Answer:
a + b + c = m
=> (a + b+ c)³= m³
⇔m³ = a³ + b³ +c³ + 3(a + b)(a + c)(c + b)
=> m³ + 2p³ = 3a³ + 3b³ + c³ + 3(a + b)(a + c)(b + c)
with c = 0 => m³ + 2p³ = 3a³ + 3b³ + 3ab(a + b)
have:
3mn = 3(a + b + c)(a² + b² + c²)
with c = 0
=> 3mn = 3(a + b)(a² + b²) = 3[a³ + ab² + ba² + b³]
= 3a³ + 3b³ + 3(a²b + ab²)
= 3a³ + 3b³ + 3ab(a + b)
= m³ + 2p³
=> 3mn = m³ + 2p³
Step-by-step explanation:
Given the conditions a + b + c = m, a² + b² + c² = n, and a³ + b³ + c³ = p, we are required to prove that if c = 0, then m³ + 2p³ = 3mn.
If c = 0, then the equations become a + b = m, a² + b² = n, and a³ + b³ = p.
Using the sum of cubes identity (a³ + b³ = (a + b)(a² - ab + b²)), we can rewrite the third equation as (a + b)(a²- ab + b²) = p.
Since a + b = m, we can substitute this value into the above equation: m(a² - ab + b²) = p.
Now, we'll square the first equation (a + b = m) to get a² + 2ab + b² = m². Rearranging, we find ab = (m² - n)/2.
Substituting this value of ab into the equation m(a² - ab + b²) = p, we get m(a² + b² - (m² - n)/2) = p.
Now, we know that a² + b² = n, so we can replace a² + b² in the equation: m(n - (m² - n)/2) = p.
Simplifying the equation further, we get
mn - (m³ - mn)/2 = p.
Finally, rearranging the equation, we find that
m³ + 2p³ = 3mn.
Thus, we have proved that if c = 0, then m³ + 2p³ = 3mn.
To know more about Cubes:
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A high school football team scored 39 points in the game last night, with a combination of touchdowns (6 points each), extra points (1 point each), and field goals (3 points each).
The team make 1 more extra point than field goals, represented by the equation e=f+1, where e is the number of extra points and f is the number of field points scored.
They also scored five times as many points on touchdowns as field goals, represented by the equation 6t=15f, where t is the number of touchdowns and f is the number of field goals scored.
Write a system of equations representing this situation and use it to complete the statement.
The team scored __ touchdowns, __ extra points, and __ field goals.
Answer:
39=6t+3f+e
39=19f+1
5 touchdowns, 3 extra points, and 2 field goals.
Step-by-step explanation:
e=f+1
6t=15f
39= 6t +3f +e
^ ^ ^
39=(15f)+(3f)+(f+1) | e=f+1 | 6t=15f
39=19f+1 | e=2+1 | 6t=15(2)
38=19f | e=3 | 6t=30
f=2 | | t=5
Six times the sum of a number
and two is 30. Find the number
Answer:
x=5
Step-by-step explanation:
6(5)= 30
What is the equation of the line that passes through (-2, 92) and has a slope of −33/2 ?
A.) 33x + 2y = 75
B.) 33x + 2y = -24
C.) 33x + 2y = -57
D.) 35x + 2y = -75
A football team needs to move the ball at least 10 yards forward from the original starting point in order to get a first down. Angel runs for 6 yards on the first play. On the second play, he is sacked for −9 yards. At least how many yards does his team need on the third play to get a first down?
Answer:
13 yards
Step-by-step explanation:
Required distance moved from original position should be ≥ 10 yards in other to get a first down.
Run on first play = 6 yards
Second play = - 9yards
The least number of yards needed on third play :
Let yard needed on third play = x
First play + second play + third play = 10
6 + (-9) + x = 10
6 - 9 + x = 10
-3 + x = 10
x = 10 + 3
x = 13 yards
At least 13 yards is needed on third playbto get a first down.
Byron's MP3 player holds 75 songs. He has space for 26 more songs. Write an equation to find how many songs are already on Byron's MP3 player.A.) 75 + s = 26 B.)75/s = 26 C.) 26s = 75 D.)s + 26 = 75
Answer:
D
Step-by-step explanation:
let the number of songs Byron have be s songs.
s + 26 = 75
Answer:
D
Step-by-step explanation:
s= number of songs played.
s+26=75
s-26=75-26
s=49
can some one please help me
Answer: Number one is C I believe
Step-by-step explanation: 4x - 5 =7
4x -5 + 5=7+5
4x=12
4x-4=12 divided by 4
x= 3
Answer:
A and D
Step-by-step explanation:
When you have an equation that has an x on one side with other things you do the opposite of the thing on the same side as the x. You would add 5 to 17 then you would divide by 4 to seperate the four from the x.
In functions one input has only one output. Since 3 has two outputs it is not a function.
2) Compare the following functions to determine which has the greater rate of change. Function 1: y = 2x + 6 Function 2: 0 4 -2 2 Y ] == a
You did not clearly mention the second function. So, I am assuming you meant to say that the second function has the table values such as:
x y
0 4
-2 2
So, I am solving the question based on this information table of the 2nd function, which anyways will clear your concept.
Answer:
We conclude that the rate of change of a function '1' is greater than the rate of change of function '2'.
Step-by-step explanation:
Given the function 1
[tex]y = 2x + 6[/tex]
Comparing the function with the slope-intercept form of the line equation of a linear function
[tex]y=mx+b[/tex]where m is the rate of change or slope of the line
so
[tex]y = 2x + 6[/tex]
rate of change = m = 2
Now, given the function 2
x y
0 4
-2 2
Taking the slope of the two points in the table
(0 4), (-2, 2)
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:4\right),\:\left(x_2,\:y_2\right)=\left(-2,\:2\right)[/tex]
[tex]m=\frac{2-4}{-2-0}[/tex]
[tex]m=1[/tex]
So, the rate of change or slope of the function 2 is: m = 1
Hence, we observe that:
Rate of change of function 1 = m = 2Rate of change of function 2 = m = 1As the rate of change of a function '1' is greater than the rate of change of function 2.
i.e.
m = 2 > m = 1
Therefore, we conclude that the rate of change of a function '1' is greater than the rate of change of function '2'.
Hey luvs I NEED HELP ON THIS
Answer:
F. Outta. Here
Step-by-step explanation:
Answer:
a. 260m
b. 50m
Step-by-step explanation:
First, triangle POQ and triangle PNR are similar triangles, b/c they have one same angle(OQP), and OQ//NR.
Therefore, OP/OQ = NP/NR.
NP = OP + ON = 175 + 175 = 350
(a) 175/130 = 350 /NR, NR = 260
(b) 175/ (X+10) = 350/ (3X+5) , x = 15, NR = 50
A cab company charges $2.75 per mile, plus an extra surcharge. Bernardo took a cab to the
airport, which was 8 miles from his home. His total fare came to $29.50. Let x represent the
number of miles and y represent the total cost of the cab ride.
a. What is the slope-intercept equation of the line that fits this information?
b. If a customer paid $35, how many miles did they travel in the cab?
Answer:
a) $7.50
b) 10 miles
Step-by-step explanation:
a)
y=mx+b
y=$29.50
x=8
m=$2.75
b=unknown
29.50=2.75(8)+b
29.50-22=22-22+b
7.50=b
Check:
2.75(8)+7.50=29.50
b)
y=$35
x=unknown
m=2.75
b=7.50
35-7.50=2.75x+7.50-7.50
27.5/2.75=2.75/2.75x
10=x
What is the value of x in this equation? 2x + 2 = -46
Answer:
x = -24
Step-by-step explanation:
1. Subtract 2 from -46 to cancel out the addition. 2x = -48
2. Divide both sides by 2. x = -24
If c=48y+.99n what is y?
Suppose y varies directly as x. If y = 150 when x = 3, find y when x = 5.
The normal to the curve y =root x, at the point where x=1 and x=4 meet at P, find the coordinates of P.
The curve is y = sqrt{x}.
Replace x in the curve with 1 and then with 4 to find your point.
y = sqrt{1}
y = 1
First point (1, 1).
y = sqrt{4}
y = 2
Second point (4, 2).
Take it from here.
Need help. Forgot how to do this type
Answer:
AB=707
Step-by-step explanation:
In the video game Digging Up Dinos, players gain and lose points while digging for dinosaur
bones. In Level 1, Emmet earned 14 points for finding the foot bone of a dinosaur. Then, he
lost 17 points for accidentally stepping on and breaking the bone.
What was Emmet's score at the end of Level 1?
what is the equation of the line in slope intercept form
Answer:
y=-3/2+1
Step-by-step explanation:
7y + 8y can be simplified to 15y true or false
Answer:
True
Step-by-step explanation:
7y and 8y are like terms, so you can add them together
True.
How? By combining like terms.
7y + 8y = what?
We keep the variable y and simply add the numbers.
7 + 8 = 15
We now include y in our answer.
So, 7y + 8y = 15y.
work out
a. 5 x 1/8
b.1/7 x 6
plzz help
Answer:
Step-by-step explanation:
5 * 1/8= 5/8
1/7*6= 6/7
Place the whole number over 1 and multiply.
A bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients. How many flavors have chocolate and how many don’t?
Answer: 10 with chocolate, 30 without chocolate.. I think
Answer:
30 with chocolate, 10 without chocolate
Step-by-step explanation:
Find the value of x for which m parallel n 3x - 38 and 2x + 24
Answer:
35x
26x
Step-by-step explanation:
it help to understand..:)
please help asap, will give brainiest. TY! :3
Answer:
Page 1::1 & 3 & 4
Page 2:6
Page 3:8/1
Page 4:15 3/4
Step-by-step explanation:
HOPE THIS HELPS!!
Jamal drew the function below. Which explains whether or not his function is linear?
On a coordinate plane, a line with negative slope goes through points (0, 1.5) and (1.5, 0).
Answer:
"line" a straight line graph is always linear once the line isn't straight, it'll no longer be called a line and will never be linear anymore
Answer:
it is linear because it has a constant rate of change
Step-by-step explanation:
1. COORDINATE GEOMETRY Classily AABC with vertices A-2, -1), B(-1,3), and C(2,0) as scalene, equilateral or isosceles.
Answer:
I'm pretty sure its a equilateral
Step-by-step explanation:
I graphed it
Anyone mind helping me. Correctly
Answer:
-6
Step-by-step explanation:
By looking at the graph, you can see that the graph intersects the x-axis at (-6,0), that is the zero of g.
Answer:
-9
Step-by-step explanation:
The graph's y-intercept is -9, which is the zero of g.
Please help with this question, thank you so much.
PLEASE HELP I NEED THIS TODAY!!
Answer: 201.06
Step-by-step explanation: The formula is pi times the radius squared.
6. The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measures, while angle C is 57 degrees larger than the other two angles. Find the measure of angle C. a. 41 degrees b. 98 degrees c. 82 degrees d. 139 degrees Answer:
Answer:
well, if we want to know the measure angle c. we need to know the other angles measures. We know that c. is 57 more than a. and b.
So, if the triangle is 180 degrees in total, than we need to subtract 57 frm 180 to get 123. Now we divide that by 2 because that is what the other 2 angles will measure. 123 divides by 2 is 61.5.
now we subtract 61.5 from 180 to get 118.5
now to subtract 61.5 again because the 2 angles are the same measure. 118.5-61.5 is 57. so it cant be any of the answers you provided if angle a and b are the same
Step-by-step explanation:
plz mark brainliest!
I bought 24 donuts for 44dhs how much does each donuts cost?? 24 divided by 44 =
Answer:
54 cents
Step-by-step explanation:
The best way to solve this is by writing this as a fraction...
24/44
Next, we should divide both sides by their GCF (Greatest Common Factor) Which in this case is 4.
Now, our fraction is...
6/11
So, our final answer is 6/11 or 0.54 repeating or 54 cents
Hope this Helps!!! :)
Let me know in the comment section if I should change anything or if this answer was perfect!!!
Peter buys 12 bunches of bananas for $9.00. Use a ratio table to determine how much Peter will pay for 8 bunches.
Show that x + y : x - y= 3 : 2
Answer:
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.
Step-by-step explanation:
Given
x + y : x - y = 3 : 2
As
[tex]x + y = 3[/tex]
[tex]x - y = 2[/tex]
Solving to find x and y
[tex]\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}[/tex]
[tex]x-y=2[/tex]
[tex]-[/tex]
[tex]\underline{x+y=3}[/tex]
[tex]-2y=-1[/tex]
[tex]\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}[/tex]
solve for y
[tex]-2y=-1[/tex]
Divide both sides by 2
[tex]\frac{-2y}{-2}=\frac{-1}{-2}[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=\frac{1}{2}[/tex]
[tex]x+\frac{1}{2}=3[/tex]
[tex]x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}[/tex]
[tex]x=\frac{5}{2}[/tex]
so
[tex]x=\frac{5}{2},\:y=\frac{1}{2}[/tex]
Thus,
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.