if c is a irrational number that means a or b is also an irrational number or both of them are irrational numbers but they are different then each other
i hope that will help
There are two possible answers:
'a' is irrational and b is rational, OR'a' is rational and b is irrationalYou can only pick one of those two cases. In short, exactly one of the 'a' or b is irrational and the other is rational. Both 'a' and b cannot be rational together, and they both cannot be irrational together.
================================================
Explanation:
For a moment, let's say that 'a' and b are both rational numbers. This means they would be ratios of integers. So,
a = p/q
b = r/s
where p,q,r,s are integers. The denominators q & s cannot be zero.
Multiplying those rational numbers 'a' and b leads to
a*b = (p/q)*(r/s) = (p*r)/(q*s)
We get a result in the form of integer/integer. Recall that multiplying any two integers leads to some other integer. Since (p*r)/(q*s) is a ratio of integers, it is rational and that makes a*b = c to be rational. However, your teacher said that c is irrational which is the opposite of rational.
In short, if both 'a' and b are rational, then a*b = c is rational. This means we know for certain that both 'a' and b cannot be both rational for c to be irrational.
------------------------
Next, we'll consider 'a' and b to both be irrational. Is it possible to have a*b = c to be irrational as well? It depends.
If we have the following
a = sqrt(3)
b = sqrt(12)
then,
a*b = sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6
Showing that a*b is rational because 6 = 6/1 is a ratio of integers. This is a bit strange considering how 'a' and b themselves were irrational, but they led to a rational product.
This doesn't always happen since something like
sqrt(3)*sqrt(5) = sqrt(3*5) = sqrt(15)
is irrational. So if both 'a' and b are irrational together, then a*b could be rational or it could be irrational. We would need more information about the values of 'a' and b.
Therefore, we know that we can rule out the case that 'a' and b are irrational together.
------------------------
Lastly, we'll consider the case when one of 'a' or b is rational while the other is irrational. The order doesn't matter. So we'll make 'a' to be irrational and b to be rational.
Since b is rational, this means b = p/q for some integers p,q where q is nonzero. The value of 'a' cannot be written as a ratio like this because it is irrational.
Multiplying any nonzero rational number with an irrational one always leads to an irrational result. If a*b was rational, then we could say
a*b = r/s
a*(p/q) = r/s
a = (r/s)*(q/p)
a = (r*q)/(s*p)
Showing that 'a' is rational, but this contradicts the fact we made 'a' to be irrational at the top of this section. Therefore, a*b is always irrational if exactly one of 'a' or b is irrational and the other is rational.
In other words, if,
'a' is rational and b is irrational, or'a' is irrational and b is rationalthen a*b = c is irrational
Brainliest for answer
Answer:
C. 8 and -32
Step-by-step explanation:
-2 → 8 → -32 → 128
-4 -4 -4
f(n) = -2 • -4^(n–1)
The common ratio is -4, and the first term of the sequence is -2.
Where f(n) is the nth term of the sequence.
pls help me giving brainless. find all angle measures. Assume each truss is symmetric. All of the roofs have a total top peak angle of 120 degrees
Answer:
Pls mark me branliest
Sofia asked 50 students at her school whether they prefer music class or art class as an
elective. This table shows the relative frequencies from the survey.
Answer:
1 and 4
or say it as
More seventh graders prefer art class to music class as an elective
There is no association between a student's grade level and the electives they prefer
y
9
30°
х
Find the values of x and y. Write your answers in simplest form.
y =
Answer:
I just know
Step-by-step explanation:
X= 9 square root of 3
Y = 18
The values of {x} and {y} in the given right angled triangle is -
x = 9√3 and y = 18.
What is Pythagoras theorem?Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular. We can write the formula for Pythagoras theorem as -
(hypotenuse)² = (base)² + (perpendicular)²
Given is a right angled triangle as shown in the image.
We can write the tangent function as -
tan(30) = 9/x
x = 9/tan(30)
x = 9√3
Similarly, we can write the sine function as -
sin(30) = 9/y
1/2 = 9/y
y = 18
Therefore, the values of {x} and {y} in the given right angled triangle is -
x = 9√3 and y = 18.
To solve more questions on triangles, visit the link-
https://brainly.com/question/2773823
#SPJ2
Find the area of the polygon.
Answer:
74.5
Step-by-step explanation:
13.5 * 4.5 = 60.75
5.5 * 2.5 = 13.75
60.75 + 13.75 = 74.5
HELP DUE NOW BRAINLEST AND A THANKS
Answer:
its c bc it starts at 30
Step-by-step explanation:
Find the solutions of :
-3X + 2 2 14
Give 5 solutions
Answer:
-3(x - 738)
Step-by-step explanation:
-3x+2214
-3x+3 . 738
-3(x-738)
PLEASE I HAVE TO TURN IT IN
What is the slopes of the triangles (I’ll report you if you answer with a link)
Answer:
The slope of the line is 1.
Step-by-step explanation:
The triangles don’t have a slope. They help you find the slope of the line.
slope = rise over run
2/2=1
3/3=1
Whichever triangle you use, the slope of the line is 1.
Suppose one serving of Vegetables is 3/4 cup. How many servings are there in 35 cups?
9514 1404 393
Answer:
46
Step-by-step explanation:
The number of servings is ...
(35 cups)/(3/4 cup/serving) = (4/3)(35) servings = 46 2/3 servings
There are 46 full servings of Vegetables in 35 cups.
A random sample of 436 mothers in the United States found that their average age at first birth was 25.9 with a standard deviation of 4.5. A random sample of 364 mothers in France found that their average age at first birth was 28.6 with a standard deviation of 9.5. We will be testing if the mothers give birth to their first birth in the United States are at younger ages than those in France.
Required:
Calculate the degrees of freedom for this hypothesis test.
Answer:
Degree of freedom = 798
Step-by-step explanation:
Given that,
First random sample, n₁ = 436
Second random sample, n₂ = 364
So,
Degree of freedom = n₁ + n₂ - 2
= 436 + 364 - 2
= 798
⇒Degree of freedom = 798
helppppppppppp meeeeeeeeeeee!!!
Answer:
i think it is 3
Step-by-step explanation:
The point (-4, 6) is a solution to which of the following system of
inequalities?
x + 2y > 8 and - 4x – y > 10
x + 2y < 8 and - 4x - y = 10
x + 2y = 8 and - 4x - y s 10
x + 2y = 8 and - 4x – y < 10
Answer:
x + 2y < 8 and - 4x -y = 10
Step-by-step explanation:
make x the subject of the formula then collect like terms then subtract and make them cross the equally sign
The given point (-4, 6) is the solution of the system of equations x + 2y = 8 and - 4x - y = 10. Option C is correct.
Gvien that,
To determine the system of inequality and equation where point (-4, 6) lies.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
= x + 2y
where x = -4 and y = 6
= -4 + 12
= 8
So it matches with the equation given in option C
Now,
=-4x - y
Substitute the point
= -4 × -4 - 6
= 16 - 6
= 10
So it matches with the equation given in option C
Thus, the given point (-4, 6) is the solution of the system of equations x + 2y = 8 and - 4x - y = 10. Option C is correct.
Learn more about inequality here:
brainly.com/question/14098842
#SPJ2
??? please help i cant do it
Answer: 111 degrees
Step-by-step explanation:
all angles added up together is 360 degrees
vertical angles = 180 degrees -> 3x+15=R, 2x+5= missing angle
360 = (2x+5)+(2x+5)+(3x+15)+(3x+15)
360 = 10x+40
320 = 10x
32 = x
plug it in
3x+15 -> 3(32)+15 = 111 degrees
-what is the area and perimeter of the trapezoid.
-what are the area and perimeter of a trapezoid that is similar to this one but reduced by a linear scale factor of 1/3.
- will give you brainliest if it’s correct
Answer:
I think its 42 can you pls give brainliest I wanna level up RSM SUCKS
Step-by-step explanation:
Help Plis.......................
Answer:
C
Step-by-step explanation:
Two negative signs make a positive number. So -(-4) makes 4. I know it sounds weird, but thats what schools teach. Hope this helps!
HeLp PlEaSe ThAnKs! THIS IS A GRADE (SHOW WORK)
Answer:
1) 5400
2) 113.04
Step-by-step explanation:
40 x 135 = 5400
3.14 x 6² = 113.04
Answer:
A.
area of rectangle=l×b=135×40=5400ft²
B.
diameter=36ft
area =1/4×π×d²=1/4×π×36²=324π 0r 1017.87ff²
Create a table of values that could represent the function f(x) = 3x + 4. Justify your response.
F(x)=3/2 x2-4+C
I looked it up
Two angles in a triangle have measures of 35 and 73
What is the measure of the third angle?
Hello!
This is a question relating the interior angle sum of a triangle.
The interior angle sum of a triangle will be 180 degrees.
Since we are given two angle measures, we can set up an equation to find the unknown angle measure.
[tex]35+73+x=180[/tex]
[tex]x=180-35-73[/tex]
[tex]x=72[/tex]
The third angle's measure is 72 degrees.
Hope this helps!
Answer:
(A) P E X
Step-by-step explanation:
Histogram help!(look at the picture)The histogram below shows the admission cost of some theme parks across the country.How many theme parks have an admission cost between $7 and $22?
12 theme parks
5 theme parks
18 theme parks
8 theme parks
Answer:
12
Step-by-step explanation:
5+7=12
5 have 7-14
7 have 15-22
The final answer is 12
HELP ME ASAP
(THE ANSWER IS ALSO COULD BE NONE)
Answer:
B
Step-by-step explanation:
They have to be the same shape and size so the most probability is B
Determine if each statement is True or False. If False, determine what needs to be
changed to make the statement True.
a. In 5x - 8,5 is the constant.
b. In x - 6.5, x is the variable.
C. In 9y + 38, 38 is the constant.
Answer:
a. False. A constant is a number on it's own, and 5 would be the coefficient of x. 8 would be the constant.
b. False. -6.5 would be the constant, since it's on its own. But actually, x would be carrying on a coefficient of 1. Letters are variables, not constants.
c. True.
Flight 101, headed straight north, climbed to 30,000 feet and started its cruising speed of 360 mph 10 miles south of the point directly above our location. Flight 222, headed straight west, already cruising at 30,000 feet at 300 mph, was 5 miles east of the point above us at that time. Clearly, the paths of the planes intersect directly above us. Do they collide? Parametrize the linear paths and give the times when they are at the intersection point. By how many seconds do they miss each other?
Answer:
The answer is "40 second".
Step-by-step explanation:
Flight 101 headed north straight, ascended to a speed of 30,000 feet, and began a 360 mph cruising speed 10 kilometers from the point above our place. Flight 222, heading right west, was at the same time five miles east of the above-used spot already at 30 000 feet at 300 mph.
[tex]flight\ 101: x=0;\\\\y-10 +360 t\\\\10=360 t\\\\t=\frac{1}{36} \ hrs\\\\flight\ 222: x=5-300t\\\\ y=0\\\\5=300 t\\\\t=\frac{1}{60} \ hr\\\\[/tex]
Their [tex]\frac{1}{36}-\frac{1}{60}=\frac{1}{90}\ hr=40[/tex]seconds are missing each other.
What common base can be used to rewrite each side of the equation
2
3
5
8
Answer:
2.
Step-by-step explanation.
If 40% of a number is 28, find 10% of that number.
Answer: 7
Step-by-step explanation:
please help me out I'll give you a virtual high five
Answer:
[tex] \red{ \bold{\frac{2x(x - 1) + 3(2x - 3)}{(2x + 3)(2x - 3)(x - 1)} }}[/tex]
Step-by-step explanation:
[tex] \frac{2x}{4 {x}^{2} - 9 } + \frac{3}{2 {x}^{2} + x - 3} \\ \\ = \frac{2x}{(2 {x})^{2} - {(3)}^{2} } + \frac{3}{2 {x}^{2} - 2x + 3x - 3} \\ \\ = \frac{2x}{(2x + 3)(2x - 3)} + \frac{3}{2 {x}(x - 1) + 3(x - 1)} \\ \\ = \frac{2x}{(2x + 3)(2x - 3)} + \frac{3}{(x - 1) (2x + 3)} \\ \\ = \frac{2x(x - 1)}{(2x + 3)(2x - 3)(x - 1)} + \frac{3(2x - 3)}{(x - 1) (2x + 3)(2x - 3)} \\ \\ \purple{ \bold{ = \frac{2x(x - 1) + 3(2x - 3)}{(2x + 3)(2x - 3)(x - 1)} }}[/tex]
Jenny has $120 to spend on parking and admission to the county fair. The parking will cost $9, and the
admission will cost $18.50 per person, including tax
Answer:
what is your question to help youWhat is the value of x?
Answer:
Solution given:
38°=x°+10°[vertically opposite angle]
x°=38°-10°=28°
is your answer
What is the probability of gettting a odd number out of 1 2 3 4
Answer:
0.5
50%
1/2
Step-by-step explanation:
George drove 240 miles to his grandmother's house. The graph below shows the relationship between the distance he traveled and time.
What does the slope of the graph represent?
A.
The total distance he has traveled.
B.
George's speed in minutes per mile.
C.
George's speed in miles per minute.
D.
The total distance he has left to travel.
plz get it right
Answer:
There is no graph but I can infer that if time is on the x axis it would be C and if distance is on the x axis it would be B
Step-by-step explanation:
The picture shows a carousel. The carousel spins while the horses move up and down. A student determines to
each horse completes one up-down cycle in 30 seconds. The student rides a horse on the carousel for 2 minute
which equals 120 seconds.
raal
Answer:
4 times
Step-by-step explanation:
Note,
60 seconds = 1 minute120 seconds = 2 minutes (60*2).Since the student rode a horse for 120 seconds, to find the number of times the student riding the carousel completed the up-down cycle, we divide it by 30 seconds (which is the duration for the horse to complete one up-down cycle) because the student would be having the same duration as the horse because he was on top the horse.
Hence, we have;
120/30 = 4