Answer:
We want to expand the expression:
[tex](x - \frac{1}{x^2} )^4[/tex]
We can just do it by brute force, this is:
First, rewrite our expression as the product of two square factors:
[tex](x - \frac{1}{x^2} )^4 = (x - \frac{1}{x^2} )^2*(x - \frac{1}{x^2} )^2[/tex]
Now we can expand each one these two factors:
[tex](x - \frac{1}{x^2} )^2 = (x - \frac{1}{x^2} )*(x - \frac{1}{x^2} ) = x^2 + \frac{1}{x^4} -2*x*\frac{1}{x^2}[/tex]
That can be simplified to
[tex]x^2 - \frac{2}{x} + \frac{1}{x^4}[/tex]
Now we can replace that in our original expression to get:
[tex](x^2 - \frac{2}{x} + \frac{1}{x^4})*(x^2 - \frac{2}{x} + \frac{1}{x^4})[/tex]
Now we can expand that last product, to get:
[tex](x^2)^2 + 2*(x^2)*(-\frac{2}{x} ) + 2*(x^2)*(\frac{1}{x^4}) + 2*(\frac{-2}{x})*(\frac{1}{x^4}) + (\frac{-2}{x} )^2 + (\frac{1}{x^4})^2[/tex]
We can simplify that to:
[tex]x^4 - 4x + 2x^2 - \frac{4}{x^5} + \frac{4}{x^2} + \frac{1}{x^8}[/tex]
That is the expanded expression.
1. Draw what might be the next three figures
in this pattern?

3 arrows pointing up
because its like 123454321
i need help asap i will give brianlist
Answer:
the answer to this is a negative association.
How much? I say 80 what do you think?
Answer:
Yes, I agree
It is $80
The base of the regular triangular pyramid has sides that are 14 cm with a height of 12.1 cm. The slant height of the pyramid is 12.1 cm. What is the surface area of the pyramid?
Answer:ni
Step-by-step explanation:
What are the slope and y-intercept of the line represented by the points shown in the table?
Slope:2, y-intercept:-20
Slope:2, y-intercept:10
Slope:5, y-intercept:-20
Slope:5, y-intercept:10
It is A) Slope: 2, y-intercept: -20
help me I got 25 missing assignments
[tex]0.5 - ( - 10.5 \times 5) + 40.5[/tex] = [tex]\boxed{93.5}[/tex]
A. 93.5 ✅
Step-by-step explanation:-
[tex]0.5 - ( - 10.5 \times 5) + 40.5 \\ = 0.5 - ( - 52.5) + 40.5 \\ = 0.5 + 52.5 + 40.5 \\ = 93.5[/tex]
Note:-
[tex]\sf\purple{BODMAS\: rule.}[/tex]
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
[tex]\sf\red{(-\:x\:-)\:=\:+}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Answer:
93.5
Step-by-step explanation:
See the steps below:)
HELPPP I NEED THIS ASAP!!!! What is the next step in the proof? Chose the most logical approach
11. Jeff is taking his family and friends to the movies. Adult tickets, a, are $8 and child
tickets, c, are $5. He bought 11 total tickets for $64. Write the system of equations
necessary to compute how many adults and students were in the group.
Answer:
there are 3 adults and 8 children
Step-by-step explanation:
8*3 (3=Adults)=$24
5*8 (8 children)=$40
24+40=$64
Can someone please help me with this?? I will like your comment!
Answer:
[tex]A_{\Delta ABP}=\sin \theta[/tex]
Step-by-step explanation:
Let the center of the circle be O.
Recall that the area of a triangle can be given by:
[tex]\displaystyle A=\frac{1}{2} ab\sin C[/tex]
Where C is the angle between the two sides.
ΔABP is equal to the sum of ΔAPO and ΔBOP.
Let a = OP and b = OB. Since this is the unit circle and PO and BO are radii, they both equal one. C will be θ. Hence, the area of ΔBOP is:
[tex]\displaystyle A_{\Delta BOP}=\frac{1}{2}(1)(1)\sin \theta=\frac{1}{2}\sin\theta[/tex]
For ΔAPO, we can use the two sides OP and OA. Again, they are the radii of the unit circle, so they equal one. The angle in this case will be π - θ radians. Hence:
[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}(1)(1)\sin\left(\pi -\theta\right)=\frac{1}{2}\sin\left(\pi -\theta\right)[/tex]
However, note that sin(π - θ) = sin(θ). Hence:
[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}\sin\left(\theta\right)[/tex]
Hence, the area of ΔABP is:
[tex]\displaystyle A_{\Delta ABP}=\frac{1}{2}\sin \theta+\frac{1}{2}\sin\theta =\sin \theta[/tex]
A painter leans a 12-foot ladder against a wall. The angle of elevation of the ladder is 55.
Answer:
9.83cm
Step-by-step explanation:
Since we are not asked what to look for. We can find the height of the wall.
Let the height of the wall be H
Given
Length of the ladder l = 12fot
Angle of elevation = 55degrees
Required
Height of wall H
Using the SOH CAH TOA identity
SIn theta = opp/hyp
Sin 55 = H/12
H - 12sin55
H = 12(0.8192)
H = 9.83cm
Hence the height of the ladder is 9.83cm
X + 9y = 38 3x + 7 = 14
Answer:
x = -7, y = 5
Step-by-step explanation:
a) x + 9y = 38, b) 3x + 7y = 14
From a)
x = 38 - 9y ---- (Equation 1)
From b)
{3*(38 - 9y)} + 7y = 14 ----- (From equation 1)
114 - 27y + 7y -14 = 0
100 - 20y = 0
20y = 100
y = 5
From a)
x + (9*5) = 38 (substituting the value of y = 5)
x + 45 = 38
x = 38 - 45
x = -7
Hope, this will help
Herds of Cattle
P/S R/P Com Con Rep A/Level
Herds of Cattle ○
Rick lives on a large cattle ranch. There has been so little rain that there is not enough grass on parts of the ranch to feed the cattle. Rick needs to move four herds of cattle to be by a river where there is enough grass for the cattle to eat. The river runs through the cattle ranch from point (1, 2) to point (10, 2). The most grass is located at the east end of the river between point (7, 2) and point (10, 2). Plot four new location points where the four herds of cattle can eat the most grass by the river. Show all your mathematical thinking.
First Location of Herds of Cattle
Herd A: (5, 8) Herd B: (2, 9) Herd C: (3, 6) Herd D: (6, 7)
No links please I need this ASAP
The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals Probability 0 .05 1 .15 2 .35 3 .30 4 .15 What is the probability that in a given game the Lions will score less than 3 goals? a. .45 b. .85 c. .80 d. .55
Answer: d. 0.55
Step-by-step explanation:
The given probability distribution:
Number of Goals 0 1 2 3 4
Probability .05 .15 .35 .30 .15
The probability that in a given game the Lions will score less than 3 goals
= probability that in a given game the Lions will score less than or equal to 2
= 0.5+0.15+0.35
= 0.55
Hence, the correct option is d. 0.55
(15) Find the value of x. *
Answer:
Step-by-step explanation:
x+35=2x(opposite angles of a parallelogram are equal)
35=2x-x
35=x
What is the perimeter of an isosceles triangle with one side that
measures 5 ft. and two sides that measure 11 ft. each?
answer please I’m dying from math
Step-by-step explanation:
It's C
I hope it helped:)
What is the length of EF in the right triangle below?
Step-by-step explanation:
put sides into Pythagorean theorem
do algebra
find solution
a) 2(x+3)=x-4
Could anyone help?
Which are solution of
[tex] \frac{x}{5} = \frac{1}{x + 4} [/tex]
Answer:
x = 1, x = -5
[tex]x/5 = 1/x+4\\Apply Fraction and Multiply : \\\\x(x+4)=5 x 1\\Simplify :\\x(x+4) = 5\\Solve.[/tex]
I hope this is what you were looking for !
help me and I’ll give you brainliest
So this is complicated, but to get a general idea simple we use common sense and say its bigger than 4, since its length is bigger than the supposed 4 length. So then we get the options 6, 5, and 24. Now we can do some basic math and figure that the circle radius is around 4 so its probably 6 or 5. Slim change of 24.
People who did the physical math can check it with my answer.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 gal : 64 gal (IN THE PICTURE)
Answer:
5/8
Step-by-step explanation:
The ratio 40:64 can be written as a fraction, 40/64.
Next, simplify to get 5/8.
Hope this helps!
write the equation in slope intercept form for the line that passes through the point (1,2) and has a slope of -5
Answer:
y = -5 × 1 + 2
Step-by-step explanation:
y = y, m = slope, x = x point given (1), b = y point given, unless a zero (2)Formula - y = mx + bPlug it iny = -5 × 1 + 2Which expression is equivalent to the expression -3(4x - 2) - 2x ?
Answer:
-14x + 6
Step-by-step explanation:
-3(4x - 2) - 2x
-12x + 6 - 2x
-14x + 6
Graph the solution to the following inequality on the number line.
(x+5)(x - 2)>0
-
Step-by-step explanation:
[tex](x + 5)(x - 2) \geqslant 0[/tex]
[tex]x + 5 = 0 \\ x \geqslant - 5 \\ x - 2 = 0 \\ x \geqslant 2[/tex]
The solution of the inequality is x ≥ -5 and x ≥ 2.
The graph of the number line is given in the attached image.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality (x+5)(x-2) ≥ 0
Solving further,
(x+5) ≥ 0 and (x -2) ≥ 0
x ≥ -5 and x ≥ 2
Therefore, the solution of the inequality is x ≥ -5 and x ≥ 2.
To learn more about the inequality;
brainly.com/question/28823603
#SPJ2
Plzzzzzz I need in nowwwwwwwwwwww
Answer: -5
Step-by-step explanation:
Answer:
b = -5
Step-by-step explanation:
therefore -5 is the answer
A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $184. Determine the total number of CDs and videos sold.
Answer:
28 CD and 12 Video
Step-by-step explanation:
6 (x) + 4 (y) = 184
6 (28) + 4 (12) =184
168 + 48 = 184
como convertir una fraccion en numero entero
Answer:
Para convertir una fracción (n/m) a un número entero tenemos que dividir el numerador entre el denominador. Es decir, el número que se encuentra expresado como n (parte superior) entre el número expresado como m (parte inferir).
Step-by-step explanation:
Answer:
Para convertir una fracción en un número entero: Divida el numerador por el denominador, solo si el numerador es un múltiplo del denominador. Veamos un ejemplo de esta conversión.
Step-by-step explanation:
tenemos 4/2
Dado que 4 es un múltiplo de 2, podemos escribir 4/2 = 2
Espero que esto ayude!
The normal distributions for three different SAT examinations is displayed above what can you conclude about the standard deviations of the three exams?
Comparing the standard deviations of each distribution, you have blue < red < yellow.
For any normally distributed random variable X with mean µ and standard deviation σ, we have the property that
Pr[|X - µ| ≤ σ] ≈ 68%
In other words, roughly 68% of a normal distribution lies within 1 standard deviation of the mean. This means the plot of the density of a distribution with a smaller standard deviation forms a tighter peak (like the blue curve), whereas a larger standard deviation would be indicated by a more dispersed, flattened curve (like the yellow one).
Which product is greater than 3/4?
Answer:
4/4
Step-by-step explanation:
5/4 and so on with other numer that is higher than 3/4 lol
a triangular prism where the area of each base is about 20 square inches, the length of each side of the base is 6 inches, and the height of the prism is 2 inches
Answer:
94 square inches I don't have an explanation