Answer: b = -108
Explanation: (¾)b - (⅔)b = -9 b = -108
Plz mark brainliest:)
in the expression of (x + 1)^n, the coefficient of the x^3 term is two times the coefficient of the x^2 term. Find the value of n.
According to Khayyam-Pascal triangle ,
the value of n is 8.
[tex] look \: \\ \\ {(x + 1)}^{8} = {x}^{8} + 8 {x}^{7} + 28 {x}^{6} + 56 {x}^{5} + 70 {x}^{4} + 56 {x}^{3} + 28 {x}^{2} + 8x + 1 \\ \frac{56}{28} = 2 [/tex]
Recall the binomial theorem:
[tex](a+b)^n=\displaystyle\sum_{k=0}^n\binom nk a^k b^{n-k}[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient. So
[tex](x+1)^n=\displaystyle\sum_{k=0}^n\binom nk x^k[/tex]
The x² term occurs for k = 2, which has coefficient
[tex]\dbinom n2=\dfrac{n!}{2!(n-2)!}=\dfrac{n(n-1)}2[/tex]
The x³ occurs for k = 3, with coefficient
[tex]\dbinom n3=\dfrac{n!}{3!(n-3)!}=\dfrac{n(n-1)(n-2)}6[/tex]
The latter coefficient is twice the other one, so that
[tex]\dfrac{n(n-1)(n-2)}6=2\cdot\dfrac{n(n-1)}2[/tex]
Solve for n :
[tex]\dfrac{n(n-1)(n-2)}6=n(n-1)[/tex]
[tex]n(n-1)(n-2)=6n(n-1)[/tex]
[tex]n-2=6[/tex]
[tex]\boxed{n=8}[/tex]
What is the value of
-8(17-12)
—————
-2(8-(-2) )
• -4
• -2
• 2
• 4
Answer:
2
Step-by-step explanation:
-8(17-12)
------------
-2(8-(-2)
= -8(5)
--------
-2(10)
= -40
----------
-20
Ans 2For what values of [tex]x[/tex] is the product [tex](x+5)(x-1)[/tex] positive? Explain.
Answer:
[tex]x<-5\text{ or } x>1[/tex]
Step-by-step explanation:
We have:
[tex](x+5)(x-1)[/tex]
And we want to find the value of x such that the expression is positive. So, we can write this as the following inequality:
[tex](x+5)(x-1)>0[/tex]
Solve for the inequality. First, we can solve for the zeros like a normal quadratic. So, pretend the inequality is with an equal sign:
[tex](x+5)(x-1)=0[/tex]
Zero Product Property:
[tex]x+5=0\text{ or } x-1=0[/tex]
On the left, subtract 5.
On the right, add 1.
So, our zeros are:
[tex]x=-5, 1[/tex]
Since our inequality is a greater than, our answer is an "or" inequality with our answer being all the values to the left of our lesser zero and all the values to the right of our greater zero.
So, our solution is:
[tex]x<-5\text{ or } x>1[/tex]
And we're done!
Answer:
The regions where (x+5) (x-1) >0 is x< -5 or x>1
Step-by-step explanation:
(x+5) (x-1) >0
First find the zeros
(x+5) =0 x-1 =0
x= -5 x=1
We then have to check the regions
x< -5 -5 <x<1 x>1
First x< -5
(x+5) (x-1)
X+5 will be negative ( x-1) will be negative
(-) * (-) = + so the values will be positive
Then -5 <x<1
X+5 will be positive ( x-1) will be negative
( +) * (-) will be negative
First x>1
(x+5) (x-1)
X+5 will be positive ( x-1) will be positive
(+) * (+) = + so the values will be positive
The regions where (x+5) (x-1) >0 is x< -5 or x>1
A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be ... at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak. 2.
Answer:
concrete jungles where dreams are made of
Step-by-step explanation:
Answer:
There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.
Step-by-step explanation:
Sample response :)
find the value of a
Answer:
45
Step-by-step explanation:
81° + a° + 2a° = 180°
81° + 3a = 180°
3a = 180 - 81
3a = 99°
a = 99 ÷ 3
a = 33°
Therefore , a = 33° .
If two angles have the same measure, then they are right angles true or false
Answer:
False
Step-by-step explanation:
Answer: true
Step-by-step explanation:
According to the system of equations above, what is
the value of x ?
Need someone to explain how to do it
Answer:
7
Step-by-step explanation:
try substituting
crossmultyply
x=-9-y
substituting
-9-y=-25+9
y=16
substituting
pick one of the equations
x+y=-9
x-16=-9
x=-9+16
x=7
M=−8j−9k+9 solve for k?
Answer:
k= -8/9j+ -1/9m+ 1
Step-by-step explanation:
Let's solve for k.
m=−8j−9k+9
Step 1: Flip the equation.
−8j−9k+9=m
Step 2: Add 8j to both sides.
−8j−9k+9+8j=m+8j
−9k+9=8j+m
Step 3: Add -9 to both sides.
−9k+9+−9=8j+m+−9
−9k=8j+m−9
Step 4: Divide both sides by -9.
-9k/-9= 8j+m-9/-9
Noah receives a $5 discount each month on his cell phone bill because he signed up for a auto pay from his bank account. Over the last 8 months ,Noah has paid a total of $280 for his cell phone bill. What would Noah be charged for his cell phone bill each month if he stopped using auto-pay?
Answer:
Step-by-step explanation:
280÷8=35+5=$40
Which expression is equivalent to
Answer:
a
Step-by-step explanation:
I'm really lost?? help please
Solve the inequality.
8(x − 4) > −8
Answer:
x>3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > 3
Interval Notation:
( 3 , ∞ )
Can someone please help me with my homework???
Answer:
Step-by-step explanation:
Yes I would be glad to help you
Solve and show how you did 5 (x-1) + 3 = 13
Answer:
x=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5(x−1)+3=13
(5)(x)+(5)(−1)+3=13(Distribute)
5x+−5+3=13
(5x)+(−5+3)=13(Combine Like Terms)
5x+−2=13
5x−2=13
Step 2: Add 2 to both sides.
5x−2+2=13+2
5x=15
Step 3: Divide both sides by 5.
5x
5
=
15
5
x=3
Answer:
x=3
The clocks shows when Tisa’s movie started and ended. How long did the last movie last? Plz hurry I need to finish
Answer:
it last 2 hours and 30 min
Step-by-step explanation:
if 3(x+1)=7 find the value of 3x
Answer:
3x=4
Step-by-step explanation:
3x+3=7
3x=4
Answer plzzzzzzzzzzzzzzz
Answer:
1 63636363 /1000000000
Step-by-step explanation:
Since it is 1. ..., it would be a mixed number with the 1 out front. There are 9 numbers after the decimal, making the denominator one billion, and then take the actual numbers (63) and make them the numerator.
an 8 inch candle burns 1/4 inch every hour. a 12 inch large candle burns 1/2 inch every hour. after how many hours will the two candles be the same height?
Answer:
69
\
Step-by-step explanation:
-6a - 4(a - 3) = -6a + 15
Step-by-step explanation:
-6a - 4(a - 3) = -6a + 15
=> -6a - 4a + 12 + 6a - 15 = 0
=> -4a - 3 = 0
=> -4a = 3
=> a = -3/4
Solve: -(6x+ 8) = 4(17 - x) *
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = − 38
Step-by-step explanation:
Answer:
−38
Step 1: Simplify both sides of the equation.
−(6x+8)=4(17−x)
−6x+−8=(4)(17)+(4)(−x)(Distribute)
−6x+−8=68+−4x
−6x−8=−4x+68
Step 2: Add 4x to both sides.
−6x−8+4x=−4x+68+4x
−2x−8=68
Step 3: Add 8 to both sides.
−2x−8+8=68+8
−2x=76
Step 4: Divide both sides by -2.
−2x−2=76−2
x=−38
PLEASE HELP ME ASAP I DONT WANT TO FLUNK MATH
Find the slope given these points:
(-8,4) & (-5,1)
A. -1
B. 1
C. 3/13
D. 5/13
Answer:
A:-1
Step-by-step explanation:
Carlo’s Bakery is having a special where he packages 6 muffins together for a low price and he packages 20 cookies together for a low price. His baker realized they sold the same amount of muffins and cookies yesterday due to this great sale. What is the minimum amount of muffins that were sole yesterday? Is this a GCF or LCM problem?
Answer:
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
Step-by-step explanation:
6 muffins together
20 cookies together
To sell the same amount of muffins and cookies,
Find the lowest common multiple of 6 muffins and 20 cookies
6 muffins = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78
20 cookies = 40, 60, 80
The lowest common multiple of 6 muffins and 20 cookies is 60
Therefore,
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
State of the two triangles are congruent. if they are, state how you know.
Answer:
Both Triangle are congruent because they have equal sides (the same amount of ticks on each side) The triangles are congruent.
Step-by-step explanation:
Solve the equation to find the value of a.
✓ 4a + 5 = 7
Answer:
0.5
Step-by-step explanation:
4a+5=7
4a=7-5
4a=2
a=2/4
Answer:
a = 1/2
Step-by-step explanation:
4a + 5 = 7
4a = 2
a = 1/2
Identify the domain and range of the following function:
{(8,7),(4,9),(0,0),(1,17)}
Answer:
Domain: 8,4,0,1
Range: 7,9,0,17
F(x)=-4x+3 vertical translation of 5 units down
Answer:
Gigi Jojo Jojo hip-hop Dutch him
so do Cob zoom from chick dunno drink gum
Step-by-step explanation:
hjjjhb. bjkn
jkk.
hj. hm.
gin
ghb.
8vb.
ucnluh itg.hboy
HELP PLEASEEEE!!!!! [Easy]
Answer: 120
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Help meeeeee. Thank you
Duke is a part-time student at Horizon Community College. He currently has 22 credits, and he plans to take 6 credits per semester until he is finished.
Duke's friend Kila is also a student at the college. She has 4 credits and plans to take 12 credits per semester. After how many semesters will Duke and
Kila have the same number of credits?
Answer:
3
Step-by-step explanation:
22=6c=4+12c
-6c -6c
22=4+6c
-4 -4
18=6c
/6 /6
3=c
For part of a science experiment, Andre adds 0.25 milliliters of dye to 12.3 milliliters of water. How many milliliters does the mixture contain?
Answer:
12.55 milliliters
Step-by-step explanation:
0.25+12.3=12.55
Good luck!
The mixture contains 12.55 milliliters.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that For part of a science experiment, Andre adds 0.25 milliliters of dye to 12.3 milliliters of water.
we need to find the amount of milliliters does the mixture contain.
Add twelve point three plus zero point two five.
12.3+0.25
12.30
+ 0.25
_______
12.55
Hence, the mixture contains 12.55 milliliters.
To learn more on Equation:
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