Answer:
x3+y3+z3=k with k is integer from 1 to 100
solution x=0 , y=0 and z=1 and k= 1
For K= 1 , we have the following solutions (x,y,x) = (1,0,0) ; or (0,1,0) ; or (0,0,1) ,
For k =1 also (9,-8,-6) or (9,-6,-8) or (-8,-6,9) or (-8,9,-6) or (-6,-8,9) or (-6,9,8)
And (-1,1,1) or (1,-1,1)
=>(x+y)3−3x2−3xy2+z3=k
=>(x+y+z)3−3(x+y)2.z−3(x+y).z2=k
=>(x+y+z)3−3(x+y)z[(x+y)−3z]=k
lety=αand z=β
=>x3=−α3−β3+k
For k= 2 we have (x,y,z) = (1,1,0) or (1,0,1) or (0,1,1)
Also for (x,y,z) = (7,-6,-5) or (7,-6,-5) or (-6,-5,7) or (-6,7,-5) or (-5,-6,7) or (-5,7,-6)
For k= 3 we have 1 solution : (x,y,z) = (1,1,1)
For k= 10 , we have the solutions (x,y,z) = (1,1,2) or (1,2,1) or (2,1,1)
For k= 9 we have the solutions (x,y,z) = (1,0,2) or (1,2,0) or (0,1,2) or (0,2,1) or (2,0,1) or (2,1,0)
For k= 8 we have (x,y,z) = ( 0,0,2) or (2,0,0) or (0,2,0)
For k= 17 => (x,y,z) = (1,2,2) or (2,1,2) or ( 2,2,1)
For k = 24 we have (x,y,z) = (2,2,2)
For k= 27 => (x,y,z) = (0,0,3) or (3,0,0) or (0,3,0)
for k= 28 => (x,y,z) = (1,0,3) or (1,3,0) or (1,3,0) or (1,0,3) or (3,0,1) or (3,1,0)
For k=29 => (x,y,z) = (1,1,3) or (1,3,1) or (3,1,1)
For k = 35 we have (x,y,z) = (0,2,3) or (0,3,2) or (3,0,2) or (3,2,0) or 2,0,3) or (2,3,0)
For k =36
we have also solution : x=1,y=2andz=3=>
13+23+33=1+8+27=36 with k= 36 , we have the following
we Have : (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)
For k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)
For k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)
For k =54 => (x,y,z) = (13,-11,-7) ,
for k = 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1)
and (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)
For k = 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3)
For k =64 => (x,y,z) = (0,0,4) or (0,4,0) or (4,0,0)
For k= 65 => (x,y,z) = (1,0,4) or (1,4,0) or (0,1,4) or (0,4,1) or (4,1,0) or (4,0,1)
For k= 66 => (x,y,z) = (1,1,4) or (1,4,1) or (4,1,1)
For k = 73 => (x,y,z) = (1,2,4) or (1,4,2) or (2,1,4) or (2,4,1) or (4,1,2) or (4,2,1)
For k= 80=> (x,y,z)= (2,2,4) or (2,4,2) or (4,2,2)
For k = 81 => (x,y,z) = (3,3,3)
For k = 90 => (x,y,z) = (11,-9,-6) or (11,-6,-9) or (-9,11,-6) or (-9,-6,11) or (-6,-9,11) or (-6,11,-9)
k = 99 => (x,y,z) = (4,3,2) or (4,2,3) or (2,3,4) or (2,4,3) or ( 3,2,4 ) or (3,4,2)
(x,y,z) = (5,-3,1) or (5,1,-3) or (-3,5,1) or (-3,1,5) or (1,-3,5) or (1,5,-3)
=> 5^3 + (-3)^3 +1 = 125 -27 +1 = 99 => for k = 99
For K = 92
6^3 + (-5)^3 +1 = 216 -125 +1 = 92
8^3 +(-7)^3
Step-by-step explanation:
solve the inequality x/4+1<6
Answer:
x < 20
Step-by-step explanation:
Answer:
X<20
Interval notation
(-oo,20)
Step-by-step explanation:
Geometry On the number line point B is between points A and C. The distance between points a and b is 1/3 of AC. Where is point B located?
Answer:
hfbhlbghulbfrhbuf
Step-by-step explanation:
hbbfhhbfhfhlflb frf
9.) The city of Amsterdam is 2 meters below sea level. Lammefjord, a city in
Denmark, is 7 meters below sea level. How much higher is Amsterdam than
Lammefjord?
Answer:
5 meters
Step-by-step explanation:
below sea level:negative
above sea level :positive
-2 meters + 7 meters = 5 meters
Amsterdam is 5 meters higher than Lammefjord.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
It is given that the city of Amsterdam is 2 meters below sea level. Lammefjord, a city in Denmark is 7 meters below sea level.
Let's understand the sign convention:-
Below sea level: negative
Above sea level: positive
The level is calculated below as:-
-2 meters + 7 meters = 5 meters
To know more about Expression follow
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Will mark brainlist!! Nick’s Burgers is a fast-food restaurant that sells 140 burgers a day. If sales increase by 60%, how many burgers does the restaurant sell in a day?
A.56
B.148
C.200
D.224
Answer:
D- 224
Step-by-step explanation:
10% of 140 is 14
So then you multiply 14 by 6 to get 60%
then you add that to 140 to equal 224.
The correct statement is that if the sales of burgers at Nick's Burgers increases by 60%, the total sales per day will be increased to 224 burgers per day from 140 burgers per day.
What is Increased Sales?An increase in sales refers to as the positive shift in the sales of goods as compared to previous sessions during a given period of time, given that other factors vary.
The increase in sales will happen as a result of the strategies that may have been adopted by Nick or increase in the demand due to external factors.
The calculation of increased no. of burgers sold per day can be calculated by using the formula and putting the values given in the example as below,
increased sales = 224
So, the new sales of burgers per day is calculated as 224 per day.
Hence, an increase in sales of burgers at Nick's by 60% will result in sales of 224 burgers per day from 140 burgers per day.
Learn more about increase in sales here:
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that is $21.24÷6 and that is 28.63÷7 and 1.505÷35.thx
Answer:
$21.24÷6=$3.54
28.63÷7=4.09
1.505÷35=0.043
Here you go
Step-by-step explanation:
A recipe requires 3 cups of sugar for every 1 ½ cup of flour. At this rate, how much flour would be needed for 2 cups of sugar?
Answer:
1/2
Step-by-step explanation:
In rhombus ABCD, diagonals AC and BD intersect at point E. If AE = 5cm and BE = 12 cm, what is the length of AC?
a-24 cm
b-17cm
c-7 cm
d-10 cm
Answer:
Length of AC is 10 cm
Step-by-step explanation:
Here , we are interested in calculating the length of the diagonal AC.
Please check attachment for the pictorial representation;
From the diagram, we can see that the length
AC = AE + EC
Also, the length AE = EC
So the value of AC = 5cm + 5cm = 10 cm
I promise this the last one but how do you do these type of problems?
Answer:
0.96 + 0.43v
Step-by-step explanation:
You simplify, v and -0.57v are like terms, therefore you can add them together
v - 0.57v = 0.43 v
Answer:
0.96 + 0.43v
Step-by-step explanation:
What you are doing is combining like terms. Let's say v is candy I have v - .57v that means I have one candy and I ate .57 of it already so we subtract to get .43v and the .96 is brussel sprouts. We do NOT want to mix the candy and the brussel sprouts because they are different things.
If you need me to explain more let me know, but hopefully this helps and have a great day!
if you’re good at geometry pls text me end help me with my homework 832-343-4866
Answer: I just did
Step-by-step explanation:
Divide 1540 by 7.
Please show working
Answer:
220
Step-by-step explanation:
Jack's family left home at 9:00 AM and drove to the amusement park at 60 mph. They spent 7 hours at the park and then drove back home. On the way home, traffic was bad and they drove 20 mph slower than in the morning. They got home at 8:00 PM. How far is the amusement park from Jack's home?
Answer:
96 miles
Step-by-step explanation:
The distance from the amusement to jack's home is x (mile, x>0)
jack's family went to the amusement park at: 9 + x/60
On the way home, traffic was bad and they drove 20 mph slower than in the morning⇒ they drove: 60 - 20 = 40 mph
they left the amusement park at: 20 - x/40
have the following equation:
(20 - x/40) - (9+ x/60) = 7
⇔ 4 = x/40 + x/60
⇔ x = 96
so the distance from the amusement park to jack's home is 96 miles
2|4x-5|-2=-4 how do I solve this?
Step-by-step explanation:
in my opinion
2(4x-5)-2=-4
=2×4x-2×5-2=-4
8x-10-2=-4
8x=-4+10+2
8x=-4+12
8x=-16(divide both sides by 8)
×=2
Solve the equation x² = 10.
Answer: X= - or + square root of 10
Step-by-step explanation: both negative or positive roots would multiply to be 10
3.-8= (2.8) - 8
is it true or false
Answer: false
Step-by-step explanation:
BRAINLIEST PLEASEEEE HELP DUE IN 3hrs Can someone help me with this
Answer:
Step-by-step explanation:
14: k^-3/k^4= 1/k^7
15: answer : 1/3²
16: n^-4
17: f-g^4 = 3-(-5)^4 = -622
18: (x^5-y^2)²+x³ =
(2^5-8^2)²+2³ =1032
19: m²-n³
6²-2³ = 36-8=28
20 : 2²×3²×5³= 4500
4500/10 = 450 islands
Help pleaseee ASAP ASAP
Answer:
SAS
Step-by-step explanation:
two sides are same, and the angles between the sides are same (vertical).
Oliver's Flavored Popcorn comes in cylindrical tins divided into three equal sections of caramel, cheese, and buttered flavors. If the tin is 10 inches in diameter and 15 inches tall, what is the volume to the nearest tenth of only the cheese popcorn?
Answer:
The volume of only the cheese popcorn is 392.5 cubic inches.
Step-by-step explanation:
To determine the volume of only the cheese popcorn,
First, we will determine the volume of the cylindrical tin
The volume of a cylinder is given by
V = πr²h
Where V is the volume of the cylinder
π is a constant, (Take π = 3.14)
r is the radius of the cylinder
and h is the height of the cylinder
From the question, the tin is 10 inches in diameter and 15 inches tall.
Diameter = 10 inches, therefore, we can find radius
Radius = Diameter/2 = 10/2 = 5 inches
r = 5 inches
h = 15 inches
Now, putting the values into the equation, we get
V = 3.14 × 5² × 15
V = 1177.5 cubic inches
This is the volume of the cylindrical tin.
Since the cylindrical tin is divided into three equal sections of caramel, cheese, and buttered flavors, then the volume of only the cheese popcorn will be one-third of the total volume of the cylindrical tin.
∴ The volume of only the cheese popcorn = 1/3 × 1177.5 = 392.5 cubic inches
Hence, the volume of only the cheese popcorn is 392.5 cubic inches.
A) Chanece wants to bake
6 cakes for the school bake
sale. The recipe says each
cake needs 2/4 cup of
sugar. How much sugar
will Chanece need for
her 6 cakes?
Answer:
3 cups
Step-by-step explanation:
If you multiply 2/4 x the 6 cakes he has to make you get a total of 3. He will need 3 cups of sugar for ALL 6 cakes.
Hope this helps☺️
One lap around a track is 1/4 mile long if you ran around the track three times and then ran 5/6 mile home how far did you run
Answer:
19/12 or 1 7/12
Step-by-step explanation:
1/4*3=3/4
3/4+5/6
9/12+10/12= 19/12
Omar is putting 5 liters of water in two goldfish bowls. He spills 200 milliliters of water and divides the remaining water evenly into two bowls? A) How many liters of water was spilt? B) How many milliliters of water was remaining? C) How many milliliters of water does Omar pour in each bowl?
Answer:
a) 0.2 L
b) 4800 ml
c) 2400 ml
Step-by-step explanation:
Total volume of water = 5 litres
Since 1000 milliliters make 1 L
5L = 5000 ml
a) litres of water spilt = 200/1000 = 0.2 L
b) milliliters of water remaining = 5000 - 200 = 4800 ml
c) since it was expressly stated in the question that the remaining water was divided evenly; 4800/2 = 2400 ml in each bowl
convert 86 meters to inches. ?
I'm so stuck rn because she says show how you got the answer never In a million years i thought i would never be doing medical math
Answer:
86 meters equals 3385.83 inches
825 centimeters equals 324.803 inches
Step-by-step explanation:
The formula is divide the length value by 2.54
Hope this helps!
ive been stuck on this expression for a while now
Answer:
xy^(2)z^(6)
Step-by-step explanation:
i hope that helps you :)
Rich earns $35 per week mowing lawns in his neighborhood. Which expression can be used to show how much money he earns in 8 weeks?
(8+30) + (8+5)
(8x30) + (8x5)
PLEASE HELPPPPP
Answer:
(8x30) + (8x5)Step-by-step explanation:
Earning per week
$35Earning in 8 weeks
35 * 8 = (30 + 5)*8 = 30*8 + 5*8Second option is correct
Celea pays $50 for a 15-month subscription of a newspaper. How much does she pay per month?
Answer:
$4
For this question, we must divide 50 by 15 months.
50 ÷ 15 = 4.
So, the answer will be 4.
Celea pays $4 dollars per month.
Hope this helps!
54=__x6
Can anyone tell me
Answer:
9
Step-by-step explanation:
A store sells a 33-pound bag of oranges for \$ 3.60$3.60 and a 55-pound bag of oranges for \$ 5.25$5.25. What is the difference between the price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges? The difference is \$$ per pound.
Answer:
$0.014
Step-by-step explanation:
Given that :
Sales price of 33-pound bag of oranges = $3.60
Sales price of 55-pound bag of oranges = $5.25
Price per pound of 33-pound bag:
Sales price / number of pounds
= $3.60 / 33
= $0.109 per pound
Price per pound of 55-pound bag:
Sales price / number of pounds
= $5.25 / 55
= $0.095 per pound
Difference in price per pound of 33-pound bag and 55-pound bag of oranges :
$0.109 - $0.095
= $0.014
What is the equivalent ratio to the ratio 4:6.how do I know the ratio is equivalent?
Since you asked, simply, to know how a ratio is equivalent to another.
Ratios are like fractions in the way that they can be multiplied and simplified. 1:2, for example, can also be 10:20, 5:10, etc. This is inherent to the way a ratio works - say, for every 1 person, there are two cheese slices. This means that when the group gets larger, so does the amount of cheese slices.
Now, to find an equivalent ratio. You can simplify 4:6 by finding the GCF (greatest common factor) of these two numbers - something you can divide both of them by evenly. In this case, the GCF is 2. We divide both 'sides' by 2, and we get a simplified ratio of 2:3. You can then multiply this by different numbers (ones that are logical and could reasonably lead you to an answer on your worksheet or whatnot) until you find an equivalent ratio.
Which expression is undefined?
is n^2 x n^2 equal to (n x n) ^2
A pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of water t seconds after its release is modeled by y = − 16 t 2 − 2 t + 400 . How long will it take for the water to reach the ground? Round to one number after the decimal point.
Answer:
4.93 seconds
Step-by-step explanation:
The height y in feet of water t seconds after its release is given by the equation as follows :
[tex]y=-16t^2-2t+400[/tex]
We need to find the taken taken for the water to reach the ground. When it reach the ground, y will be equal to 0. So,
[tex]-16t^2-2t+400=0[/tex]
Above is a quadratic equation whose solutions can be calculated as follows :
[tex]t=\dfrac{-(-2)\pm \sqrt{(-2)^2-4\times (-16)\times 400} }{2\times (-16)}\\\\t=\dfrac{-(-2)+ \sqrt{(-2)^2-4\times (-16)\times 400} }{2\times (-16)}, \dfrac{-(-2)- \sqrt{(-2)^2-4\times (-16)\times 400} }{2\times (-16)}\\\\t=-5.062\ s\ \text{and}\ 4.93\ s[/tex]
Neglecting negative value.
Hence, it will take 4.93 seconds for the water to reach the ground
