prove 151^3-25^3 is divisible by 126

Answers

Answer 1

9514 1404 393

Answer:

  151 -25 = 126 is a factor of the difference of those cubes

Step-by-step explanation:

The expression can be factored as ...

  a^3 -b^3 = (a -b)(a^2 +ab +b^2)

  151^3 -25^3 = (151 -25)(151^2 +151·25 +25^2)

  = 126(151^2 +151·25 +25^2)

That is, 126 is a factor of the difference of the given cubes. The difference is divisible by 126.

__

Your calculator tells you 151^3 -25^3 = 126 · 27201.


Related Questions

please help me what would the angle be subtracting them

Answers

Answer:

r=8

the angle measurement is 95.

Step-by-step explanation:

Well, those angles would be the same, so you set them equal to each other.

95=6r+47

then solve it.

6r=48

r=8

Which equation is represented by the line

Answers

Answer:

First, we need to find the slope of this line.

Slope is defined as rise over run, or change in y over change in x. We find two  points on this line, and see that the slope is -4.

Then, we find the y-intercept, which in this case is 0.

Using slope intercept form, our answer is y=-4x

Let me know if this helps!

Answer:

y=-4x

Step-by-step explanation:

so the line goes down 4 evey 1 right so the slope is -4 and it goes through the y axis at 0 so the y intercoept is 0

Which sets of side lengths could from a triangle?
choose all that apply.​

Answers

Answer:

E

Step-by-step explanation:

Answer:

d and e

Step-by-step explanation:

for them to be possible side lengths of a triangle the two shorter sides added together have to be greater than the longest side and an answer D and e 6 + 4 is greater than 9 and 5 + 5 is greater than 9 to so those are possible side lengths

someone please help i will mark you brainliest​

Answers

f (x) = (x-1) (x+3)..........................................less the periods

A plumber chargers a fee of $75 plus $30 per hour on the job. Make a table of values for the total charge depending on the number of hours the plumber works. Determine if this can be defined by a linear or an exponential function. What is the function?
a. Linear: T=30+75h
b. Exponential: T=75(30)^h
c. Exponential: T=30(75)^h
d. Linear: T=75+30h

Answers

Answer:

d

Step-by-step explanation:

It is going at a steady rate of 30$ an hour

Total charges of the plumber depending on the number of hours he works is defined by the linear function T = 75 + 30h.

What is linear functions?

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Learn more about linear function here

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Can someone help me?

Answers

Answer:

the transfer of energy ( I think)

Sound wave

Transverse wave

I'm sorry if I got it wrong...

make t the subject of the formula. s= 8t +5​

Answers

Answer:

So I am assuming that you are wanting what a single t is. Well, here you go.

t=(s-5)/8

Step-by-step explanation:

8t=s-5

t=(s-5)/8

Hope this helps! ;)

explain what a variable is.

Answers

Answer:

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables.

Step-by-step explanation:

in other words is like x,y,z or any other letters

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables. Sometimes, we will choose a letter that reminds us of the quantity it represents, such as t for time, v for voltage,b for bacteria

1 What number is equivalent to the expanded form shown below?
A.203.043
B.203.403
C.230.430
D.230.403
Can someone help me with this

Answers

Answer

B

203.403

Cancel terms that are in both the numerator and denominator

( 2 1 0 0 ) + ( 3 1 ) + ( 4 1/1 0 ) + ( 3 1/1 0 0 0 )

( 2 1 0 0 ) + ( 3 1 ) + ( 2 1/5 ) + ( 3 1/1 0 0 0 )

Solution

( 2 1 0 0 ) + ( 3 1 ) + ( 2 1/5 ) + ( 3 1/1 0 0 0 )

8. Each box in a set of decorative storage boxes is a cube.
a) The sides of the smallest box are 30% of the length of the sides of the largest
box. The volume of the largest box is 7784 cubic inches more than the
volume of the smallest box. Define one or more variables, and write an
equation that represents the situation.
b) What are the lengths of the sides of the largest and smallest boxes?
c) Two of the other boxes have a total volume of 2457 cubic inches. The length
of the sides of the smaller of these boxes is 75% of those of the larger box.
Write and solve an equation to find the lengths of the sides of the boxes.

Answers

Answer:

20 in and 6 in12 in and 9 in

Step-by-step explanation:

a) Let the side of the larger box be x, then the side of the smaller box is 0.3x.

Their volumes are:

x³ and (0.3x)³ = 0.027x³

The difference in volumes:

x³ - 0.027x³ = 77840.973x³ = 7784x³ = 7784/0.973x³ = 8000x = ∛8000x = 20

b) The sides are 20 in and 20*0.3 = 6 in

c) The other two boxes with sides x and 0.75x

Sum of the volumes:

x³ + (0.75x)³ = 2457x³ + 0.421875x³ = 24571.421875x³ = 2457x³ = 2457/1.421875x³ = 1728 x = ∛1728x = 12

Sides of the boxes are 12 in and 12*0.75 = 9 in

8.88=-2.22(x-7)
what is x

Answers

Answer:

x=3

Step-by-step explanation:

Let's solve your equation step-by-step.

8.88=−2.22(x−7)

Step 1: Simplify both sides of the equation.

8.88=−2.22(x−7)

8.88=(−2.22)(x)+(−2.22)(−7)    (Distribute)

8.88=−2.22x+15.54

Step 2: Flip the equation.

−2.22x+15.54=8.88

Step 3: Subtract 15.54 from both sides.

−2.22x+15.54−15.54=8.88−15.54

−2.22x=−6.66

Step 4: Divide both sides by -2.22.

−2.22x /−2.22

=

−6.66 /−2.22

x=3

Adriana y Luisa fueron a la feria y decidieron subirse a la rueda de la fortuna. Si el diámetro de la rueda es de 8 metros, ¿Qué recorrido hicieron dando una vuelta completa? Considera Pi= 3.14

Answers

Answer:

Translation?

Step-by-step explanation:

NEEEED HELP!!!!!!!!!

Answers

Answer:

1/3 is your awnser also what ur name in prodigy ill play with u im level 100

Step-by-step explanation:

Answer:

[tex] \frac{2}{5} + \: x = \frac{11}{15} [/tex]

5.3=15

2.3=6

[tex] \frac{6}{15} + \frac{5}{15} [/tex]

50 to 60 as a fraction in simplest form

Answers

Answer:

5/6

Step-by-step explanation:

50/60 in simplest form is 5/6

You would divide both sides by 10

The simplified expression of the expression 50 to 60 is 5/6

How to simplify the expression

From the question, we have the following parameters that can be used in our computation:

50 to 60

Express as equation

50 to 60 = 50/60

Divide 50 by 60

So, we have the following representation

50 to 60 = 5/6

Using the above as a guide, we have the following:

The expression cannot be further simplified

Hence, the simplified expression is 5/6

Read more about expressions at

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Use the grid below to name the point at (4,3)

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In the point (4,3), the 4 is x and 3 is y. The x-axis is the bottom line so go up 4 and the vertical line is the y-axis so go right 3. The point where they meet is B.

Hope it helps!

A phone company uses the equation y 0.15x10 to find y, the monthly charge for a customer sending x text messages. How many text messages are sent if the monthly charge is $77507
A: 10
B: 21
C: 450
D: 506

Answers

Answer:21

Step-by-step explanation:

21

There are 10 coins on a table heads side up. Noah wants them all to be tails side up, but with each move, he must turn over exactly
6 coins. What is the fewest moves he can take so that he ends up with all of the coins tails side up?

Answers

Answer:

2 moves

Step-by-step explanation:

2 moves ok?!?! Dhsgbcc

what value of x makes the equation 6x - 10 = -10 true

a -3 1/3
b 0
c 5
d 8 1/3

Answers

the value of x that makes the equation true is b(0)

Area of B patios a.74.42. B.37.21. C.144

Answers

○=> Correct option :[tex]\color{hotpink}\tt\bold{(a)\ \: 74.42}[/tex]○=> Steps to derive correct option :

Length of side of patio A = 12 yards

Area of patio A which is a square :

[tex] =\tt side \times side[/tex]

[tex] =\tt 12 \times 12[/tex]

[tex]\color{plum} = \tt144 \: {yards}^{2} [/tex]

Thus, Area of patio A = 144 yards²

Length of side of patio B = 6.1 yards

Area of patio B which is a square :

[tex] =\tt side \times side[/tex]

[tex] = \tt6.1 \times 6.1[/tex]

[tex]\color{plum} = \tt37.21 \: {yards}^{2} [/tex]

Length of side of the second patio B = 6.1 yards

Area of this patio :

[tex] =\tt 6.1 \times 6.1[/tex]

[tex]\color{plum} = \tt37.21 \: yards[/tex]

Total area of Patio B :

= Area of first patio B + Area of second patio B

[tex] =\tt 37.21 + 37.21[/tex]

[tex]\color{plum} = \tt74.42 \: {yards}^{2} [/tex]

Thus :

▪︎Area of patio A = 144 yards²

▪︎Area of patio B = 74.42 yards²

▪︎Therefore, the correct option is (a) 74.42

The RADIUS of the barrel is 9.5.

What is the circumference of the barrel?

Answers

Answer:

19

Step-by-step explanation:

D=2r

D = 2(9.5)

   = 19

the dataset below represents the heights of trees(in inches) 13, 82, 83, 95, 92, 98, 96. How many outliers are in this data set?

Answers

Answer:

3

Step-by-step explanation:

There are 3 outliers. 13, 82, 83. These outliers are marginally off by the rest of the set.

There is one outlier in the data. The value of outlier is 13.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. It is a value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. The outliers can be found from median and quartile range.

For the given situation,

The heights of trees(in inches) are 13, 82, 83, 95, 92, 98, 96.

Arrange them in ascending order,

⇒ [tex]13, 82, 83, 92, 95, 96, 98[/tex]

Here, median = 95

So, first quartile Q₁ = 82

third quartile, Q₃ = 96

Interquartile range, IQR = Q₃ - Q₁

⇒ [tex]96-82[/tex]

⇒ [tex]14[/tex]

Now, [tex]IQR(1.5)=14(1.5)[/tex]

⇒ [tex]21[/tex]

Then, high value = Q₃+1.5 IQR

⇒ [tex]96+21[/tex]

⇒ [tex]117[/tex]

Low value = Q₁-1.5 IQR

⇒ [tex]82-21[/tex]

⇒ [tex]61[/tex]

From the data, the value of outlier should lie less than 61 and greater than 117.

Hence we can conclude that there is one outlier in the data. The value of outlier is 13.

Learn more about outliers here

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64+66-43x33/89x34/09=

Answers

Answer: -4293764

Step-by-step explanation:

Answer:69,78

Step-by-step explanation: 43*33=1,419

1,419/89=15,94

15,94*34=541,96

541,96/09=60,22

64+66=130

130-60.22=69,78

there are 63 boys in sixth grade. the number of girls in the sixth grade is 56. Shelby says that means the ratio of the number of boys to the number of girls in sixth grade is 9:7. is Shelby correct. use a tape diagram, to support your answer.

Answers

Answer:

Yes, Shelby is correct.

Step-by-step explanation:

Basically, if you divide 63 by 9 you get 7, and if you divide 56 by 7 you get eight, so yah.

what is the simplest form of 874/942

Answers

Answer:

437/471

Step-by-step explanation:

would consider downloading photomath

Elenista made an estimate that the angle below was about 170°.
Why did her estimate not correctly describe the angle
measurement?
HELPP MEEE PLSSS PLSS:(

Answers

Answer:

C. The estimate is too large

My bad, wasn't looking at it carefully. The angle seems to be close to 90° than 180°.

Answer:

i believe the answer would be B

Step-by-step explanation:

Abox of cereal states that there are 81 calories in a
4-cup serving. What is the unit rate for calories
per cup? How many calories are there in 4 cups of the cereal?

Answers

Answer:

20.25 per cup because 81÷4= 20.25 then

1) read the label=81 per 4-cups

2) 20.25x4=82 calories

Step-by-step explanation:

hope this helps :D

When Mr. Day's family moved to town, the rented a house fo $215 a moth. The land lord recently increased the rent by $8.50 a month. What is the percent of increase in rent? Round to the nearest Hundredth of a percent.

Answers

32 percent is the answer obviously

Mike is recording his baby sister's weight in pounds and ounces each week. This week she weighs 10 pounds. How many ounces does she weigh?

Answers

Answer:

160 ounces

Step-by-step explanation:

In each pound, there are 16 ounces.

Therefore we can do 10*16=160

Answer: she weighs 160 ounces. just do 10x16

The perpendicular bisectors of triangle RST intersect at K. Find KR

Answers

Answer:

Step-by-step explanation:

Remark

The diagram is a mess of lines; you have to guess where that 12 belongs. Just to make the question a bit more interesting, I'm going to say the 12 belongs to the perpendicular.

If that's true you can find KT using Pythagorus. KT and RT are equal. (SSS)

So, let's go.

Givens

1/2 of ST = 1/2 32 = 16

12 is the leg of the small triangle KT and the third point where the perpenduclar line meets ST.

Solution

KT^2 = 16^2 + 12^2

KT^2 = 256 + 144

KT^2 = 400

KT = sqrt(400)

KT = 20

RK = KT because parts of a congruent triangle = parts of the other triangle containing the line (KT) that you are trying to find the length of.

what is the appoximate distance between T and U? round your answer to the nearest hundreth

Answers

Answer: 3.16


The first point, T = (x1,y1), and the second point, U = (x2,y2). Can be approximated as 3.16,so the distance between the two points is 3.16 units.
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