Explain how to distinguish between a rational number and an irrational number

Answers

Answer 1

Answer:

Sample Response: A rational number can be expressed as a whole number, a fraction, or decimal that has either terminating or repeating digits. A square root of a perfect square is rational. If it is none of these, then the number is irrational.

Answer 2

Answer: A rational number has a end but an irrational number doesn't.

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The edge of one cube is 4 m shorter than the edge of a second cube. The volumes of the two cubes differ by 1216 m^3. Find the edge of the smaller cube.

Answers

Volume of cube, V = edge^3
Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m
Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m
Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ]
= x^3 - [(x-4)(x-4)(x-4)]
= x^3 - [x^2 - 8x +16(x - 4)]
= x^3 - [ x^3 - 12x^2 + 48x - 64 ]
= 12x^2 - 48x + 64
= 4 (3x^2 - 12x + 16)
Therefore 4 (3^2 - 12x + 16) = 1216
3x^2 - 12x + 16 = 1216/4 = 304
3x^2 - 12x - 288 = 0
3 (x^2 - 4x - 96) = 0
(x^2 - 4x - 96) = 0
(x - 12) (x + 8) =0
(x-12) = 0
Therefore x = 12 m
Edge of cube#2 = x m = 12m
Edge of cube#1 = (x-4) m = 8m

$a- the\ edge\ of\ the\ smaller\ cube\ \ \ \wedge\ \ \ a>0\nV_a-the\ volume\ of\ the\ smaller\ cube\ \ \ \Rightarrow\ \ \ V_a=a^3\n \n(a+4)^3-a^3=1216\ \ \ \wedge\ \ \ (x+y)^3=x^3+3x^2\cdot y+3x\cdot y^2+y^3\n \na^3+3a^2\cdot 4+3a\cdot 4^2+4^3-a^3=1216\n \n12a^2+48a+64-1216=0\ \ \ \Rightarrow\ \ \ 12a^2+48a-1152=0\ /:12\n \na^2-4a-96=0\ \ \ \Rightarrow\ \ \ \Delta=(-4)^2-4\cdot 1\cdot(-96)=16+384=400\n \n √(\Delta) =20\n \na_1= (4-20)/(2\cdot1) =-8<0,\ \ \ a_2= (4+20)/(2\cdot1) =12>0$

$Ans.\ The\ edge\ of\ the\ smaller\ cube=12\ m$

I need help with this question.

Answers

Answer:

2 1/8 is located on the first line after 2 and 1 3/4 i think is located on the 3rd line after one

Step-by-step explanation:

Write an equation in slope-intercept form then Graph. 3x-6y=-12

Answers

Here is the graph for 3x-6y=-12

Which answer would make △WTV~△RSP by the AA similarity postulate?Select one:

m∠W=m∠V and m∠R=m∠P

m∠T=m∠S and m∠V=m∠P

WTRS=SPTV=WVRP

WTRS=TVSP=WVRP

Answers

sigh smhhhh BRUH I SWEAR- anyways

Answer:

The third one hope this helpsssssssssssssssssssss

Step-by-step explanation:

A music school charges a registration fee in addition to a fee per lesson. Music lessons last 0.5 hour. The equation y = 40x + 30 represents the total cost y of x lessons. Find and interpret the slope and y-intercept of the line that represents this situation. Then find four points on the line.

Answers

y=mx+b M is the slope.Therefore, 40 is slope.

To find Y intercept, you substitute X for 0
So it becomes, y=40(0)+30
Solve it, y=0+30
y=30
If Y=30 x=0
Y intercept is (0,30)
x y
To find four points, you use the slope.

Final answer:

The slope of the line in the provided equation represents the cost of each music lesson, while the y-intercept represents the registration fee. These two components are used to calculate the total cost of taking 'x' number of music lessons. Examples of four points on this line include: (0,30), (1,70), (2,110) and (3,150).

Explanation:

In the equation y = 40x + 30, 'y' represents the total cost of music lessons, 'x' represents the number of lessons, 40 is the slope, and 30 is the y-intercept.

The slope, 40, means that each music lesson costs $40. This is a constant rate and doesn't change no matter how many lessons a student takes.

The y-intercept, 30, represents the registration fee that is charged in addition to the cost per lesson. This is a one-time fee that's added to the total cost of the lessons.

For example, four points on the line could be (0,30) when no classes are taken, (1,70) for one class, (2,110) for two classes, and (3,150) for three classes.

Learn more about Slope and Y-Intercept here:

brainly.com/question/19824331

#SPJ3

Simplify 9 to the second power over 9 to the seventh power.

Answers

9^2 subtract the exponents. 9^-5 can't have that so flip the fraction.
----
9^7

1
--- is the answer
9^5

Answer:9^5

Step-by-step explanation:

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Donna charges $25.75 for a haircut and $40.50 for a color treatment. Donna did 5 haircuts and 3 color treatment each day for 6 days. How much money did Donna earn altogether?