Step-by-step explanation:
[tex]a {}^{3} + b {}^{3} [/tex]
Notice how that for both a and b are raised to an odd power. This means we can factor this by a binomial raised to an odd power.
Let divide this by
[tex]a + b[/tex]
Since that is also a odd power.
[tex]( {a}^{3} + {b}^{3} ) \div (a + b)[/tex]
We get
a quotient of
[tex]( {a}^{2} - ab + {b}^{2} )[/tex]
So our factors are
[tex](a + b)( {a}^{2} - ab + {b}^{2} )[/tex]
Answer:
[tex](a+b)(a^{2} -ab+b^{2} )[/tex]
Step-by-step explanation:
[tex]\textbf{We need to factor this expression}[/tex] [tex]\textbf{by applying the sum of two cubes rule:}[/tex]
[tex]\Longrightarrow[/tex] [tex]A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )[/tex]
Here,
A= a
B= b
So, [tex](a+b)(a^{2} -ab+b^{2} )[/tex]
[tex]\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto[/tex]
[tex]\textsl{OAmalOHopeO}[/tex]
Mini wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
2) Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
Answer:
Option c, Scheme C
Step-by-step explanation:
scheme A: 45000/6 = 7500 per month
scheme B: 46800/9 = 5200 per month
scheme C: 48000/12 = 4000 per month
Which Expression is equivalent to -2(x + 6) 2x + (-12) 2x + 12 2x + 6
Answer:
-2x -8
Step-by-step explanation:
find the surface area of the prism HURRY HURRY
Answer:
should be 192
Step-by-step explanation:
ch of the following collections are w A collection of first six even number A collection of tall girls of class X. A collection of good football player A collection of wild animals. A collection of days of a week. he symbols e or €: {a, e, i, o, u}
Pls Tell question corretly
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 7 large boxes and 9 small boxes has a total weight of 192
kilograms. A delivery of 5 large boxes and 3 small boxes has a total weight of 114 kilograms. How much does each type of box weigh?
A grocery store sells apples in bags. Each bag weighs 3/5 of a pound. Alberto's mother buys 6 pounds of apples to make applesauce. How many bags of apples does she buy?
Answer:
10
Step-by-step explanation:
these are small bags (just as comment), so in real life the cost of using bags would add significantly to the price of the apples.
anyway, so we need to find how many units of 3/5 pounds do we need to get 6 pounds ?
3/5 × x = 6
3 × x = 30
x = 10
she buys 10 bags to get 6 pounds.
Find the value of x.
Answer: x = 6
Concept:
From the given graph, we can see that it is an isosceles triangle since the two base angles are congruent.
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.
Solve:
Given information
One side = 6
Second side = x
Given expression deducted from the definition of an isosceles triangle
Second side = First side
Substitute values into the expression
[tex]\boxed {x=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What are the solutions of the system 7x + 3y=-3 and y= -2*?
Answer:
opt 4
Step-by-step explanation:
when x=0, 0+3y= -3, so y=-1 (0,-1) is solution
when x=3 , 21+3y=-3, 3y= -3-21= -24
y= -8 (3,-8) is also solution
If a=120° , find the measure of angles b, c and d.
Explain your reasoning.
Answer:
b=120°
c=60°
d=60°
SEE THE IMAGE FOR SOLUTION
If 8x+5(3+x)-a=15+5x, then a = ?
Answer:
a = 8x
if you want to find x also, then x = a/8
Step-by-step explanation:
Rewrite the following expressions using the distributive property.
1. 5(3x - 2)
2. 2x(6x + 5)
3.
2x
(9x + 6)
3
2
Challenge for you:
You deposit $400 each month into an account earning 5% annual interest compounded monthly.
a) How much will you have in the account in 20 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
9514 1404 393
Answer:
a) $164,413.47
b) $96,000
c) $68,413.47
Step-by-step explanation:
a) The account value is given by the annuity formula:
A = P(12/r)((1 +r/12)^(12·t) -1)
where monthly payment P earns interest at annual rate r compounded monthly for t years.
A = $400(12/0.05)((1 +0.05/12)^(12·20) -1) = $400(240)(1.712640285)
A ≈ $164,412.47
You will have $164,413.47 in the account after 20 years.
__
b) You put $400 in the account each month for 240 months, for a total of ...
$400 × 240 = $96,000 . . . . total of your deposits
__
c) The account balance in excess of your deposits is the amount of interest you earned:
$164,413.47 -96,000 = $68,413.47 . . . . interest earned
The mass varies directly as the Kinetic energy (K) and inversely as the square of the velocity (V). if the kinetic energy is 80 Joules and the velocity is 4 meters per second, then the mass is 10 kilograms. Express the mass as a function of kinetic energy and velocity.
Answer:
m = [tex]\frac{2K}{v^2}[/tex]
Step-by-step explanation:
Given mass (m ) varies directly as K and inversely as v² then the equation relating them is
m = [tex]\frac{kK}{v^2}[/tex] ← k is the constant of variation
To find k use the condition m = 10 when K = 80 and v = 4 , then
10 = [tex]\frac{80k}{4^2}[/tex] = [tex]\frac{80k}{16}[/tex] ( multiply both sides by 16 to clear the fraction )
160 = 80k ( divide both sides by 80 )
2 = k
m = [tex]\frac{2K}{v^2}[/tex] ← equation of variation
The expression of mass as a function of kinetic energy and velocity is m = 2K/V².
What is an expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
We have been given that the mass varies directly as the Kinetic energy (K) and inversely as the square of the velocity (V).
m ∝ K/V²
m = cK/V²
Here c is the constant of variation,
If the kinetic energy is 80 Joules and the velocity is 4 meters per second, then the mass is 10 kilograms.
We have to determine the value of c
Here m = 10 , K = 80 and V = 4 , then
Substitute the values in m = cK/V²
10 = c(80)/4²
10 = c(80)/16
10 = 5c
c = 10/5
c = 2
Substitute the value of c = 2 in the equation of variation,
⇒ m = 2K/V²
Hence, the expression of mass as a function of kinetic energy and velocity is m = 2K/V².
Learn more about the expressions here:
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Need help please thank you
Answer:
first term (a1) = 3/2
common difference (d) = 7/4-3/2 = 1/4
Jeremiah has $10 to spend at the football
game. Pizza costs $3 per slice, and soft drinks
cost $2 each. Suppose p represents the number
of slices of pizza and d represents the number
of drinks. The equation 3p + 2d = 18
represents this situation. If the domain (d) is
{0,3,6}, what is the range (p)?
Answer:
if;
d=0 p=6
d=3 p=4
d=6 p=2
Step-by-step explanation:
just substitute the value into d and use algebra rules to solve!
additive inverse of 2/8
Answer:
-2/8is it's answer
Step-by-step explanation:
mark as Brainlist
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answer:
Use Guathmath app. you will get answer with explaination and full formula.
download Guathmath if you have interest to do this activity.
if 7a - 11b = 0, what will be the value of a:b
Answer:
11:7
Step-by-step explanation:
Solution
Here
7a-11b=0
a:b=?
we know that
a=7
b=11
ans =11:7
Hence proved
Answer:
[tex]thank \: you[/tex]
pls help! I need the answer quickly! thank you!
Answer:
C) 82/2
Step-by-step explanation:
The area of a square is calculated by multiplying a side by itself
so one side of the square is 9 in
the area of a triangle is calculated by multiplying height and base and that divided by 2
since E is the midpoint, if we draw a line show the height from there
the height would be 9
9*9/2 = 82/2
Simplify: 2(6+1)-|-10|+3x2
Answer:
10
Step-by-step explanation:
2(6+1)-|-10|+3*2
First start with the absolute values and parentheses
2(7)-10+3*2
Then multiply from left to right
14 -10 +6
Then add and subtract from left to right
4 +6
10
Which is the best way to write (8/x) as a verbal expression?
Answer:
None of these.
Step-by-step explanation:
8/x is the result when 8 is divided by x.
(x+1).(x/2 +2).(x/3+3).(x/4+4).(x/5+5)
Answer:
Please see the attached picture below to understand the steps I've typed to get to the final solution.
find the probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit. What is the probability of being dealt this hand is
Answer: 20/52 x 4/51 x 3/50 x 2/49 x 1/48 = .00000153908
Step-by-step explanation:
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the number of cards in deck be = 52 cards
Total number of cards selected = 5
The number of ways of choosing 5 cards = ⁵²C₅
The cards selected are of the same suit
So , there are 4 ways to select them , Hearts , Clubs , Spades and Diamonds = ⁴C₁
And there is only one way to select the cards 6 , 7 , 8 , 9 , 10 = 1
Now , we use combination to select the cards in a deck,
So,
The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit is calculated by,
P ( x ) = 1 / ⁵²C₅ x ⁴C₁ x 1
P ( x ) = 1 / 52! / ( 47! x 5! ) x 4! / 3! x 1
P ( x ) = 1 / ( 52 x 51 x 50 x 49 x 48 ) / ( 2 x 3 x 4 x 5 ) x 4
P ( x ) = 1 / ( 2598966 ) x 4
P ( x ) = 4 / 2598966
P ( x ) = 0.00000153908
Hence , The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908
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The value of my coins if I have p pennies, n nickels and twice as many quarters as pennies.
Answer:
Total value in cents = 51p+5nTotal value in dollars = (51p+5n)/100The answer varies depending if your teacher wants the answer in cents only, or in dollars only.
====================================================
Explanation:
p = number of penniesn = number of nickels2p = number of quarters, since we have twice as many quarters compared to pennies.Based on that, we know,
p = number of cents from the pennies (1 penny = 1 cent)5n = number of cents from the nickels (5 nickels = 5 cents, multiply both sides by n)25(2p) = 50p = number of cents from the quartersand ultimately
p+5n+50p = 51p+5n
represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars
----------------
As an example, let's say
p = 4n = 5So we have
p = 4 penniesn = 5 nickelsq = 2p = 2*4 = 8 quartersThis would mean we have
p = 4 cents from the pennies only5n = 5*5 = 25 cents from the nickels only25q = 25*8 = 200 cents from the quarters onlyOverall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29
We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).
In order to pass a class, Amanda needs to have a score higher than 86 on her final. Which graph represents possible scores that Amanda could get to pass this class?
Answer:
graph C
Step-by-step explanation:
Amanda needs to have a score higher than 86 on her final.
That means she can't get lower than 86 (Obviously) but not even an 86.
It has to be higher than 86 for her to pass
Let x represent Amanda's score
[tex]x>86[/tex]
Bolded dots on graphs mean that she can have a 86 but if it's not a bolded dot she can have either higher or lower
Just keep that in mind
The answer will be C. because it describes Amanda's score higher than 86
Answer:
c
Step-by-step explanation:
(4.8 × 10⁷) + 6,500,000
Answer:
5.45 * 10^7
Step-by-step explanation:
[tex](4.8 * 10^7) +6,500,000[/tex]
= [tex](4.8 * 10^7) + 6.5 * 10^6[/tex]
= [tex](4.8 * 10^7) + (0.65 * 10^7)[/tex]
= [tex]5.45 * 10 ^7[/tex]
Please help as quickly as possible.
Answer:
D
Step-by-step explanation:
take a calculator and try a few points.
I used x = 10.3 and x = 22.
and only D is really getting close to 0.4 and 3.5 as functional results.
HELLO PLEASE HELP ASAP
Answer:
5th degree monomial
Step-by-step explanation:
5 is the highest degree, thus 5th degree.
monomial because it is only 1 term, not three or more
In a survey 75 people, 60% said they have more than one tv at home. How many people have more than one tv at home?
Answer:
45
Step-by-step explanation:
Take the number of people surveys and multiply by the percent that said they have more than one tv
75 *60%
75 *.60
45
Simplify the product. 7(–9)
Answer:
have a great day
god is great
