What is the coefficient of x3 in the expansion of (2x−3)5?
Group of answer choices
a) -360
b) 720
c) 10
d) -5
e) -120
Answer:
B 720
Step-by-step explanation:
same process as the previous image I sent ya
Answer:
B) 720.
Step-by-step explanation:
We can use the Binomial Expansion Theorem:
[tex]\displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^kb^{n-k}[/tex]
We have the expression:
[tex]\displaystyle (2x-3)^5[/tex]
Therefore, a = 2x, b = -3, and n = 5.
We want to find the coefficient of x³. To get x³, we can cube a. Therefore, we can find our coefficient by letting k = 3. Hence:
[tex]\displaystyle \binom{5}{3}(2x)^3(-3)^{5-3}[/tex]
Evaluate:
[tex]\displaystyle =10(8x^3)(9)=720x^3[/tex]
Our answer is B.
Can x3 – 3x + 1 be the quotient on division of x5+ 2x3 + x – 1 by a polynomial in x of degree 3? Justify
Answer:
No
Step-by-step explanation:
x⁵ + 2x³ + x - 1 -> degree of the polynomial is 5
So, when x⁵ is divided by x³, the quotient should be x⁵⁻³ = x².
So, x³ - 3x + 1 cannot be a quotient
Helpppp ,I will mark you brainlist
Answer:
Okay
Step-by-step explanation:
HOW TO I REMEMEBER MULTIPLICATION (I NEVER PAYED ATTENTION IN MATH LOL) AND I CANT SEEM TO REMEMEBER IT :(
I NEED TO REMEMBER 1-12
help I need help with my homework no link please BTW its 9th grade work I need help with number 1 a) I still need help with it
Answer:
you need to learn how to "prime factor" numbers....
primes are 2,3,5,7,11,13,17....
they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.
take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...
15 = 3 * 5
24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6
thus [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex] now just cancel all the SAME numbers from to to bottom
"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top
result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]
~~~~~~~~~~~~~~~~~~~~
[tex]\frac{21}{35}[/tex]
21= 3 * 7
35= 5* 7
[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]
Step-by-step explanation:
A jug holds 10 pints of milk. If each child gets one cup of milk, it can serve children. (Hint: 1 cup = 8 fluid ounces and 1 pint = 16 fluid ounces.)
Answer:
20 children
Step-by-step explanation:
We can see that 1 pint is equal to 2 cups. Since the jug holds 10 pints of milk, we can convert that to cups by multiplying by 2. We realize that the jug holds 20 pints of milk.
Since each child needs one cup of milk to be satisfied, we can state that the jug can satisfy 20 children.
Answer:
20 childrenyjvvvvggguggggyg
line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3
Answer:
105
Step-by-step explanation:
l is parallel m so angle 3+angle 6=180
Solve for x. Round to the nearest tenth, if necessary.
Answer:
X would be 63.9
Hope it helps
Step-by-step explanation:
The value of the variable 'x' using the cosine formula will be 63.9 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of 'x' is given by the cosine of the angle ∠QSR. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have
cos 35° = x / 78
x = 63.9
The value of the variable 'x' using the cosine formula will be 63.9 units.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ7
Please help me w the answer
Answer:
[tex]\frac{2(x-6)(x-10)}{(x-4)(x-5)}[/tex]
Step-by-step explanation:
In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.
The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:
[tex]\frac{()}{(x-4)(x-5)}[/tex]
The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be ([tex](x - 6)(x-10)[/tex]). Now one has this much of the function assembled
[tex]\frac{(x-6)(x-10)}{(x-4)(x-5)}[/tex]
Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following:
[tex]\frac{2(x-6)(x-10)}{(x-4)(x-5)}[/tex]
Determine the period.
N
10
Hello,
f(x+5)=f(x)
Periode is 5
Answer:
It's 4 on acellus, not 5 :)
Step-by-step explanation:
3x
2x
x + 30
The diagram shows a triangle.
The sizes of the angles, in degrees, are
3x
2x
x + 30
Work out the value of x
Answer:
x = 25°
Step-by-step explanation:
3x + 2x + x + 30° = 180°
6x + 30° = 180°
6x = 150°
x =25°
=> 3x = 25 * 3 = 75°
=> 2x = 25 * 2 = 50°
=> x + 30° = 25° + 30° = 55°
Help ASAP
Determine reflections (advanced)
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'.
Answer:
Line that connects points (0,4) to (4,0)
Step-by-step explanation:
Just imagine where you should fold the paper to overlap one figure on another
How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows
Answer:
2850
Step-by-step explanation:
1+2+3+4+5+6+7...74+75
just add up all the numbers from 1 to 75
PLS HELP SOON WILL MARK BRAINLYEST
A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.
According to the question
b= 35 and (8,21) lies on the ellipse
After calculation we get a= 10
equation for the ellipse.
[tex] \frac{ {x}^{2} }{100} + \frac{ {y}^{2} }{1225} = 1[/tex]
find the value of x in each case
Step-by-step explanation:
180-(90° +32°)
180- 122= 58
triangle =180°
180° - (58° +58°)
180° - 116°= 64°
Answer:
x=64
Step-by-step explanation:
∠A = 180-(90°+32°)
=> ∠A=180-122= 58
Angle sum property in Triangle=180°
=> x = 180° - (58°+58°)
=> x = 180° - 116°= 64°
Find the center and radius of the circle. Help !!
Answer:
the center is -1,1 and the radius is 4 i think
Step-by-step explanation:
Angle A and B are supplementary angles. The measure of angle B is twice the measure of angle A minus 24. Find the measure of the angle A and B.
Answer:
A = 58
B = 112
Step-by-step explanation:
A + B = 180 Supplementary angles
B = 2A - 24 Given
Substitute for B in the first equation
A + 2A - 24 = 180
3A - 24 = 180 Add 24 to both sides
3A = 180 + 24 Combine the right
3A = 204 Divide both sides by 3
A = 204/3
A = 68
B = 2A - 24
B = 2*68 - 24
B = 136 - 24
B = 112
Can ya’ll help me out
Answer:
Step-by-step explanation:
[tex]volume of cone=\frac{1}{3} \pi r^2h\\=\frac{1}{3} \pi (4)^2 \times 3\\=16 \pi \\\approx 50 in^3[/tex]
Answer:
answer is C 50 in³are you fine with it
Use the factors of the numbers to explain why
45 x 56 = 5 x 7 x 8 x 9
Answer:
45 x 56=
2520 and
5 x 7=35*8=280*9=2520
2520=2520
Hope This Helps!!!
Subtract 11.485-18.38
Answer:
-6.895
Step-by-step explanation:
11.485
-18.38
______
-6.895
I need help pls !!!!!!!
if each square is 2cm long then the perimeter is
Answer:
for each square the perimeter would be length times width. so 2x2 =4
Now if there are multiple squares then the answer would be different. but 4 is the answer for the individual square.
WOrth 10 pts ... pls help
A group of friends wants to go to the amusement park. They have $214.25 to spend on parking and admission. Parking is $6.75, and tickets cost $20.75 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
10 friends can go to the amusement park
Step-by-step explanation:
214.25 = 6.75 + 20.75x
207.50 = 20.75x
x = 10 friends can go
Find the measure of the missing angle using the triangle angle sum theorm
Answer:
31°
Step-by-step explanation:
The theorem states that all angle sums of any triangle add up to 180°.
128 + 21 = 149, and to find ?°, subtract 149 from 180 to get 31°.
HELP ME PLZ!!
-x - 1 = 221 + 2x
Answer:
[tex]-x\:-\:1\:=\:221\:+\:2x[/tex]
[tex]-x-1+1=221+2x+1[/tex][tex]-x=2x+222[/tex][tex]-x-2x=2x+222-2x[/tex][tex]-3x=222[/tex][tex]\frac{-3x}{-3}=\frac{222}{-3}[/tex][tex]\hookrightarrow Answer:x=-74[/tex]
-------------------------
hope it helps...
have a great day!!
What is the answer to this question?
Answer:
yeah,I think it's 16 ...
Solvex - 7x - 34 = 10 halo pls helppppppp
Answer:
x-7x-34=10
-6x-34=10
Step-by-step explanation:
x=-22/3
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass?
Answer:
f=x−32
Step-by-step explanation:
Subtract 3232 from both sides.
Answer:
f=32.2m
Step-by-step explanation:
got it right on edge
A man borrows $800 for 2 years at a simple interest rate of 20%. What is the total amount that must be repaid
Answer: [tex]\$1120[/tex]
Step-by-step explanation:
Given
Man borrows $800 for 2 years
Rate of interest is R=20%
Simple interest is given by
[tex]\Rightarrow S.I.=\dfrac{P\times R\times T}{100}[/tex]
Insert the values
[tex]\Rightarrow S.I.=\dfrac{800\times 20\times 2}{100}\\\\\Rightarrow S.I.=\$320[/tex]
So, total payable amount is
[tex]\Rightarrow 800+320\\\Rightarrow \$1120[/tex]