Rational numbers are indeed closed under the operations of addition, subtraction, and multiplication is true.
We have,
A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero.
The set of rational numbers is closed under the operations of addition, subtraction, and multiplication.
This means that if we take any two rational numbers and add them, subtract them, or multiply them together, the result will always be another rational number.
To see why this is true,
Consider two rational numbers a/b and c/d, where a, b, c, and d are integers and b and d are not equal to zero.
To show that rational numbers are closed under addition, we can add the two rational numbers as follows:
a/b + c/d = (ad + bc) / bd
Since a, b, c, and d are all integers, ad + bc is also an integer.
Also, since b and d are not equal to zero, bd is also not equal to zero.
And,
(ad + bc) / bd is a ratio of two integers, where the denominator is not equal to zero.
This means that it is a rational number.
To show that rational numbers are closed under subtraction, we can subtract the two rational numbers as follows:
a/b - c/d = (ad - bc) / bd
Again, since a, b, c, and d are all integers, ad - bc is also an integer, and bd is not equal to zero.
Therefore, (ad - bc) / bd is a rational number.
Finally, to show that rational numbers are closed under multiplication, we can multiply the two rational numbers as follows:
(a/b) x (c/d) = (ac) / (bd)
Once again, ac and bd are integers, and since b and d are not equal to zero, bd is also not equal to zero.
Therefore, (ac) / (bd) is a rational number.
Thus,
Rational numbers are indeed closed under the operations of addition, subtraction, and multiplication.
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Complete the equations so that the solution of the system of equations is (-3, 5)
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the solid part of the box? Enter your answer below.
Answer:
1242
Step-by-step explanation:
PLEASE HELP! Due in a few hours!!
You need to workout the area of the shape :)
Answer:
breakdown the initial figure into 2 rectangle
and add their area
Line segment JK has endpoints at J(-3,4) and K(3,6). Which is an equation of a line that is perpendicular to line segment JK and passes through the point (3,-12)
Answer:
y = -3x - 3.
Step-by-step explanation:
Find the slope of the line JK:
Slope = (6-4)/(3- (-3))
= 2 / 6
= 1/3.
Therefore the slope of the line perpendicular to it is - 1 / 1/3
= -3.
Now we use the point-slope form of a line to get the required equation:
y - y1 = m(x - x1)
Here m = -3 and (x1, y1) = (3, -12) so we have
y - (-12) = -3(x - 3)
y + 12 = -3x + 9
y = -3x + 9 - 12
y = -3x - 3 is the answer.
Urgent please help..
Answer:
72
Step-by-step explanation:
Solve. Use paper to show your work. Enter your answer in the box.
4\frac{5}{6}-2\frac{1}{2}=4
6
5
−2
2
1
=
4
4
Answer: illegel input- too many equals signs
Step-by-step explanation:
What is 7.0483 rounded to the nearest hundredth?
Answer:
7.080
Step-by-step explanation:
The rounding off to the number nearest hundredth will be 7.048.
What is rounding off the numbers?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
The given number will be rounded off as below:-
7.0483 = 7.048
Therefore, the rounding off to the number nearest hundredth will be 7.048.
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What conclusion can you make about
three lengths that do not make a
triangle?
Step-by-step explanation:
if the 2 shorter sides add up to less than the larger side, then it's not a triangle.
what are the rules for multiplying negative numbers?
Answer:
When multiplying negative numbers, just remember 2 things. 1: 2 negative values will always give a positive value. 2: If you only have 1 negative value, your answer will also be negative. Just remember these rules and the rest is simple multiplication.
Answer:
Hi there! Your answer is down below!
Step-by-step explanation:
The rule of how to multiply negatives is simple: For a case where a negative number is multiplied by a positive, the rule above can be restated as: take the positive number, and the negative WITHOUT the minus sign, multiply them and add the inus sign to the product.
Have a nice day!
can someone please help me, i have to turn this in soon.
I need help it's due by 7
Answer:
Step-by-step explanation:
w=204.8
Answer:
204.8
Step-by-step explanation:
8x25.6=204.8
DOuble Check:
204.8 divided by 25.6=8
Please help me I will mark you brainliest !!
Answer:
it would be 5x+2y=10 look at pic for math
In 50 trials both coins land in a shaded box twice. What is the experimental probability that both coins fall into a shaded box?
Answer:
1 / 25
Step-by-step explanation:
Number of trials = 50
Number of successes (number of times both coins land in a shaded box) = 2
Experimental probability = (number of successes / number of trials)
Experimental probability (both coins landing into a shaded box) = 2 / 50
= 1 / 25
What is the scale factor from triangle DEF to triangle ABC?
Answer:
i think you need to include a picture
Step-by-step explanation:
Expand: logh(9jk) Log Subscript h Baseline 9 times log Subscript h Baseline j times log Subscript h Baseline k Log Subscript h Baseline 9 + log Subscript h Baseline j + log Subscript h Baseline k Log 9 + log j + log k
Answer:
log h 9 + log h j +log h k
Step-by-step explanation:
i got it right on edg
Answer:
it is B for all u speed run edge people
Step-by-step explanation:
big luck in life
The formula A-lw is used to calculate the area A of a rectangular surface using the length and the width
(w) of the surface. Which formula could be used to find w in terms of A and I?
Identify these foil solutions by using the screenshots below!
Hope it helps and is correct!
para que sirve el álgebra
Answer:
si mamacita
Step-by-step explanation:
El álgebra es un tipo de matemática. Se trata de ecuaciones y resolución de incógnitas. El álgebra se usa para calcular números basados en una ecuación. ¡Espero que esto ayude!
find x using the pythagorean theorem
Use Inverse trig functions to solve for the missing angles
D
8.5
F
E
6.5
Answer:
Angle <E is approximately 40 degrees, and angle <D is approximately 50 degrees
Step-by-step explanation:
Since angle <F is clearly 90 degrees, we can find angle E using the cosine function that relates the adjacent side to the angle with the hypotenuse:
[tex]cos(\theta)=\frac{adj}{hyp} \\cos(E)=\frac{6.5}{8.5}\\E = arccos(\frac{6.5}{8.5})\\E\approx 40.12^o[/tex]
And we use the sin function to deal with angle <D:
[tex]sin(\theta)=\frac{opp}{hyp} \\sin(D)=\frac{6.5}{8.5}\\D = arcsin(\frac{6.5}{8.5})\\D\approx 50^o[/tex]
Rhian sat a maths test and an English test. in the maths test, she scored 14/17. in the English test, she scored 31/39. in which test did she do better
Answer:
She did better on the Math test.
Step-by-step explanation:
14/17 is 82 percent, and 31/19 is only about 80%.
Find the tangent of the larger acute angle in a right triangle with side lengths 3, 4, and 5. Write your answer as a fraction
Answer:
4/3
Step-by-step explanation:
The larger accute angle in a 3 4 5 right triangle will always be the angle in between 3 and 5. Tangent theta = opposite side ÷ adjacent side, so 4/3.
The tangent should be in fraction is [tex]4\div 3[/tex]
Calculation of the tangent:Since in a right triangle with side lengths 3, 4, and 5
Here there is the larger acute angle in the 3, 4 and 5 so it should be lies between 3 and 5
So, it should be like
= opposite side ÷ adjacent side
= [tex]4\div 3[/tex]
Hence, The tangent should be in fraction is [tex]4\div 3[/tex]
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Steps for -3(x+2)=4+2x
Answer:
x = -2
Step-by-step explanation:
-3(x + 2) = 4 + 2x
= -3x + -6 = 4 + 2x (Distribution: -3)
= -3x + -2x - 6 = 4 (Moving the variables to the left and change the signs)
= -3x + -2x = 4 + 6 (Move consatnts to the right and change signs)
= -3x - 2x = + 6 --> (Collect like terms)
= -5x = 10 (Then add)
= (divide -5x = 10 by -5)
= x = 2
Select all that apply.
Chandler can mow 2 lawns per hour. If L represents lawns and H represents hours, which of the following equations represent this rate relationship?
L = 2 × H
H = × L
H = 2 × L
L = × H
Answer:
L = 2 × H
Step-by-step explanation:
The amount of lawns mowed would equal 2 times how many hours because he can mow 2 lawns in a hour.
Answer:
mark other guy brainliest pls. good answer guy above my head
Step-by-step explanation:
Solve 5x=45 using the opposite operation
Answer:
the answer is 8
Step-by-step explanation:
5 times 8 =45 5 time table
Answer:
9
Step-by-step explanation:
8x9=45
y=x/3+2.
Its a benchmark pls help
Answer:
Slope:
y= 1/3
Se sabe q la suma de tres numeros es de 850. El primer es un tercio del segundo y el tercer número es el doble del segundo.¿Cuales son los numeros apollese en el esquema de barra para solucionar el problema?
Answer:
Primer número = x = 85
Segundo número = y = 255
Tercer número = z = 510
Step-by-step explanation:
Se sabe que la suma de tres números es 850. El primero es un tercio del segundo y el tercer número es el doble del segundo.
Representamos:
Primer número = x
Segundo número = y
Tercer número = z
Se sabe que la suma de tres números es 850.
x + y + z = 850 ...... Ecuación 1
El primero es un tercio del segundo
x = 1/3 años
El tercer número es el doble del segundo.
z = 2 años
Sustituimos 1 / 3y por x y 2y por z en la Ecuación 1
1 / 3y + y + 2y = 850
y / 3 + 3y = 850
Multiplica ambos lados por 3
y + 9y = 850 × 3
10 años = 2550
y = 2550/10
y = 255
Resolviendo para x
x = 1/3 años
x = 1/3 × 255
x = 85
z = 2 años
z = 2 × 255
z = 510
Por eso,
Primer número = x = 85
Segundo número = y = 255
Tercer número = z = 510
for what values of x and y is PQRS and parallelogram
Answer:
x = 2
y = 3
Step-by-step explanation:
Measures of opposite sides of a parallelogram are equal.
Therefore,
PQ = SR
2y + 2 = y + 5
2y - y = 5 - 2
y = 3
QR = PS
2x + 3 = y + 4
2x + 3 = 3 + 4 (y = 3)
2x = 7 - 3
2x = 4
x = 4/2
x = 2
Thus, for x = 2 and y = 3, PQRS is a parallelogram.
Describe how an equation ditt
from an expression.
7. 24 less than the number of snakes is 35.
Answer:
idek
Step-by-step explanation:
Kayden and his children went into a bakery and will buy donuts and cookies. Each donut costs $1 and each cookie costs $0.75. Kayden has a total of $15 to spend on donuts and cookies. Write an inequality that would represent the possible values for the number of donuts purchased, dd, and the number of cookies purchased, c.c.
Step-by-step explanation:
1+.75= blank
then subtract 15 and answer above. make sure when you write your final answer to label it. is it chairs, puppies? hope this helps! you got this