Answer:
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
Step-by-step explanation:
Let be [tex]a[/tex] and [tex]b[/tex] rational numbers whose forms are, respectively:
[tex]a = \frac{m}{n}[/tex] and [tex]b = \frac{q}{r}[/tex], [tex]m[/tex], [tex]n[/tex], [tex]q[/tex], [tex]r[/tex] [tex]\in \mathbb{Z}[/tex]
We proceed to demonstrate if the Pythagorean sum of two rational numbers leads to a rational number.
1) [tex]a = \frac{m}{n}[/tex], [tex]b = \frac{q}{r}[/tex], [tex]m[/tex], [tex]n[/tex], [tex]q[/tex], [tex]r[/tex] [tex]\in \mathbb{Z}[/tex] Given.
2) [tex]c^{2} = a^{2}+b^{2}[/tex] Given.
3) [tex]c^{2} = \left(\frac{m}{n} \right)^{2}+\left(\frac{q}{r} \right)^{2}[/tex] 1) in 2)
4) [tex]c^{2} = (m\cdot n^{-1})^{2}+(q\cdot r^{-1})^{2}[/tex] Definition of division.
5) [tex]c^{2} = [m^{2}\cdot (n^{-1})^{2}]+[q^{2}\cdot (r^{-1})^{2}][/tex] [tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
6) [tex]c^{2} = m^{2}\cdot n^{-2}+q^{2}\cdot r^{-2}[/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]
7) [tex]c^{2} = [m^{2}\cdot (n^{2})^{-1}]+[q^{2}\cdot (r^{2})^{-1}][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]
8) [tex]c^{2} = \frac{m^{2}}{n^{2}}+\frac{q^{2}}{r^{2}}[/tex] Definition of division.
9) [tex]c^{2} = \frac{m^{2}\cdot r^{2}+q^{2}\cdot n^{2}}{n^{2}\cdot r^{2}}[/tex] [tex]\frac{x}{y} +\frac{w}{z} = \frac{x\cdot z+w\cdot y}{y\cdot z}[/tex]
10) [tex]c^{2} = \frac{(m\cdot r)^{2}+(q\cdot n)^{2}}{(n\cdot r)^{n}}[/tex] [tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]/Result.
If [tex]c[/tex] is a rational number, then [tex](m\cdot r)^{2}+(q\cdot n)^{2} = a^{2}[/tex], so that [tex]a \in \mathbb{Z}[/tex]. Which means that [tex]c[/tex] will be rational number if and only if the square root of [tex](m\cdot r)^{2}+(q\cdot n)^{2}[/tex] is an entire number.
Which means that correct answer is B.
3X-7>5 SOLVE THIS INEQUALITY PLEASE
50 points if you answer this
A diver dives 17 and two-thirds yards and then comes back to the surface. Then, she dives 9 and StartFraction 3 over 8 EndFraction yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?
Answer:
answer is -27 1/24.
Step-by-step explanation:
Don't need points here to help.
Answer:
answer is -27 1/24.
Step-by-step explanation:
I=?. P=$475.00,r=4%,t = 3 years Find the missing value
Answer:
I=$57.00
I=Prt
I=(475)(.04)(3)
I= $57.00
Betty earns $15 per hour at her job. Her
husband earns a weekly salary of $90, but he
only earns $12 per hour. How many hours
must Betty work to make the same as her
husband?
URGENT PLEASE HELP ASAP
Answer: 90?
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
mean = sum of all / number of quizzes
x = the remaining student's score
(2(30) + 1(30) + 3(80) + x)/8 = 50
[multiply each side by 8]
2(30) + 1(30) + 3(80) + x = 400
[simplify]
60 + 30 + 240 + x = 400
330 + x = 400
[subtract 330 from each side]
x = 70
Please answer correctly !!!!!!!! Will mark brainliest answer !!!!!!!!!!!!
Answer:
it was X =5
Step-by-step explanation:
Name the quadrant where the ordered pair is located (6, 2)
Answer:
Quadrant 1!
Step-by-step explanation:
The first quadrant has positive values for both of the coordinates.
help?? IJODFZUSDJIOKPXFIGLDROEPKFIJNHCLDFISEKPORQJLNH.KL
Answer:
>
Step-by-step explanation:
.386 is greater than .368
Answer:
greater than because 45.386 is greater 45.368
Step-by-step explanation:
look at each place value
if m JKG = 98 then what is m LKO
Answer:
98 degrees
Step-by-step explanation:
Angle JKG and angle LKO are vertical angles, which are equal.
Savvas Realize
Tonya’s dog-walking service charges a flat rate of $20 per month, plus $3 per mile that each dog is walked. Beth does not charge a monthly fee for her dog-walking service, but she charges $5 per mile that each dog is walked.
Part A
Choose the equation that can be used to find the number of miles m for which Tonya and Beth would charge the same amount.
A. 20 + 3m = 5m
B. 20 = 3m + 5m
C. 20 + 5m = 3m
D. 20 + m = 8m
Part B
m = _____ miles
Answer:
A 10 miles
Step-by-step explanation:
If I'm not mistaking I'm pretty sure we can write the two problems with an equal sign between as we're trying to find the same amount.
Using this information, we know that we Automatically have a +20 charge with a 3 dollar charge for every mile walked. Now we have 20+3x=
Now we plug in the 5x to get 20+3x=5x
From here you subtract 3x and you get 20=2x. Now divide!
10=x
Hope this helps! (Side Note: You should probably get some sleep as I'm sure it's pretty late where ever you live. Also, keep trying even if you feel like giving up!) :)
A recipe calls for 40 ounces of rice. How many grams of rice does the recipe require?
Answer:
1133.98
Step-by-step explanation:
Answer:
1134
Step-by-step explanation:
There are 28.3495 grams per oz
28.3495 x 40 = 1133.98
20-x/y-x if x=2 and y=4 what is the answer
Answer:
20-x/y-x
=20-2/4-2
=18/2
=9 is the answer.
А x = -x+x +0+x
B x = 0 + (x +0)
C None of the above
What does 1,000,000,000divided by 18 • 20 - 108 equal?
Answer:
3,968,253.968253968
Step-by-step explanation:
PLSSS HELP ME I WILL MARK YOU!!
Answer:
-4
Step-by-step explanation:
g=-2
for a negative number times a positive number makes a negative number.
2 to the second power is 4
so -g to the second power is -4
what is the value of x
Answer:
The value of x is 25.
Step-by-step explanation:
Answer:
112+3x^2-7 = 180
105+3x^2 = 180
3x^2 = 180-105
3x^2 = 75
x^2 = 25
x = [tex]\sqrt{25}[/tex]
x = 5
A prescription bottle contains 150 pills. For how many weeks will the bottle last, if the recommended daily dosage is two pills?
Answer:
75
Step-by-step explanation:
150/2=75
Answer:
About 10.5 weeks
Step-by-step explanation:
As each day two pills need to be consumed, 14 pills need to be consumed per week. 150 divided by 14 is roughly 10.5, but slightly more. Hope it helps!
Leann makes an average of 36 cookies per week. About how many cookies will she make in a year
Answer:
The answer is 1872 cookies.
Step-by-step explanation:
First we know that in one year there are 52.18 weeks or 52 weeks. You take that number of weeks and multiply it by 36.
If you multiply 36 by 52 you get 1872 cookies.
Or, if you multiply 52.18 by 36 you get 1878.48
How do I write this equation? Pls help ASP
This is a question about angles and equations! Let's see how to solve this.
The angle [tex]\angle PQR[/tex] is the sum of the angles [tex]\angle MQR[/tex] and [tex]\angle PQM[/tex]. So, we can do a equation with this information and solve it:
[tex]\angle PQR = \angle MQR + \angle PQM\\\\138x -1 = 115 + 23x -1\\138x - 23x = 115 + 1 - 1\\115x = 115\\x=\frac{115}{115} \\x= 1[/tex]
Therefore, the value of x is 1.
The function f has the property that as x gets closer and closer to 4, the values of f(x) get closer and closer to 7. Which of the following statements must be true?
Answer:
C
Step-by-step explanation:
x going to 4 is given by limx->4 and closer to 7 is given by =7
The correct statement is [tex]\lim_{x \to 4} f(x)[/tex] = 7.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given statement:
x gets closer and closer to 4, the values of f(x) get closer and closer to 7.
So, x gets closer and closer to 4 shows
x-> 4
and, f(x) get closer and closer to 7 shows
f(x)=7
Combining both we can write using the limit function x gets closer and closer to 4 require limit
[tex]\lim_{x \to 4} f(x)[/tex] = 7.
Learn more about function here:
https://brainly.com/question/12431044
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If Cody makes 10$ an hour at his after school job, how many hours will it take him to earn 150?
Answer:
15 hours
Step-by-step explanation:
150 divided by 10 equals 15
Answer:
It will take him 15 hours
Step-by-step explanation:
Because if you divide 150 by 10 you get fifteen.
So its basically like divide 150 by the 10$ and then it will take 15 hours.
Use mental math to find the quotient.
2,386.7 ÷ 100
Answer:
23.86700
Step-by-step explanation:
[tex]3x18=3(10+8) is a example of what property
what are the intersections between the lines y=x squared and 6x + 3y= 24?
Answer:
The intersection points between the functions are (-4,16) and (2,4)
Step-by-step explanation:
Intersection Between Functions
We are given the functions:
[tex]y=x^2[/tex]
[tex]6x+3y=24[/tex]
To find the intersections between them, we have to solve the system of equations. Let's start by simplifying the second equation by 3:
[tex]2x+y=8[/tex]
Now we substitute [tex]y=x^2[/tex] into this equation:
[tex]2x+x^2=8[/tex]
Solve the quadratic equation by any of the available methods.
Subtract 8:
[tex]2x+x^2-8=0[/tex]
Sort the polynomial:
[tex]x^2+2x-8=0[/tex]
Factor:
[tex](x+4)(x-2)=0[/tex]
Solve:
[tex]x=-4, x=2[/tex]
Now find the y-coordinate of each solution:
[tex]y=x^2=(-4)^2=16[/tex]
The point is (-4,16)
For x=2:
[tex]y=x^2=2^2=4[/tex]
The point is (2,4)
The intersection points between the functions are (-4,16) and (2,4)
what is 2:10 simplifyed
Answer:
1/5
Step-by-step explanation:
Answer:
1:5
Step-by-step explanation:
you can divide both 2 and 10 by 2
2/2=1
10/2=5
DESCRIBING A TRANSLATION
Describe the translation of the point to its image
(3,-2) (1,0)
The translation of points (3,-2) → (1,0) is 2 units up and 2 units left.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Given the coordinate (3,-2) transformed in coordinate (1,0)
Now,
3 + x = 1
x = -2
It means graph shift 2 units left.
Now,
-2 + y = 0
y = 2
It means the graph shifts 2 units up.
Hence "The translation of points (3,-2) → (1,0) is 2 units up and 2 units left".
To learn more about the transformation of graphs,
brainly.com/question/3099136
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Evaluate the following f(x)=2x+4 if x=8
Answer:
Step-by-step explanation:
2(8)+4=(8)f equals 16+4=(8)f, which equals 20=8f
Answer:
20
Step-by-step explanation:
A family is planning a camping trip at a state park. The state park has 9 campgrounds, each with 6 campsites. The family wants to go on a hike, and the park has 4 hiking trails. The children also want to go for a swim at one of the 4 beaches. How many different ways can the family plan a camping trip?
Answer:
62
Step-by-step explanation:
Camping trip different ways = No of campgrounds x campsites each campground
9 x 6 = 54
Hiking trip different ways = 4 (hiking trails)
Swimming different options = 4 (beaches)
Total ways of planning trip = 54 + 4 + 4 = 62
- 6 + 6(2- 12) divided by (-15) please and thank you
Answer:
4.4
Step-by-step explanation:
-6 +12-72
6-72
-66÷(-15)
4.4
RS = 12, ST = 2x, RT = 34
Answer:
x=11
Step-by-step explanation:
34(RT) minus 12(RS)=22. 22 divided by 2 equals 11.