Answer:
[tex]a^3 + b^3 = -4[/tex]
Step-by-step explanation:
Given
[tex]a + b = 3ab = 2[/tex]
Required
Solve: [tex]a^3 + b^3[/tex]
Rewrite the expression as:
[tex]a^3 + b^3 = a^3 - a^2b +ab^2 + a^2b - ab^2 + b^3[/tex]
Factorize
[tex]a^3 + b^3 = a(a^2 - ab +b^2) + b(a^2 - ab + b^2)[/tex]
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex]
Rewrite as:
[tex]a^3 + b^3 = (a + b)(a^2 + b^2- ab)[/tex]
[tex]a^3 + b^3 = (a + b)(a^2 + b^2+2ab - 3ab)[/tex]
Factorize
[tex]a^3 + b^3 = (a + b)((a + b)^2 - 3ab)[/tex]
Open brackets
[tex]a^3 + b^3 = (a + b)^3 - 3ab(a + b)[/tex]
Given that:
[tex]a + b = 3ab = 2[/tex]
This means that:
[tex]a + b = 2[/tex] and [tex]3ab = 2[/tex]
So, we have:
[tex]a^3 + b^3 = (a + b)^3 - 3ab(a + b)[/tex]
[tex]a^3 + b^3 = 2^3 - 3 * 2 * 2[/tex]
[tex]a^3 + b^3 = 8 - 12[/tex]
[tex]a^3 + b^3 = -4[/tex]
Below are two parallel lines with a third line intersecting them.
Answer:
x = 53 degree
Step-by-step explanation:
53 degree angle = x angle( alternate exterior angle)
Therfore, x = 53 degree
Mark as brainliest
please can someone tell me what is 687.7856 rounded to the nearest hundredth
Answer:
i think its (687.79)
Step-by-step explanation:
Answer:
687.79
Step-by-step explanation:
since when the number before the digit is five above
And 8 is the hundredth , the one after eight is 5 so it gives 1 to eight that's how you get your answer
0, 4, -2, 2/3, -1.8, 16, 3.2, -5/4 Which numbers are rational numbers that are not integers?
Answer:
rational but not integers: 2/3, -1.8, 3.2, -5/4
Step-by-step explanation:
Can someone help me on this plzz thank you.
Answer:
zoom in
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Solve for k.
A.10
B.2
C. 5
HELP NOW PLEASE
Please help What is the distance between points (5, 2) and(-3,-4) on the coordinate
plane? *
Answer:
10 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (- 3, - 4)
d = [tex]\sqrt{(-3-5)^2+(-4-2)^2}[/tex]
= [tex]\sqrt{(-8)^2+(-6)^2}[/tex]
= [tex]\sqrt{64+36}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
HELP
8.
Which ordered pair is the solution of the following
system of equations?
3x + 2y = 4
–2x + 2y = 24
A. (2, -1)
B. (2,-5)
C. (-4,8)
D. (-4,-8)
Answer:
C
Step-by-step explanation:
Given the 2 equations
3x + 2y = 4 → (1)
- 2x + 2y = 24 → (2)
Multiplying (2) by - 1 and adding to (1) will eliminate the y- term
2x - 2y = - 24 → (3)
Add (1) and (3) term by term to eliminate y
5x + 0 = - 20
5x = - 20 ( divide both sides by 5 )
x = - 4
Substitute x = - 4 into either of the 2 equations and solve for y
Substituting into (1)
3(- 4) + 2y = 4
- 12 + 2y = 4 ( add 12 to both sides )
2y = 16 ( divide both sides by 2 )
y = 8
solution is (- 4, 8 ) → C
pleaseeeee helppppppp
how much food can this container hold if its 3 on the top and 9 on the side
Plz help......................
Answer: A is your aswer hope thsi helped
Step-by-step explanation:
pleas make brainly
Answer:
the answer is A) subtract 7 on both sides
Step-by-step explanation:
because you need to get the x and numbers on one side so it would be like this
2x+7=23
-7 -7
2x=16
Dr.dre is a dentist. He needs to report on the average number of cavities that his patients have 1,0,5,6,4
Answer:3.2
Step-by-step explanation: add them all up and divide by the sample size.
Answer:
The average number of cavities is 3.2
Step-by-step explanation:
To find the answer we will put them in order from least to greatest.
0, 1, 4, 5, 6. Now add all the numbers up and we get 16. Because we are trying to find the average number, we will count up how many numbers there are. Since their are 5 numbers total, we divide 16 by 5 and we get 3.2. Therefore, 3.2 is our answer.
Samantha knows that she needs $22,000 for a 10% down payment on a house she can afford. She found an investment that earns 2.75% interest compounding monthly. How much should she put in the account now, rounded to the nearest dollar, to ensure she has the down payment amount in 5 years?
$4,320
$19,177
$13,371
$5,649
Answer:
19,177
Step-by-step explanation:
I took the test
Eli won 2 out of 3 chess games one day. At this rate, if he played 33 games, how many did he win?
Answer: 16.5
Step-by-step explanation:
Mrs.Zomoro is 36 years old and her son is 4.When will the mother be thrice as o old as her son?
Answer:
12 years
Step-by-step explanation:
Represent the mother's age by m and the son's by 4. Currently m = 36 years old.
In x years the mother will be three times as old as her son:
mother: 36 + x years old
son: 4 + x years old
The pertinent equation to solve is:
36 + x = 3(4 + x)
Performing the multiplication, we get:
36 + x = 12 + 3x, or
24 = 2x. Then x = 12.
Check: In 12 years, will the mother's age be 3 times the son's age?
Does 36 + 12 = 3(4 + 12)?
Does 48 = 48? YES
The mother will be 3 times as old as her son in 12 years from now.
Triangle JKL with vertices J(1,-1), K(2,3), and L(3,-2) in the line x=4 ANSWER RIGHT NOW BEEN WAITING AN HOUR NOW
Answer:
hahhahahqhqhqhhajajahahahahahwhwhwhwhwh
I Mark Brainliest ! No Bots Plz
Select All that apply
Answer:
Option 2
Step-by-step explanation:
m/m+5=6.somebody help?
Answer:
m= -6
that's if it's "m" over "m+5" equals 6
let me know if it's "m" over "m" and then plus 5 equals 6
2.
A. 6.5
B. –5.5
C. 3
D. 30
Answer: C. 3
-6v< x v>-.5
divide by -6 flips the inequality
v> x/-6
so x/-6 = -.5
multiply by -6 on each side
x = -.5 * -6
x=3
Choice B.... 3
Step-by-step explanation:
HELP ITS TIMED AND I SUCK AT MATH
Answer:
[tex]28x+8y+2[/tex]
Step-by-step explanation:
Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?
(x – 9)2 + (y + 4)2 = 25
(x + 4)2 + (y – 9)2 = 25
(x – 9)2 + (y + 4)2 = 100
(x + 4)2 + (y – 9)2 = 100
Answer:
(x + 4)^2 + (y – 9)^2 = 25
Step-by-step explanation:
The standard form for a circle is
[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex] where (h, k) is the center and r is the radius
In your case, h = -4 and k = 9 and r = 5
So, (x + 4)^2 + (y – 9)^2 = 25
The equation for this circle is given as
[tex](x+4)^2 + (y-9)^2 = 25[/tex]
Data
h = -4k = 9r = diameter/2 = 10/2 = 5Equation of CircleThe equation of circle is given by
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Let's substitute our values and get our equation
[tex](x--4)^2 + (y-9)^2 = 5^2\\(x+4)^2 + (y-9)^2 = 25[/tex]
we substituted the values of h and k and made sure it's in the standard form of equation of a circle.
The equation for this circle is given as
[tex](x+4)^2 + (y-9)^2 = 25[/tex]
This looks exactly like
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Learn more on equation of a circle here;
https://brainly.com/question/15214797
Stephen spent $12.35 at a food truck. He bought 3 burgers for $1.25 each and 4 corndogs.
How much did Stephen pay for each corndog?
$2.86
$8.60
$2.77
$2.15
Answer:
The 3rd one 2.15
Step-by-step explanation:
12.35 in whole
1.25 x 3 = 3.75
12.35-3.75= 8.60
[tex]\sqrt[4]{8.60}[/tex] = 2.15
pls give brainlist <33
Answer:
$2.15
Step-by-step explanation:
Start off by multiplying $1.25 by 3 to find out how much the burgers are all together. This would be $3.75 for all three of the burgers. Then subtract $3.75 from the total amount spent ($12.35). This would give you $8.60. To find how much he spend on each corndog, you do $8.60 divided by 4. This would give you the answer of $2.15.
please i need help!!!!!
question:25y²-1
answer
Answer:
(5y - 1)(5y + 1)
Step-by-step explanation:
Assuming you require the expression to be factorised.
25y² - 1 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
25y² - 1
= (5y)² - 1²
= (5y - 1)(5y + 1)
Answer:
Below.
Step-by-step explanation:
25y²-1
This is the difference of 2 squares and it factors to (5y - 1)(5y + 1).
Correct Answer Gets a Brainlest! + 15 points.
Answer:
Step-by-step explanation:
there were 370 children in the swimming pool
87654x0987
Would anyone like to r p with me??
Answer:
Answer is 86514499
Hope you like my answer
Answer:
hello how have u been?
Step-by-step explanation:
Taylor bought some jeans on sale. The number of jeans she bought is 1-fith the amount of money she spent. She bought 6 jeans. Find the amount of money Taylor spent,
Answer:
30
Step-by-step explanation:
Let the amount of money Taylor spent = x
The number of jeans she bought is 1-fith the amount of money she spent. She bought 6 jeans.
Hence
1/5 × x = 6 jeans
x/5 = 6 jeans
Cross Multiply
x = 5 × 6 jeans
x = 30
The amount of money Taylor spent = 30
Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.
The function in vertex form is f(x) = (x – 4)2 – 11.
The vertex of the function is (–8, 5).
The axis of symmetry is x = 5.
The y-intercept of the function is (0, 5).
The function crosses the x-axis twice.
The equation is f(x) = x² – 8x + 5. Then the y-intercept is at (0, 5) and the function crosses the x-axis twice. Then the correct options are A, D, and E.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic equation is given below.
f(x) = x² – 8x + 5
Convert the equation into vertex form, then the equation will be
f(x) = x² – 8x + 5
f(x) = x² – 8x + 16 – 16 + 5
f(x) = (x – 4)² – 16 + 5
f(x) = (x – 4)² – 11
The graph of the function is given below.
From the graph, the y-intercept is at (0, 5) and the function crosses the x-axis twice.
Then the correct options are A, D, and E.
More about the equation of parabola link is given below.
https://brainly.com/question/20333425
#SPJ6
HELP!! URGENT!! 75 POINTS + BRAINLIEST!!
Solve the system by substitution.
y = 2x + 35
y = 9x
Answer:
(5,45)
Step-by-step explanation:
Hi,
y = 2x + 35
y = 9x
To solve, we can substitute 9x for y.
9x = 2x + 35
Subtract 2x...
7x = 35
Divide by 7...
x = 5
Now plug in 5 for x...
y = 9x
y = 9(5)
y = 45
Your answer is (5,45)
I hope this helps :)
Answer:
x=5, y=45. (5, 45).
Step-by-step explanation:
y=2x+35
y=9x
-------------
2x+35=9x
35=9x-2x
35=7x
x=35/7
x=5
y=9(5)=45
what is the pathygorean theorum?
who down to ch.at?
Answer:
The sum of the squares of two legs of a right triangle is equal to the square of the hypotenuse (the longest side).
Equation: a^2+b^2=c^2
where a and b are legs and c is the hypotenuse
Answer:
Step-by-step explanation:
sure
