The first three terms of the binomial expansion of (2 – ax)" are 64 – 16bx +100bx?.
Find the value of each of the integers n, a and b.
Ans: n=6, a=5, b=60
Answers
Answer:
n = 6, a = 5, b = 60
Step-by-step explanation:
In a binomial function (a + b)ⁿ expression that represents the terms,
(a + b)ⁿ = [tex]\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k[/tex]
By this formula,
1st term = [tex]\binom{n}{0}a^{n-0}b^0[/tex] = aⁿ
2nd term = [tex]\binom{n}{1}a^{n-1}b^1[/tex] = [tex]n.a^{n-1}b^1[/tex]
3rd term = [tex]\binom{n}{2}a^{n-2}b^2[/tex] = [tex]\frac{n(n-1)}{2}.a^{n-2}.b^2[/tex]
For the binomial expansion initial 3 terms of (2 - ax)ⁿ = 64 - 16bx + 100bx²
Terms of (2 - ax)ⁿ = [tex]2^n+n(2)^{n-1}(-ax)+\frac{n(n-1)}{2}(2)^{n-2}(-ax)^2[/tex]
= [tex]2^n-n(2)^{n-1}(ax)+n(n-1)(2)^{n-3}(a^2x^2)[/tex]
Comparing the terms of both the expansions,
1st term
2ⁿ = 64
2ⁿ = 2⁶
n = 6
2d term
[tex]n(2)^{n-1}(ax)=16bx[/tex]
[tex]6(2)^{6-1}(a)=16b[/tex]
192a = 16b
b = 12a -----(1)
3rd term
[tex]n(n-1)2^{n-3}(a^2x^2)=100bx^2[/tex]
[tex]6(6-1)2^{(6-3)}(a^2)=100b[/tex]
[tex]30(2)^3(a^2)=100b[/tex]
240a² = 100b
b = 2.4a² -----(2)
From equation (1) and (2),
b = 12a = 2.4a²
a = [tex]\frac{12}{2.4}=5[/tex]
From equation (1)
b = 12a = 60
Therefore, n = 6, a = 5, b = 60
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Answer:
Step-by-step explanation:
1). Swap the order of equations.
2). Yes, system of equations are equivalent with the same solution.
29x = 46 ⇒ x = [tex]\frac{46}{29}[/tex]
y = - [tex]\frac{184}{29}[/tex] + [tex]\frac{203}{29}[/tex] = [tex]\frac{19}{29}[/tex]
( - [tex]\frac{46}{29}[/tex] , [tex]\frac{19}{29}[/tex] )
Please do 11 vote you brainiest
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Answer:
ITS B
Step-by-step explanation:
Solve each equation. Write The properties that justify each step in the solution method
a. 3x - 8 = -7x + 18
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Answer: I’m not sure how to explain so you look at what I did and if it is an equation then I did solve it but if I should did the two separately then tell me so I can do it , have a great and funny day :)
Step-by-step explanation:
f(x)=-(x-3)²+1 determine the vertex
Answers
Answer:
vertex = (3, 1 )
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x - 3)² + 1 ← is in vertex form
with vertex (h, k ) = (3, 1 )
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Answer:
Just give me a few min ill be right back to help :)
Step-by-step explanation:
) In each diagram, line p is parallel to line f, and line t intersects lines p and f. Based
on the diagrams, which statement is true? (8.8D)
A. The value of x should be 75, because the angles shown in the diagrams are
congruent
B. The value of x should be 105, because the measures of the angles shown in the
diagrams add up to 180°.
C. The value of x should be 140, because the measures of the angles shown in the
diagrams should add up to 360and 360 - (110 + 110)
D. The value of x should be 70, because the measures of the angles shown in the
diagrams are both 70
Answers
Answer:
A. The value of x should be 75, because the angles shown in the diagrams are congruent.
Step-by-step explanation:
I did the test
need help asap please!!!!!!1
Answers
Answer:4/3 I think
Step-by-step explanation:
A gumball machine contains 23 green gumballs, 52 red gumballs, 34 blue gumballs, 61 yellow gumballs, and 30 pink gumballs.
What percentage of the gumballs are red?
Answers
Answer:
26%
Step-by-step explanation:
if a =(1 2 3 4 5 then the number subsets a is
Answers
Answer:
Every choice doubles the number of subsets previously built, so the 4 subsets of {1,2} become 8 when we think of subsets of {1,2,3}. Then 16, and finally 32 subsets for {1,..5}.
Step-by-step explanation:
hopefully this helps!
1. 133 1/3% of 36=?
2. 260% of 360=?
Answers
Answer:
1. 133 1/3% of 36=48
2. 260% of 360=936
Step-by-step explanation:
1. 133 1/3% of 36
=(133 1/3)% of 36
=(133/1+1/3)% of 36
=(399+1/3)% of 36
=(400/3)% of 36
=(400/3 *100) *36
=(400/300*36)
=4/3*36
=4*12
=48 Ans
---------------------------------------------------------------------------------------
2. 260% of 360
=260% of 360
=260/100*360
=26/10*360
=26/1*36
=936 Ans
Which statement best explains the relationship between
lines AB and CD?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative
reciprocals.
They are not parallel because their slopes are not
equal.
They are not parallel because their slopes are
negative reciprocals.
Answers
Answer:
A
Step-by-step explanation:
Thats what im pretty sure it is, you didnt provide a picture but i know that parallel slopes are equal to each other
Answer:
A Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
EASY!!!! Answer this question correctly
Answers
Answer:
1st answer choice- You do not have enough jars because 20 jars will only hold 35 cups of applesauce.
Step-by-step explanation:
So 1.75 cups of applesauce fits in a jar. You have 20 jars so you multiply the cups of applesauce that can fit in the jar by how many jars you have. It will look like this: 1.75x20=? Now you multiply them and you get 35 which is how many cups of applesauce 20 jars will hold. You will have 5 cups of applesauce left over that cannot be transformed into a jar.
If you can please make my answer the brainliest that would be much appreciated. Thanks!
Answer:
You do not have enough jars because 20 jars will only hold 35 cups
Step-by-step explanation:
PLS PLS PLS HELPPPP NO EXPLANATION NEEDED
Answers
Answer:
i believe its C
Step-by-step explanation:
Answer:
it is a little hard to see but yeah from what I can tell it looks like it would be C
Step-by-step explanation:
Hope this helps
Tell me if it is wrong
Please answer this correctly, and you'll recieve brainliest!
Which figure can be transformed into figure L by a 90° rotation clockwise about the origin followed by a translation 2 units down?
Question Options:
Question 2 options:
figure J
figure M
figure N
figure P
Answers
Answer:
J can be rotated
Step-by-step explanation:
Answer: Figure J
Clockwise and 2 units down
Find the slope of the equation y=2x+5
Answers
Answer:
the slope is 2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
i really need help with this!!
Answers
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[tex]y = - \frac{1}{6} x - 1 \\ [/tex]
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Let me know if you need explanation.
can someone help me with this one.
i will give you a brainlist if you give the answers. thanks!
Answers
Answer:
A= 115
B= 65
C= 90
D= 65
E= 15
F= 90
Step-by-step explanation:
If you need explanations, tell me.
please please help me quickly
Answers
Answer:
1/4
Step-by-step explanation:
A rectangular frame has length (x+2) units and width (x-2) units. If the area is 96 square units, what is the value of x?
Answers
Answer:
x=10
Step-by-step explanation:
according to the question
(x+2)(x-2)=96
=>x^2-4=96
=>x^2=96+4
=>x^2=100
=>x=√100
Therefore
x=10
x=-10
As width and length can't be negative
So x=10
Width=10-2=8
Length=10+2=12
12×8=96 (proven)
Answer:
Please check the explanation.
Step-by-step explanation:
As we know that the area of a rectangle is defined by multiplying the length by the width.
[tex]A=l\times w[/tex]Given
rectangular frame length = l = (x+2) unitsrectangular frame width = w = (x-2) unitsArea = 96 square unitssubstituting all the given values in the formula to find the value of x.
[tex]A=l\times w[/tex]
[tex]96=\left(x+2\right)\times \left(x-2\right)[/tex]
[tex]96=x^2-4[/tex]
[tex]x^2-4=96[/tex]
subtract 96 from both sides
[tex]x^2-4-96=96-96[/tex]
[tex]x^2-100=0[/tex]
[tex]x^2=100[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]x=\sqrt{100},\:x=-\sqrt{100}[/tex]
[tex]x=10,\:x=-10[/tex]
Putting x = -10 in the length and width will make the length and width negative, which can not be possible.
i.e.
length = l = x+2 = -10+2 = -8 units
width = w = x-2 = -10-2 = -12 units
Therefore, x=-10 must be excluded.
Now, putting the length of x = 10.
i.e.
length = l = 10+2 = 10+2 = 12 units
width = w = x-2 = 10-2 = 8
[tex]A=l\times w[/tex]
96 = 12 × 8
96 = 96
Therefore, the correct value of x = 10
PLEASE HELPP!! I WILL GIVE BRAINLIEST!
Answers
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1.5 white 2 blue
Step-by-step explanation:
what is 1/2 divded by 3/4
Answers
Answer:
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {1}{2}} \div {\dfrac {3}{4}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {1}{{\cancel{2}}}}\times {\dfrac{{\cancel {4}}}{3}}[/tex]
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Answers
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Step-by-step explanation:
Wendy jarred 8 liters of jam after 2 days. How many days does Wendy need to spend making jam if she wants to jar 32 liters of jam in all? Assume the relationship is directly proportional.
Answers
Answer:
8 days
Step-by-step explanation:
it takes her two days to make 8 liters so for every 8 liters you add on two more days. 8:2, 16:4, 24:6, 32:8
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(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - X
(c) 4x+8 = 2x + 7 + 2x - 20
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Answers
Answer:
a. infinite solutions, answer is x = 30, identity equation
b. no solution, a contradiction equation
c. no solution, a contradiction equation
Step-by-step explanation:
Please help with this math problem ASAP!
Answers
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0
Step-by-step explanation:
0 time difernce because a negative numbers means it will have an world record , while a positive time diference means it did not beat the world record
Will mark brainliest
Answers
Answer:
Step-by-step explanation:
We know she gets 4 more quarters so: q+4
She gives away 3 dime so: d-3
And the nickels stay the same: n
In total the expression would be: q+4+d-3+n
Hope this helps :D
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Answers
Answer:
4
Step-by-step explanation:
4
ANSWER THE QUESTIONS PLS. SERIOUS ANSWERS ONLY. 100 POINTS
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Step-by-step explanation:
Tnd 50 dia w2 wop p.35.00 dma fw
Answer: the answer is wha the other dude said
Step-by-step explanation:
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Answers
Answer:
no
when you enter the point into the equation and solve, it does not work
Answer:
NO
Step-by-step explanation:
if x=5 then what is x squared?
Answers
Answer:
25
Step-by-step explanation:
[tex]x^2\\\\x=5\\\\5^2=5*5=25[/tex]
Hope this helps.