Recall that for |x| < 1, we have
[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]
Differentiating both sides gives
[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty n x^{n-1} = \sum_{n=0}^\infty (n+1) x^n[/tex]
so that the Maclaurin expansion of the given function is
[tex]\displaystyle \frac5{1-x} = \boxed{\sum_{n=0}^\infty 5(n+1) x^n} = 5 + 10x + 15x^2 + 20x^3 + \cdots[/tex]
Translate the shape A three squares right and one square down.What are the coordinates of the vertices of the image?
If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-2, 5), (-2, 2) and (0, 2)
Translation of coordinatesTranslation is a transformation technique of changing the position of an object on the xy plane
Given the coordinates of the vertices (1, 4), (1, 1), (3,1)
If the shape A is translated three squares right and one squares up, the resulting coordinate point will be at (-2, 5), (-2, 2) and (0, 2)
Note that 4 was subtracted from the x-axis and 2 added to the y-coordinates.
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Find an algebraic expression equivalent to 3 over 2 left paren 6 x squared minus two over 3 x right paren
The equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x
How to determine the equivalent expression?The expression is given as:
3/2(6x^2 - 2/3x)
Open the bracket
3/2*6x^2 - 3/2*2/3x
Evaluate the product
9x^2 - x
Hence, the equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x
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Whic
the following is an angle? (3 points
Figure A has two rays connected at a vertex, Figure B is a line with one endpoint and the other end has an arrow, Figure C is a line with two endpoints, and Figure D is a line with an arrow at each end
Figure A
Figure B
Figure C
Figure D
Figure A which has two rays connected at a vertex is an angle in this scenario.
What is an Angle?This is formed when two rays share a common endpoint with there being different types of angles.
The common endpoint shared forms a vertex which is why Figure A was chosen as the most appropriate choice.
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Please help, thanks!!!
Problem 4
Draw any right triangle you want. Afterward, draw a perpendicular segment that goes from the 90 degree angle to the hypotenuse. Call this new segment the altitude. It might help to have the hypotenuse laying flat or horizontal.
The length of this altitude can be found using the geometric mean formula. Search out "geometric mean for triangles" (or similar) and you should get a diagram that visually summarizes what is going on. I've provided a screenshot of an example using GeoGebra. See below.
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Problem 5
The two special types of right triangles are: the 45-45-90 triangle and the 30-60-90 triangle.
If x is the leg length of the first triangle type mentioned, then [tex]x\sqrt{2}[/tex] is the hypotenuse. We can confirm this using the pythagorean theorem. Recall that the legs of any 45-45-90 triangle are the same, meaning we have an isosceles triangle.
For the second type of triangle, the short leg x leads to the hypotenuse 2x and long leg [tex]x\sqrt{3}[/tex]
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Problem 6
If you know say the opposite and adjacent sides of a right triangle, then you can use the tangent ratio because tan = opposite/adjacent.
Sine is used for opposite/hypotenuse, while cosine is used for adjacent/hypotenuse. Those are the main 3 trig functions. Technically there are 3 more, but they are just reciprocals of the previous three.
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Problem 7
Use inverse trig functions to find the missing angles if you know the sides. The inverse trig functions have an exponent of -1.
For instance, let's say the triangle has an opposite side of 10 and hypotenuse of 15
The reference angle would be...
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(x) = \frac{10}{15}\\\\x = \sin^{-1}\left(\frac{10}{15}\right)\\\\x \approx 41.81^{\circ}\\\\[/tex]
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Problem 8
Imagine looking completely horizontal at the horizon. The angle in which you are currently looking is 0 degrees. If you look upward, say 10 degrees, then the angle of elevation is 10 degrees. Looking down means we have an angle of depression. These two types of angles help us determine various distances and lengths.
Use the alternate interior angle theorem to help show that angles of depression are congruent to angles of elevation. It will depend on context which type of angle is more useful.
You have a list of 7 letters, of which 3 are vowels (a, i, e) and 4 are consonants (b, c, d, f). you need to use these letters to form four-letter words in such a manner that they should contain exactly 2 vowels from the given 3 and exactly 2 consonants from the given 4. how many such four-letter words can you form using the seven given letters?
There are 432 four-letter words you can form using the seven given letters if you have a list of 7 letters.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
A list of 7 letters, of which 3 are vowels (a, i, e) and 4 are consonants (b, c, d, f).
a, i, e - 2 vowels can be selected in 3C2 ways.
b, c, d, f - 2 consonants can be selected 4C2 ways.
We can arrange 4 alphabets in 4! ways.
Total ways = C(3, 2)×C(4, 2)×4!
= 3×6×24
= 432
Thus, there are 432 four-letter words you can form using the seven given letters if you have a list of 7 letters.
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Solve the following system of equations by substitution. Show all steps.
f (x) = -x^{2} + 2x +3
g (x) = -2x + 3
Answer:
Given system of equations:
[tex]\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}[/tex]
To solve by substitution, equate the equations and solve for x:
[tex]\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}[/tex]
Therefore, the x-values of the solution are [tex]x = 0[/tex] and [tex]x = 4[/tex].
To find the y-values of the solution, substitute the found values of x into the functions:
[tex]f(0)=-(0)^2+2(0)+3=3[/tex]
[tex]g(0)=-2(0)+3=3[/tex]
[tex]f(4)=-(4)^2+2(4)+3=-5[/tex]
[tex]g(4)=-2(4)+3=-5[/tex]
Therefore, the solutions to the given system of equations are:
[tex](0, 3)[/tex] and [tex](4, -5)[/tex]
Simplify each expression -21v6/-6v8
Answer: The answer to this is [tex]\frac{7\sqrt{3} }{4}[/tex].
I looked it up on my scientific calculator. I hope this helps!! :)
Answer:
7/2v^2
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
A circle representing a pool is graphed with a center at
the origin. Grant enters the pool at point A and swims
over to a friend who is located at point B.
-10-
6-
4
2-
A
2 4 6 8 10 x
B
-106422-
№t
4-
-6-
-10-
Which equation represents Grant's path?
O y = 2-4x
Oy=4-
O y = 6-
Oy=8-2x
The equation that represents Grant's path is; y = 4 - ¹/₂x
How to find the equation of a graph?
We are given;
Point A: (8,0),
Point B: (-4,6)
Thus, the slope is;
m = (6 - 0)/(-4 -8)
m = -¹/₂
Thus;
Equation of Grant's path is;
y = -¹/₂(x - 8)
y = 4 - ¹/₂x
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Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B
rents for $150 and $50 an hour. Let t= the number of hours and c = cost.
Part A
Write a system of equations to represent the cost at each studio.
Part B
Solve the system of equations from Part A. Explain your method.
Part C
Explain what the solution to the system means in terms of where your band will rent a studio.
Answer:
Step-by-step explanation:
Studio A rents for $75 plus $75 an hour .
Studio B rents for $150 and $50 an hour.
Let t = the number of hours and c = cost.
Part A
Write a system of equations to represent the cost at each studio.
Studio A: c = 75 +75·t
Studio B: c = 150 +50·t
Part B
Solve the system of equations from Part A. Explain your method.
We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.
150 +50·t = 75 +75·t, subtract 75 and 50t from both sides
150 -75 = 75t -50t, combine likes terms
75 = 25t, divide both sides by 25
3 = t
Now we know that t = 3 so we find c by substituting t with 3 in the second equation.
c = 150 +50·t
c = 150 +50·3
c = 300
The solution of the system of equations is c = 300 and t = 3
Part C
Explain what the solution to the system means in terms of where your band will rent a studio.
The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.
The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.
A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk? Round your answer to the nearest hundredth. Use 3.14 for π.
Your friend walks about
miles farther than you.
The distance further the friend walked is 0.41 miles.
How much farther did the friend walk?The distance the friend walked can be determined by calculating the circumference of a semicircle.
Circumference of a semicircle = πr + 2r
r = 0.25 / 2 = 0.125mi
3.14 x 0.125 + 0.25 = 0.66 mi
Difference in the distance = 0.66 - 0.25 = 0.41 miles
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11/12 - 7/9
5/36
5/72
25/36
25/72
c
Step-by-step explanation:
If 6:2=8:x, then
a. 6x = 16
b. 6x = 10
c. 2x = 48
d. 2x = 14
Answer:
6x = 16
Step-by-step explanation:
Given:
[tex]\displaystyle \large{6:2 = 8:x}[/tex]
The equation can be rewritten as:
[tex]\displaystyle \large{\dfrac{6}{2}=\dfrac{8}{x}}[/tex]
Multiply both sides by 2x.
[tex]\displaystyle \large{\dfrac{6}{2}\cdot 2x=\dfrac{8}{x}\cdot 2x}[/tex]
Simplify the equation in simplest form.
[tex]\displaystyle \large{6x=8\cdot 2}\\\\\displaystyle \large{6x=16}[/tex]
Therefore, the answer to this question is 6x = 16.
Please let me know if you have any questions regarding my answer or explanation!
3. A farmer needs to dig a rectangular pit that is 5m long, 4m wide and 6m deep. How many cubic meters of soil must he removed?
156 m3
120 m3
231 m3
345 m3
wrong answer/nonsense = report
Answer:
120 m3
Step-by-step explanation:
The volume of a rectangular prism is l*w*h. plug in the 3 measurements and get 5*4*6 = 120
Two angles of a quadrilateral measure 105° and 150°. The other two angles are in a ratio of 4:17. What are the measures of those two angles?
Answer:
20 degrees and 85 degrees.
Step-by-step explanation:
105 degrees+ 150 degrees is equal to 255 degrees. 360 degrees - 255 degrees is 105 degrees. To get the ratio equivalent to 105 degrees you have to multiply both sides by 5 in order to get 20 degrees, and 85 degrees. I hope this helps! :)
Uv has endpoints at u(4, 6) and v(10, 4). find the midpoint m of uv.
write the coordinates as decimals or integers.
m =
submit
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ U(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad V(\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 10 +4}{2}~~~ ,~~~ \cfrac{ 4 +6}{2} \right)\implies \left( \cfrac{14}{2}~~,~~\cfrac{10}{2} \right)\implies (7~~,~~5)[/tex]
solve pls brainliest
Latoya created a factor tree and wrote the prime factorization of 90 shown below.
Answer:
it’s b
Step-by-step explanation:
the answer is 2x3x3x5, but it’s the same thing when you put an exponent of two on a 3.
Hope it helps
Sry if I’m wrong
Use completing the square to rewrite the function in vertex form. f(x)=x2+6x−5
Answer:
f(x) = (x + 3)² - 14
Step-by-step explanation:
f(x) = x² + 6x - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
f(x) = x² + 2(3)x + 9 - 9 - 5
= (x + 3)² - 14 ← in vertex form
The function in vertex form is f : x → (x + 3)² - 14.
To convert the equation.
f : x → x² + 6x - 5 into the vertex form, you will need to complete the square.
First, you will need to add and subtract the square of half of the coefficient of the x term, which is (6/2)² = 9.
This will give you the equation.
f : x → x² + 6x - 5 + 9- 9
Next, you will need to factor the left side of the equation,
f : x → (x² + 6x + 9) - 5 - 9
Now, you can see that the left side of the equation is the square of
(x + 3)² so you can rewrite it as:
f : x → -(x + 3 )² - 5 - 9
Finally, you can simplify the right side of the equation to get:
f : x → (x + 3)² - (5 + 9)
f : x → (x + 3)² - 14.
Therefore, the vertex form is f : x → (x + 3)² - 14.
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3. Eden has completed 7⅝ laps of a 10 lap race How many more laps does she still need to run?
eden must run 2 3/8 laps to complete the race.
How to calculate the laps that Eden is missing?To calculate the laps that Eden is missing, we must perform the following operation:
We must take into account that he has already completed 7 laps and a segment of the eighth lap that is equivalent to 5/8, that is to say that he has 3/8 to complete the eighth lap.
On the other hand, once he completes the eighth lap, he will have 2 full laps left to finish the race. Due to the above, it can be stated that it is missing 2 3/8 laps.
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3 substracted from 9 times 2 and 5 is added
Answer:
20
Step-by-step explanation:
It is because 9x2=18
3 subtracted from 18 is 15
15+5=20
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How to convert no. Ito persentage
To turn a number (either an integer or a decimal) into a percent, simply multiply by 100. That is the same as moving the decimal point two places to the right. You may need to round to the desired precision. Add a percent (%) sign.
What is percentage? :A percentage is a way of expressing one number as a portion or share of a whole number, and percentages are always based on their relation to 100, which represents the whole number or object.For example, 75% is the same as 75 out of 100. Any percentage lower than 100 is just part of the whole or total.Definition of a number : A number is an arithmetic value used for representing the quantity and used in making calculations.What is Maths? : MATH stands for "Mathematics" in its entire form. Mathematics is a branch of science that studies the logic of form, quantity, and arrangement.Learn more about Mathematics, refer:
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Solve for h: h+4/-2=0.3 ([tex]h+\frac{4}{-2} =0.3[/tex])
Give Explanation please.
Answer: [tex]h=\frac{23}{10} =2.300[/tex]
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
[tex]h+\frac{4}{-2} -((\frac{3}{10} ))=0[/tex]
[tex]Simplify~ \frac{3}{10}[/tex]
[tex](h+\frac{4}{-2} )-\frac{3}{10} =0[/tex]
Subtracting a fraction from a whole
Rewrite the whole as a fraction using 10 as the denominator :
[tex]h-2=\frac{h-2}{1} =\frac{h-2x10}{10}[/tex]
Equivalent fraction: The fraction thus generated looks different but has the same value as the whole
Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to the lowest terms if possible:
[tex]\frac{(h-2)x10-(3)}{10} =\frac{10h-23}{10}[/tex]
[tex]\frac{10h-23}{10} =0[/tex]
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, CalderonJ multiplys both sides of the equation by the denominator.
Here's how:
[tex]\frac{10h-23}{10} *10=0*10[/tex]
Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
10h-23 = 0
Add 23 to both sides of the equation :
10h = 23
Divide both sides of the equation by 10:
h = 23/10 = 2.300
Final Answer: 2.3(decimal form) aka 23/10 (fraction)
Which statement about ABCD isn’t true
Answer:
The answer is B. AC = BD.
Step-by-step explanation:
ABCD is given as a parallelogram. Most of the line is given to be parallel.
AB = CD and BC = AD are told that they are in a parallel line to each other.
The line inside the parallelogram is yet to be said if they equal each other, thus, statement B. AC = BD must be false.
Which shows the equation of the line containing the point (4, 6) and having a slope of 4 in slope-intercept form?

4y=x−28
y=4x−10
y=−4x+10
y=−52x+4
Answer:
y=4x-10
Step-by-step explanation:
See attached image
In the given figure if AOB = 132°, COD = 141°, if measure of BOD equals x°, then x is
Answer:
BOD = 189 °
Step-by-step explanation:
that is the answer above
Ayuda porfa doy corona
Answer:
goto chrome and search spankbang
Step-by-step explanation:
thet the answer
Which relation is a function? PLEASE HELP
Answer:
A
Step-by-step explanation:
for the relation to be a function then each value of x in the domain must map to exactly one unique value of y in the range
this is the case for A
in B : 3 → 2 and 3 → 8 ← not a function
in C : - 2 → 5 and - 2 → 7 ← not a function
in D : 2 → 2 and 2 → 3 and 3 → 3 and 3 → 2 ← not a function
Ax -c=bx+d solve for x
Answer:
[tex] x = \dfrac{c + d}{a - b} [/tex]
Step-by-step explanation:
ax - c = bx + d
ax - bx = c + d
x(a - b) = c + d
[tex] x = \dfrac{c + d}{a - b} [/tex]
Classify each polynomial according to its degree and type. Look at the screenshot below!
Answer:
Monomial Binominal Trimoninal
Degree 1: -9x x + 6
Degree 2: -4[tex]x^{2}[/tex] [tex]4x^{2} -x[/tex] [tex]x -3x^{2} + 1[/tex]
Degree 3: 4[tex]x^{3}[/tex] 5 - 2[tex]x^{3}[/tex] [tex]3x^{2} + 3x^{3} -10[/tex]
Step-by-step explanation:
I do not know how to explain how I got to this answer, but here is the answer.
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Question:
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Answer:
Bobby need 20 friends.
Step-by-step explanation:
8 x (9 + 1) = 8/o = 80 hours
Suppose Bobby needed to call x friends.
10 x 2 + 2 (10 + x) = 80
20 + 20 +2x = 80
2x = 40
x = 20
Therefore, Bobby needs to call 20 friends to get the cleaning done in time.