Notice that
(1 - x)⁵ (1 + 1/x)⁵ = ((1 - x) (1 + 1/x))⁵ = (1 - x + 1/x - 1)⁵ = (1/x - x)⁵
Recall the binomial theorem:
[tex]\displaystyle(a+b)^n = \sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]
Let a = 1/x, b = -x, and n = 5. Then
[tex]\displaystyle\left(\frac1x-x\right)^5 = \sum_{k=0}^5\binom5k\left(\frac1x\right)^{5-k}(-x)^k = \sum_{k=0}^5 (-1)^k\binom5k x^{2k-5}[/tex]
We get an x ³ term for
2k - 5 = 3 ==> 2k = 8 ==> k = 4
so that the coefficient would be
[tex](-1)^4\dbinom54 = \boxed{5}[/tex]
solve. x/2 + 1/3 greater than 0
Answer:
x > -2/3
Step-by-step explanation:
[tex]\frac{x}{2} +\frac{1}{3} > 0[/tex] , subtract 1/3 from both sides
[tex]\frac{x}{2} > \frac{-1}{3}[/tex] , multiply both sides by 2
[tex]x > \frac{-2}{3}[/tex]
A cube with a volume of 216 cubic feet has all but the top and bottom faces painted. What is the total area of the two unpainted sides?
The volume of a cube is Side ^3
Find the cubic root of the volume to find the side length:
Side = cubicroot(216) = 6 feet.
The area of a face of a cube is s^2
Area of a face = 6^2 = 36 square feet.
Area of 2 faces = 36 x 2 = 72 square feet
Answer: 72 square feet
Answer:
72 ft²
Step-by-step explanation:
To find the length of each side we have to cube root the volume
∛216 = 6
We only have to find the areas for two faces (the top and bottom)
6 x 6 = 36 = area for one face
36 x 2 = 72 = area for two faces
Which expression is equivalent to 4 + 36x?
Answer:
A
Step-by-step explanation:
4(1)+4(9x)=4+36x
what is the answer?
Answer:
Not similar.
Step-by-step explanation:
The answer is D.
Find the area of the following composite figure. Assume angles that look like they are a right angle are
right angles.
14 in
14 in
Q
Leave your answer in terms of . For example your answer might to 98 + 107.
square inches
NOTE: Figures are NOT to scale.
Answer:
7π + 7π + 196 ( could also be 14π + 196)
Step-by-step explanation:
14 is the length of the square. However it is also the diameter of the circle.
If you do diameter x π you will get the circumfrance. Which in this case is 14π. If your trying to find half of the circumfrance you would do 14π ÷ 2 which is 7π.
After finding 7π for one half a circle you do the same for the other and also get 7π
After finding the 2 half circles find the square which is 14 x 14 = 196
196 + 7π + 7π if you don't want bother pi's there it could also be seen as 196+ 14 π
write following ratio in simplest form :
125 g : 1 kg
Answer:
125g:1Kg
=> 125g : 1000g
=> 1:4Answer:
1:8
Step-by-step explanation:
125 g:1 kg
125g:1000 g
1 g:8 g
Keep smiling and hope u will be satisfied with my answer.Have a good day :)
Find the first three terms of the sequence below. 3n^2+5n−2
Answer:
-2, 6, 20 ,...
Step-by-step explanation:
3n² +5n -2
if n=0 , then 3*0² +5*0 -2= -2
if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6
if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20
Greater than (-3) but less than or equal to 3
Answer:
-3 < x <= 3
Step-by-step explanation:
draw it on a number line to check
Answer:
-3>x[tex]\leq \\[/tex]3
Step-by-step explanation:
> is the greater than
< is the less than
hope this helped have a great day
Use the graph below to describe the linearization of the data. How would you expect the linearization to change if the data were to extend beyond age 20?
Answer:
It is expected that linearization beyond age 20 will be use a function whose slope is monotonously decreasing.
Step-by-step explanation:
The linearization of the data by first order polynomials may be reasonable for the set of values of age between ages from 5 to 15 years, but it is inadequate beyond, since the fourth point, located at [tex](x,y) = (20, 5.5)[/tex], in growing at a lower slope. It is expected that function will be monotonously decreasing and we need to use models alternative to first order polynomials as either second order polynomic models or exponential models.
how do you solve for y?
Tom makes two deliveries of bricks.
The distance of one delivery is 20 miles more than the distance of the other delivery.
(b) Work out the difference between the two delivery costs.
Find the remainder when the polynomial 9x2 - 4x - 7 is divided by x - 3.
Answer: 62
Step-by-step explanation:
[tex]\displaystyle\bf 9x^2-4x-7 =0 \\\\ Synthetic \ \ division\ \ if \ \ x-3 =0 => x=3 \\\\ then \ \ 3| \underline{ \ 9 \ | \ -4 \ | \ -7 \ | } \\\\ . \!\! \qquad\qquad +|3*9| \ \ 23*3 | \\ .\!\!\!\!\!\1 \qquad \qquad \qquad | \ 23 \ | \ \ \ \boxed{62}[/tex]
Julie assembles shelves for a department store and gets paid $3.25 per shelf. She can assemble 5 per hour and works 8 hours per day. Determine Julie’s gross pay for 1 week
Pay per shelf = $3.25
No of shelfs per hour = 5
Total hours per day = 8
Total days to find pay of = 7
= 3.25×5×8×7
= 910
Therefore she is paid $910 after 1 week.
Must click thanks and mark brainliest
Select the polynomial that is a perfect square trinomial.
9x^2 + 9x + 1
36b^2 − 24b + 8
16x^2 + 24x + 9
4a^2 − 10a + 25
Answer: 16x^2 + 24x + 9
Step-by-step explanation:
Simplified version: (4x+3)^2
Match function with its corresponding graph
Answer:
Step-by-step explanation:
We can see that there are roots at (-2,0) and (-1,0)
also, the root at (-2,0) should bounce right off
and the root at (-1,0) should go through
With all that being said it has to be B
HURRY!!!!! HELP PLEASE!!!! NO SPAM!!!!!!!!!There are two identical oil tanks. The level of oil in Tank A is 6 ft and is drained at the rate of 0.5 ft/min. Tank B contains 10 ft of oil and is drained at the rate of 1 ft/min. After how many minutes will the level of oil in the two tanks be the same?
Answer:
8 munutes
Step-by-step explanation:
let :
x is the final level for both tanks (in ft) and
t is the time (in minutes)
the equation :
x = 6 - 0.5 t (eq.1)
x = 10 - 1t (eq.2)
eq. 1 = eq. 2
=>
6-0.5t = 10-1t
1t - 0.5t = 10-6
0.5t = 4
t = 4/0.5 = 8
t = 8 minutes
Answer: 8 minutes
Step-by-step explanation:
Write an equation for the level of oil in each tank.
Let t = the number of minutes.
Tank A: y = 6 − 0.5t
Tank B: y = 10 − 1t
Solve the system by using a table of values
When t = 8 minutes, the level in both tanks will be at 2 feet.
I am so confused..please help 0-0
A real estate agent receives a 3%
commission for selling a house. Find the
commission that the agent earned for
selling a house for $131,000.
you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,
131000/100 = 1310 x 3 = 3930
the commission is $3930.00
hope it helps :)
Solve, using the substitution method.
y = 3x + 5
4x – y = 5
10, 35)
(15, 10)
There are an infinite number of solutions.
There is no solution.
Answer:
the answer is (10,35)
Step-by-step explanation:
i took the quiz and im 100% sure
ty have a great day :)
Is the following number rational or irrational?
13
12
Choose 1 answer:
А
Rational
B
Irrational
Answer: Rational
This is because the number is in the form P/Q where P and Q are integers
We have P = -13 and Q = 12.
You can think of "rational" as in "ratio" which is very closely tied to fractions. Any rational number is a fraction of two integers. The denominator can never be zero.
Answer:
Rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Decimal form: − 1.08 3
3 repeats itself, so it's rational.
Javier works at a print shop. He starts printing at 8:00 a.m. The number of printed brochures is a linear function of the number of minutes since Javier started printing. By 8:50 a.m. he had printed 240 brochures, and by 9:00 a.m. he had printed 288. Write an equation in the form y = mx + b that represents the number of brochures, y, that were printed after x minutes.
Answer:
y = 4.8(x) + 0
Step-by-step explanation:
In this question, Javier managed to print 240 brochures in 50minutes from 8:00 to 8:50. If we divide these values we see that he printed 4.8 brochures per minute. The same result is given for the 10 minutes from 8:50 to 9:00 where he printed 48 brochures. Therefore, we can get the following linear formula from these values.
y = 4.8(x) + 0
In this case, b would equal 0 because Javier is starting from 0 brochures made when he gets to work at 8:00 a.m
Solve for 2. Round to the nearest tenth of a degree, if necessary.
w
36
V
20
50
X
PLS HELP
Answer:
Step-by-step explanation:
This is classic right triangle trig. If you're solving for x, which you are, you have to consider how the given sides relate to that angle. The side with a length of 50 is opposite the angle x, while the side of length 36 is adjacent to angle x. The trig ratio that utilizes the sides opposite and adjacent is tangent; HOWEVER, we are looking for a missing angle. Finding missing angles on your calculator requires the 2nd button. To find the missing angle x, you are looking for the angle that has a tangent ratio of 50 over 36 (opposite over adjacent...Toa in SohCahToa). Hit the 2nd button on your calculator and then the tangent button (in degree mode, not radian mode) and you will see this on your screen:
[tex]tan^{-1}([/tex]
After the parenthesis, enter the fraction and then hit the enter button to get the angle measure in degrees:
[tex]tan^{-1}(\frac{50}{36})=54.2[/tex] degrees.
It's very important that you learn how to use your calculator to find the trig identities that give you the ratio in decimal form and how to find the missing angles. Missing angles always use the 2nd button along with whatever trig identity you are using.
What is a linear system?
Answer:
Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up
What is the slope-intercept equation for the line below?
Step-by-step explanation:
given that the coordinate is (0,1)(4,3)
x¹=0, y¹=1, x²=4 y²=3
M=> Gradient => (y²-y¹)/(x²-x¹)
M=(3-1)/(4-0) => 1/2
Therefore the slope-intercept equation
M=(y-y¹)/(x-x¹)
1/2 = (y-1)/(x-0)
x=2y-2
2y=-2-x
y=-x/2 - 1
Find the value of f(x) at the given value of x: f(x) = (x -4)(x + 3), x = 3
Answer:
-6
Step-by-step explanation:
f(x)= (3- 4)(3+3)
=( -1 )(6)
= -6
Martas school has 325 desks for 13 classrooms . If the desks are shared evenly how many desks will each classroom have
Answer:
25
Step-by-step explanation:
Hi, Which option is correct??
Answer:
B
Step-by-step explanation:
option B is not similar.
the ratio of each side isn't same
Instructions: Find the missing length
Someone plssss help me with this question!!
Answer:
There are 3 possible values for a.
Step-by-step explanation:
a/b=2/3
3a=2b
If b>5 and b<13
apply all possible values
b=6 -> 3a=12 ==> a=4 1st possibility
b=7 -> 3a=14 ==> a=4.something Not a possibility
b=8 -> 3a=16 ==> a=5.something Not a possibility
b=9 -> 3a=18 ==> a=6 2nd possibility
b=10 -> 3a=20 ==> a=6.something Not a possibility
b=11 -> 3a=22 ==> a=7.something Not a possibility
b=12 -> 3a=24 ==> a=8 3rd possibility
PLEASE SOMEONE HELP ME ANSWER THIS !!!!
Write the equations of the linear and exponential functions that pass through the points (0, 15) and (1, 5)
Linear Equation, y = mx+b
Exponential Equation, y = a(b)^x
PLEASE ANSWER IT I HAVE AN IMAGE ATTACHED IF NEEDED !!!!
Step-by-step explanation:
Part A: Linear Equation.
One of the points is (0,15). This means 0,15 is the y intercept so b=15.We can find the slope
[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]
So our equation is
[tex]y = - 10x + 15[/tex]
Part B: Exponential Equation
We know that
[tex]15 = a \times b {}^{0} [/tex]
B to the zero power is 1 so
[tex]15 = a[/tex]
This means a =15. Now let find b.
[tex]5 = 15 \times b {}^{1} [/tex]
[tex] \frac{1}{3} = b[/tex]
So the equation is
[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]
