

12y=7

y=7/12

Answer:

280

Step-by-step explanation:

-2 x 7 = -14

-14 x 5 = -70

-70 x -4 = 280

Answer:

280

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

According to the order of operations (PEMDAS), when multiplying, work from left to right:

Given expression:

(-2) · (7) · (5) · (-4)

Multiply -2 by 7:

⇒ (-14) · (5) · (-4)

Multiply -14 by 5:

⇒ (-70) · (-4)

Finally, multiply -70 by -4, remembering that if both numbers are negative, the answer is positive:

⇒ 280

Answer:  13π/6    √45

Step-by-step explanation:

[tex]\displaystyle\\\sqrt{11} +3\approx6.32\\\\\pi +3,8\approx6.94\\\\Hence,\\\\6.32 < x,6.94\\\\\frac{61}{10}=6.1 \notin\\\\\frac{13\pi }{6}\approx6.81\in\\\\\sqrt{45}\approx6.71\in \\\\6\frac{1}{9}\approx6.11\notin\\\\\sqrt{83}-3\approx6.11\notin[/tex]

Based on the price of hot dog buns decreasing, the impact on the market would be the equilibrium price of hot dogs decreases.

The equilibrium quantity of hot dogs decreases.

The supply curve shifts left. The demand curve shifts right.

When the price of a good like the hot dog duns decreases, supplier will have less incentive to keep making it and so will reduce the quantity supplied to the market. This would mean that the supply curve would shift left.

The demand curve on the other hand would shift right because more people would demand the cheaper hotdogs. The equilibrium price which had fallen would then have to rise.

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The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
x - 5 = 12
Now,
Adding 5 on both sides,
x = 17

Thus, The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.

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I might me wrong, but i believe that its -36.

Have a nice day <3

Step-by-step explanation:

hey try out the questions urself some tips would be to make the 1/2 and 3/5 have the same denominator as those shown in the diagram denominator means the number below

so1/2 x5 would give u 5/10 and 3/5 would give you 6/10

Answer: 9.5 and 9.500

Answer:

One would be 9/5 and another could be 1.8

The difference between the area of the square and the area of the circle is C. 9x²(4 - π).

The area of the square will be:

= Side ×Side

= 6x × 6x

= 36x²

The area of the circle will be:

= πr²

= 3.14 × (3x)²

= π × 9x²

= 9πx²

The difference will be:

= 36x² - 9πx²

= 9x²(4 - π)

Therefore, the correct option is C.

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