Hey there!
Before we get to know an Integer and Rational Number, we have to know the Real Number system first.
1. What is Real Number System?
Real Number System is very commonly used in mathematics. It is a number system that is "logical", at least when it comes to solving an equation.But do you know that the Real Number system can be broken into two categorizes? And what are them?
Real Numbers can be broken into these main two categorizes which are:
Irrational NumberRational NumberThese numbers can also be broken into other categorizes as well! Crazy, ain't it? Well that's how maths work!
Anyways, we will skip Irrational Number since it is off-topic and not related to your question. We will talk about Rational Number instead.
2. What is Rational Number?
Rational Number is a number that can be written in fraction form. That is a simple explanation for the Rational Number. Please lecture or note that approximations aren't considered as rational numbers. Even though π ≈ 22/7 which is in fraction form but it is just an approximation which is considered as Irrational Number. Also if infinity/endless decimal can be written in fraction form as well, they are considered as Rational Number too!Now we know the meaning of Rational Number. But like I said, the Rational Number can be broken into other categorizes which are:
Integers - Whole number or number without fraction or decimal.Fractions and Decimals that can be written in fraction form.And Integers can also be broken into:
Negative IntegersZeroPositive Integers3. Conclusion and Answer
Since Integers are subset of Rational Number, we can conclude that Integers are Rational Number.Hope this helps, and let me know if you have any doubts regarding Real Number system.
Choose the function whose graph is a parabola.
y = |x + 9|
y = 3\sqrt{x}
y = x 2 - 10
y = -2x
Answer:
y=x2 -10
Step-by-step explanation:
it is because x is squared
Last year, of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of business owners. a. How many business owners in the survey planned to provide a holiday gift to their employees this year
1. When 36 is subtracted from the square of a number, the result is five times the number. Create and solve an equation to find the possible values of this number.
Answer:
[tex]x^{2} -36 = 5x[/tex]
[tex]x^{2} -5x -36 =0[/tex]
(x-9)(x+4) = 0
x = 9 or x= -4
Step-by-step explanation:
In parallelogram GHJK if mJKG=115° find m&KGH.
Answer:
x = 65 degree
Step-by-step explanation:
x + 115 = 180 degree (sum of adjacent angles of a parallelogram is 180 degree)
x = 180 - 115
x = 65 degree
Translate the description as an algebraic expression:
the ratio of 3 and the product of 7 and r
-BRAINLIEST IF ANSWERED RIGHT-
Given the equation
5+x−12=x−7:
Part A. Solve the equation
5+x−12=x−7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values
x=−4,0,5 to verify your solution to the equation
5+x−12=x−7.
In your final answer, include all of your calculations.
Answer:
Part A:
[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers)
Part B:
[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]
Step-by-step explanation:
Part A:
Given [tex]5+x-12=x-7[/tex], combine like terms:
[tex]x-7=x-7[/tex]
Add 7 to both sides:
[tex]x=x[/tex]
Since this is merely a true statement for all real numbers (reflexive property), this equation is true for any real value of [tex]x[/tex].
Therefore,
[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers).
Part B:
Using arbitrary values [tex]x=-4, x=0, x=5[/tex] as requested in part B, verify:
[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]
does this graph show a function pic out of the multiple choice to explain how
Answer:
B
Step-by-step explanation:
The vertical line test means that if there can't be two y values on the same x point. For example, if you put a vertical line through the red line, it would hit two points, meaning that it isn't a function.
For the given function, determine consecutive values of x between which each real zero is located. f(x)= -8x^4-3x^3-11x^2+8x+16
Answer:
Option C: there are zeros between x = 1 and x = 2, x = 0 and x = -1
Step-by-step explanation:
The function is given as;
f(x) = -8x⁴ - 3x³ - 11x² + 8x + 16
Since it's the real zero of the polynomial we are looking for, it means there is a possibility of getting an imaginary zero of the polynomial.
A zero is the value of x that will make the polynomial equal to zero.
Let's try;
x = -2;
f(-2) = -8(-2)⁴ - 3(-2)³ - 11(-2)² + 8(-2) + 16
f(-2) = -128 + 24 - 44 - 16 + 16
f(-2) = -148
Let's try x = -1;
f(-1) = -8(-1)⁴ - 3(-1)³ - 11(-1)² + 8(-1) + 16
f(-1) = -8 + 3 - 11 - 8 + 16
f(-1) = -8
Let's try x = 0;
f(0) = -8(0)⁴ - 3(0)³ - 11(0)² + 8(0) + 16
f(0) = 16
Lets try x = 1
f(1) = -8(1)⁴ - 3(1)³ - 11(1)² + 8(1) + 16
f(1) = -8 - 3 - 11 + 8 + 16
f(1) = 2
Let's try x = 2;
f(2) = -8(2)⁴ - 3(2)³ - 11(2)² + 8(2) + 16
f(2) = -128 - 24 - 44 + 16 + 16
f(2) = -164
From the values of f(x) gotten from x= -2 to x =2, we can see that the zeros will be closest to x = 0 and x = - 1 and also between x = 1 and x = 2 since that is the range that produced f(x) to be close to zero.
find the surface area of the square pyramid
1. 26 ft²
2. 36 ft²
3.40 ft²
4. 56 ft²
Answer:
4. 56 ft²
Step-by-step explanation:
SA = (4×4)+(4×½×4×5)
= 16+40
= 56
What is the ratio of the side length of the side opposite any 30 degree angle and the length of the hypothesis ?
Answer:
1 : 2
Step-by-step explanation:
the ratio is 1 : 2
_____
Find the area of the shape below 9cm 6cm 15 cm 11 cm
Answer:
8910cm^2
Step-by-step explanation:
Since there is no photo ill just multiply the 4 measurements
9x6x15x11
What's the shape? I'll be more than glad to help but I don't see the shape below. Comment underneath this and I'll try helping out.
A rectangular room is 4 times as long as it is wide, and its perimeter is 50 meters. Find the dimension of the room
Answer:
Width=5m
Lenght= 20m
Step-by-step explanation:
L= Lenght
W= width
perimeter = (2L + 2W) ......eqn(1)
From the question, length of the rectangle is 4 times of it's width
Then
L = (4W)........eqn(2)
But perimeter = 50
Fromeqn(1)
(2L + 2W)= 50........eqn(3)
Sub eqn(1) in eqn(3)
2(4W) + 2W = 50
8W + 2W= 50
10W= 50
W=5
From (1)
L = (4W)
L= 4×5= 20
Lenght= 20
I really need help with this one
Answer:
i thinh 20 in
Step-by-step explanation:
Answer:
20pi in
Step-by-step explanation:
The formula for the circumference of a circle is 2\pi r
R is radius
2 * pi * 10
20 pi
Units - 20 pi in.
Complete the angle addition postulate for the following angle
Answer:
measure of angle GEO.....
Which table shows a proportional relationship between a and b?
A.
a b
3 9
4 12
5 20
B.
a b
20 25
24 30
32 40
C.
a b
4 12
5 15
6 24
D.
a b
3 4
6 9
12 16
Answer:
A
Step-by-step explanation:
3 goes into 9
4 goes into 12
And 5 goes into 20
Range of f(x)=4x+6
^help please
Answer:
Step-by-step explanation:
the range of f(x) = 4x + 6 is all real numbers
Answer:
it's a linear function, so the range is all real numbers
In triangle CVR, the midpoint of segment CR is S and the midpoint segment CV is T. What term can be used to describe segment ST
a. angle bisector
b. chord
c. midsegment
d. perpendicular bisector
Answer:
C. Midsegment
Step-by-step explanation:
A midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments. A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side.
The picture below is just an example of what midsegments look like. If you draw out triangle CVR, put points in between CR and CV, and draw a line connecting the two points. You'll see that it looks exactly like a midsegment.
The term "midsegment" is being used to denote the ST segment.
A midsegment is a line that connects the midpoints of 2 triangle edges. A triangle's midsegment is half the size of the triangle's 3rd side and runs parallel to it.
If we create a triangle CVR, insert points across CR and CV, and link the two points with a line.
So, Option "C" is the correct answer to the following question.
Learn more:
https://brainly.com/question/2273557?referrer=searchResults
The perimeter of parallelogram ABCD is 96cm. AD is 9 cm more than twice AB. Find the lengths of all four sides of ABCD.
Answer: [tex]AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm[/tex]
Step-by-step explanation:
Given
ABCD is a parallelogram
Side AD is 9 cm more than twice AB i.e.
[tex]AD=9+2AB[/tex]
Also, for parallelogram
[tex]\Rightarrow AB=CD,BC=CD[/tex]
Perimeter is the sum of the sides
[tex]\therefore AB+BC+CD+AD=96\\\Rightarrow AB+AD+AB+AD=96\\\Rightarrow AB+AD=48\\\\\text{Substitute the value of AD}\\\Rightarrow AB+9+2AB=48\\\Rightarrow 3AB=39\\\Rightarrow AB=13[/tex]
So, [tex]AD=35\ cm[/tex]
Thus, [tex]AB=CD=13\ cm\ \text{and}\ BC=AD=35\ cm[/tex]
Answer: AB=11
AD=31
BC=31
CD=11
Step-by-step explanation:
need help with this Q&A 5
Answer:
C
Step-by-step explanation:
Which of the following sets is closed under subtraction?
none of the above
prime numbers
rational numbers
positive odd numbers
Which graph represents the function y - 3 = 3/2 (x-4)
Answer: Should be the graph with the slope of (3/2)
The terminal side of 0 is in quadrant II and cos 0 = -5/13. What is sin 0?
Answer:
[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos\theta =-\frac{5}{13}\text{ where $\theta$ is in QII}[/tex]
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using the Pythagorean Theorem, solve for the opposite side (we can ignore the negative for now):
[tex]o=\sqrt{13^2-5^2}=12[/tex]
And since θ is in QII, sine is positive, and cosine and tangent are both negative.
Sine is the ratio of the opposite side to the hypotenuse. Therefore:
[tex]\displaystyle \sin\theta=\frac{12}{13}[/tex]
Please help i just need to know how to answer these kind of questions
Answer:
Since you didn't ask for the answer
Step-by-step explanation:
sec(∆)=1/cos(∆)
For the above diagram,cos(∆)=15/17
sec(∆)=1/(15/17)
NOTE:I replaced theta
anyone know the answer
Answer:
i have no clue
Step-by-step explanation:
The expression x^2 - 10x + 24 is equivalent to
Answer:
[tex](x−6)(x−4)[/tex]
Step-by-step explanation:
[tex]x^2 - 10x + 24[/tex]
[tex] {x}^{2} −6x−4x+24[/tex]
[tex]x(x−6)−4(x−6)[/tex]
[tex](x−6)(x−4)[/tex]
Hope it is helpful...Answer:
(x - 4 )(x - 6 )
Step-by-step explanation:
[tex]x^2 - 10x + 24 \\\\=x^2 - 6x - 4x +24 \\\\=x(x - 6) -4(x - 6) \\\\=(x - 4)(x-6) \\[/tex]
The bus ride was 35 minutes long. If the ride ended at 12:05 a.m., what time did the ride begin?
Answer:
11:30 A.M.
Step-by-step explanation:
Answer:
11:30
Step-by-step explanation:
12.05- 35 min and its 11:30
hope that helps bby<3
What is the distance from the origin to point P graphed on the complex plane below?
Answer: (b)
Step-by-step explanation:
Given
Point P can be written as [tex]z=2-5i[/tex]
Distance of Point P can be given by [tex]\left | z \right |[/tex]
[tex]\Rightarrow \left | z\right |=\sqrt{2^2+(-5)^2}\\\Rightarrow \left | z\right |=\sqrt{4+25}\\\Rightarrow \left | z\right |=\sqrt{29}[/tex]
Thus, option (b) is correct.
Answer:
the answer is b
Step-by-step explanation:
THE AMOUNT RECIEVE BY JOY IF SHE WORKED m HOURS AT PHP300 PER HOUR?
Step-by-step explanation:
THE AMOUNT RECIEVE BY JOY IF SHE WORKED m HOURS AT PHP300 PER HOUR?
hi please mark me as brilliant
Find the ratio of sin (A) please help
Answer:
8/17
Step-by-step explanation:
take angle A as reference angle
using sin rule
sin A = opposite / hypotenuse
sin A = 16/34
sin A = 16/34
sin A = 8/17
Answer this question pls? Its 20 pts
Answer:
B a = 180 -77-60
Step-by-step explanation:
The angles add to 180 degrees since they form a straight line
77+ 60+a = 180
a = 180 -77-60
The answer is B.
Step-by-step explanation:
We know that the sum of angles in a straight line = 180°
Therefore:
77° + 60° + a = 180°
a = 180° - 77° - 60°
Hence, option B is the answer.