Answers
The expression (3a + 2b)^7 is a binomial expression;
The coefficient of the fourth term is 15120
How to determine the coefficient fourth term?The equation is given as:
(3a + 2b)^7
The above expression is a binomial expression;
Assume the expression is:
(x + y)^n
The equation of the expansion is:
[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]
When the expression is expanded, the parameters of the fourth term are
n = 7
r = 4
x = 3a
y = 2b
So, we have:
(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4
Evaluate each factor
(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4
Evaluate the powers
(3a + 2b)^7 = 35 * 27a^3 * 16b^4
Evaluate the product
(3a + 2b)^7 = 15120a^3b^4
The coefficient of the above expression is 15120
Hence, the coefficient of the fourth term is 15120
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Related Questions
pls help me how do they get 9 7/5 = 10 2/5 ( its in the example number 1) plss help me i don't know :⊂
Answers
Answer:
INSTRUCTION FOLLOWED: write the sum as a mixed number where the fractional number is less than one.5/5 out of the 7/5 make ONE whole while 2/5 is left over.
The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5
Step-by-step explanation:
INSTRUCTION FOLLOWED: write the sum as a mixed number where the fractional number is less than one.5/5 out of the 7/5 make ONE whole while 2/5 is left over.
The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5
Lola bought 4.25 yards of ribbon. The ribbon cost $1.59 per yard. What was the
total cost of her ribbon to the nearest cent?
Fill in the blanks with an operation symbol and a number to complete the
equation.
4.25___$1.59 = $_
Answers
Answer: multiply
Rectangular rug has a perimeter of 3320 inches the length is 25 inches more than twice the width find the length and width of the rug
Answers
Answer:
length= 1115 inches
width= 545 inches
Step-by-step explanation:
The perimeter of the rectangular rug is the sum of the lengths of all its sides.
Start by defining the variables that we are going to use throughout our working.
Let the length and the width of the rug be L and W inches respectively.
Perimeter= 2(L +W)
Given that the length is 25 inches more than twice the width,
L= 2W +25 -----(1)
3320= 2(2W +25 +W)
Divide both sides by 2:
1660= 2W +W +25
1660= 3W +25
3W= 1660 -25
3W= 1635
Divide both sides by 3:
W= 1635 ÷3
W= 545
Substitute W= 545 into (1):
L= 2(545) +25
L= 1115
Thus, the length and width of the rug is 1115 and 545 inches respectively.
Jonathan wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift boxIf all the triangles are equilateral, how much wrapping paper did he use, in square meters
Answers
Jonathan will need a warping paper of 420.78m^2
Data;
slant height = 12mlength of sides = 10.39mSurface Area of an Equilateral TriangleTo find the amount of warping paper used, we can use the formula of surface area of an equilateral triangle since the triangle used here is an equilateral triangle.
[tex]Surface Area = base area + \frac{1}{2}(perimeter * slant height)[/tex]
Let's calculate the base area and perimeter of the triangle.
base area of an equilateral triangle is given as
[tex]B.A = \frac{\sqrt{3} }{4} a^2[/tex]
a = length of the sideLet's substitute the value and solve
[tex]B.A = \frac{\sqrt{3} }{4} a^2\\B.A = \frac{\sqrt{3} }{4}*10.39^2\\B.A = 46.74m^2[/tex]
The base area is 46.74m^2
Let's calculate the perimeter of the triangle
[tex]P = 3a\\[/tex]
Substitute the value into the equation and solve
[tex]P = 3a \\P = 3 * 10.39\\P = 31.17m^2[/tex]
We can proceed to substitute the values of the base area and perimeter of the triangle into the formula of the surface area of an equilateral triangle.
[tex]S.A = base area + \frac{1}{2}(perimeter * slant height)\\S.A = 46.74 + \frac{1}{2}(31.17*12)\\S.A = 46.74 + 374.04\\S.A = 420.78m^2[/tex]
The surface area of the equilateral triangle is 420.78m^2
Jonathan will need a warping paper of 420.78m^2
Learn more on surface area of an equilateral triangle here;
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Answer:c
Step-by-step explanation:
Make x the subject of the formula
y = x^2
Answers
Answer:
[tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle \large{y=x^2}[/tex]
Make ‘x’ the subject of the formula by square root both sides:
[tex]\displaystyle \large{\sqrt{y}=\sqrt{x^2}}[/tex]
Cancel the square root and square in RHS and write plus-minus in LHS:
[tex]\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Therefore, the solution is [tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
__________________________________________________________
Summary
To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.
You may also be curious why do you have to add plus-minus on another side when cancelling [tex]\displaystyle \large{\sqrt{x^2}}[/tex] because [tex]\displaystyle \large{\sqrt{x^2}=|x|}[/tex] and [tex]\displaystyle \large{|x|}[/tex] for their positive and their counterparts (opposite/negative) will always give same y-value.
From an example:
[tex]\displaystyle \large{\sqrt{x^2}=4}[/tex] can be rewritten as [tex]\displaystyle \large{|x|=4}[/tex], cancel absolute sign/square root then write plus-minus which the solution is [tex]\displaystyle \large{x=\pm 4}[/tex] and if you substitute x = 4 or -4, the equation will be true for both values.
__________________________________________________________
Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
A pencil has a mass of 25 grams of there are 8 pencils what is the total mass of all the pencils
Answers
Answer:
200g/0.2kg
Step-by-step explanation:
8 × 25g = 200g
The total mass of the pencil is 200 grams.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
A pencil has a mass of 25 grams.
there are 8 pencils.
Total number of pencils = 8
Mass of each pencil = 25 grams
Total mass of the pencils = 8 × 25 = 200 grams
Hence the total mass is 200 grams.
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I have a question whats 2+2
Answers
Answer:
22
Step-by-step explanation:
You add the to numbers together and the answer will be 22
I hope it helps! Have a great day!
Muffin ^^
What the line measures
Answers
Help picture below problem 17
Answers
Answer:
40
Step-by-step explanation:
Angle KPJ is going to have the same measure as Angle DPE. This problem is a bit tricky, but I'll try my best to explain it. A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.
To find the measure of Angle KPJ, we first have to find the measure of angle DPE, and the way we're gonna do that is add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).
That might have sounded a bit confusing, but that's the best way I could explain it. Now, let's add Angle FPD and Angle EPG.
105 + 35 = 140
Now, let's subtract that from 180.
180 - 140 = 40
We now know that the measure of Angle DPE is 40, and since it's equivalent to Angle KPJ, our answer is 40!
I know that was confusing, but I hope it helped a little bit! Have a lovely day!! :)
Mike is buying a car for $24,300. He wants to make a maximum down payment of $3.000. TWo. deals are available, both for 48-month loans. In the first deal, with a factory rebate his down payment will be $1,000. His monthly loan payments would be $573 21 at 8.4% interest. In the second deal, he gets no rebate and makes a $3,000 down payment but his interest rate is 0.9% resulting in a $451.95 loan payment. a) What total amount will Mike pay with the first deal? b) What total amount will Mike pay with the second deal?
Answers
Answer:
1,000
Step-by-step explanation:
[tex]5xy { - x} ^{2} {t} + 2xy + 3x {}^{2} t[/tex]
what's the answer
Answers
Answer: 7xy + 2x^2t
Step-by-step explanation:
At 2:00 PM the temperature is 18°F. At 10:00 PM the temperature is -9°F.
What is the change in temperature from 2:00 PM to 10:00 PM?
Answers
Answer:
To figure out the change, we subtract the original temperature by the following after temperature.
18°F - original
-9°F - subsequent time after original
So we set up the equation;
18°F - (-9°F)
(Two negatives combine to form a positive)
18°F + 9°F
= 27°F was the change in temperature.
The change in temperature from 2:00 PM to 10:00 PM is -27° F.
What is Temperature?Temperature is a physical quantity that measures the coldness or hotness of an object in reference to some standard value.
Change in temperature can be defined by the difference of the final temperature with that of the initial temperature.
Temperature is usually measured in degree Celsius or degree Fahreheit.
Temperature at 2:00 PM = 18° F
Temperature at 10:00 PM = -9° F
Change in temperature = Final temperature - Initial temperature
= -9° F - 18° F
= -27° F
Hence, the change in temperature can be calculated as -27° F.
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An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1750 feet apart . As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If If A=30 degrees and B=20 degrees how high is the airplane?
Answers
Answer:
at aircraft(at z) sported by
please I need help with this question
Answers
Dave pays 15 * (1+0.08) = $16.2
So the difference is:
$21.6-$16.2 = $5.4
Answer:
$5.40
Step-by-step explanation:
First, find Dave's purchase. To do this, you multiply 15 by the tax percent and add that to the original.
So:
15 x 8% = 15 x 0.08 = 1.2
15 + 1.2 = 16.2
Next, do the same for Mel's purchase:
20 x 8% = 20 x 0.08 = 1.6
20 + 1.6 = 21.6
Then, you subtract Dave's purchase from Mel's:
21.6 - 16.2 = 5.4
This comes out to $5.40
2. An object of mass 20kg is released from a height of 10m above the ground level. The kinetic energy of the object just before it hits the ground is (g=10ms-²
Answers
Answer:
2000j
Step-by-step explanation:
Kinetic Energy = mgh
= 20 x 10 x 10 J
= 2000J
The equation is :
Answer x =
Answers
Answer:
4x-11=73,
x=21
Step-by-step explanation:
11 subtracted from means -11
four times a number means 4(x) because x is the number
is = equals
so
4x-11=73
+11 +11
4x=84
/4 /4
x=4
Sayeed is buying a crate for his puppy. The crate is 20 inches long, 13 inches wide, and 16 inches high. What is the volume of the crate?
Answers
V = 4,160 cu in
Sorry if this was confusing, this was my first time answering a question, if I got it wrong I apologize, have a nice day/night!
what is 2+2 because i just decided to ask this
Answers
Answer:
4
Step-by-step explanation:
2+2 = 4
Hope this helps:)
what is 6(8x+1) equil to ?
Answers
Hello!
Let's use the Distributive Property & simplify:
6(8x+1)
distribute 6 by multiplying it times 8x and 1:
48x+6
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Answer:
[tex]\displaystyle 6 + 48x[/tex]
Step-by-step explanation:
[tex]\displaystyle 6[8x + 1] \hookrightarrow \boxed{48x + 6}[/tex]
I am joyous to assist you at any time.
I need help with this question please
Answers
Answer:
Step-by-step explanation:
As ABCD is a rectangle, ∠A = 90°.
Diagonal BD will be the hypotenuse.
[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]
Length = AB = 33.8 cm
[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]
Width = 25.5 cm
can you please help me
Answers
Answer:
Angle ABC = 6x
Step-by-step explanation:
this is an isosceles triangle so the values of angle ACB and angle ABC are the same.
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answers
Dilation is the change in size of of object. The length of the side OB' will be 3 units
Dilation of coordinateFrom the given diagram, we can see that there is a change in the side of the triangle OAB to OA'B'
Given the following parameters
OB = 3/4 units
Scale factor = 4 units
The measure of OB' = 4 * 3/4 = 3 units
Hence the length of the side OB' will be 3 units
Learn more on dilation here: https://brainly.com/question/10253650
Answer:
3
Step-by-step explanation:
edg 2022
Define the algebraic terms by counting how many terms given on the expression below.
4x + 3n + 5
Answers
Answer:
Two terms ( [tex] x [/tex] and [tex] n [/tex])
Step-by-step explanation:
If simplified it gives 3n+4x+5
And cannot be factored
=======================================================
We're given the following expression:
[tex]\bigstar{\boxed{4x+3n+5}[/tex]
Here,
4x is a term
3n is a term
5 is a term
4 is the coefficient of x
x is a variable
3 is the coefficient of n
n is a variable
5 is a constant
Details:-
A coefficient is a number before a variable
A variable is a letter
A constant is a number without any variables next to it
=========================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Find the product. (6y - 2)2
A. 36y2 - 24y + 4
B. 36y2 + 24y = 4
C. 36y2 + 4
D. 12y2 - 16y + 4
Answers
Answer:
A. 36y² - 24y + 4Step-by-step explanation:
Use identity
(a ± b)² = a² ± 2ab + b²Here we have a = 6y, b = 2
(6y - 2)² = (6y)² - 2(6y)(2) + 2² = 36y² - 24y + 4Correct choice is A
(This is a multiple choice question)Suppose you are rehearsing for a dance competition and you fall and hurt your shoulder. At the hospital, they take X-rays, consult a shoulder specialist, and give you a stabilizer brace. You pay a $50 co-pay at the time of service, and the ER bills your insurance company for the rest. The total hospital bill is $3,720. The table below shows the payment structure for your health insurance policy. If the injury happened in July, what is your total paid in monthly premiums?
A. 1,050$
B. 150$
C. 900$
Answers
Choose the correct graph of the function y=√x+2 .
Answers
Answer:
[D]
Step-by-step explanation:
Graph using the end point and a few selected points.
x y
0 2
1 3
2 3.41
Graph is below:
[RevyBreeze]
What equation results from completing the square and then factoring?
x^2 + 4x = 5
A. (x + 2)^2 = 3
B. (x + 2)^2 = 7
C. (x + 2)^2 = 1
D. (x + 2)^2 = 9
Answers
Answer:
(x+2)^2 = 9
Step-by-step explanation:
To complete the square we need to add 4 to both sides of the equation,
Why we add 4 to both sides? Because if we add it to one side only, the equation will turn into an inequation
x^2 + 4x + 4 = 5 + 4
x^2 + 4x + 4 = 9 and the factor of the expression is (x+2)*(x+2) = 9
(x+2)^2 = 9
These points are linear.
Find the slope.
Х 2 4. 6 8 10
y 7 13 19 25 31
Hint: First calculate the change
between each y-value.
Answers
Answer:
3
Step-by-step explanation:
Select an ordered pair: (2, 7)
Select another ordered pair: (6, 19)
slope = (difference in y)/(difference in x)
slope = (19 - 7)(6 - 2)
slope = 12/4
slope = 3
Answer:
Step-by-step explanation:
Pick any two points.
(2 ,7) & (4, 13)
x₁ = 2 ; y₁ = 7 & x₂ = 4 ; y₂ = 13
[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]=\dfrac{13-7}{4-2}\\\\\\=\dfrac{6}{2}\\\\\\= 3[/tex]
How do you solve this?
Answers
Answer:
22
Step-by-step explanation:
5x + 8 = 118
5x = 110
x = 22
X^2 - 2x = 8
Find the value of X
Answers
To find the solutions to the quadratic equations
⇒ factor the equation
[tex]x^2-2x = 8\\x^2-2x-8=0\\(x-4)(x+2) = 0[/tex]
Now to find the exact solutions, we have to set 'x - 4' and 'x + 2' equal to 0
[tex]x - 4 = 0\\x = 4\\\\x + 2 = 0\\x = -2[/tex]
Thus the solution to this problem is -2 and 4
Hope that helps!
Answer:
4 and - 2
Step-by-step explanation:
x² - 2x = 8
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x ( x + 2 ) - 4 ( x + 2 ) = 0
( x + 2 ) ( x - 4 ) = 0
x + 2 = 0
x = - 2
x - 4 = 0
x = 4
The values of x are - 2 and 4.