Answer:
a unit rate is a rate with one in the denominator
Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to four decimal places.) [infinity] (−1)n + 1n 2n n = 1
Answer:
0.1875
Step-by-step explanation:
The well formatted expression for the series has been attached to this response.
Each term in the series is govern by the rule, Tₙ
Where
n = term position
Tₙ = [tex]\frac{(-1)^{n+1}n}{2^n}[/tex]
To get the first six terms, we substitute n = 1 through 6 into Tₙ as follows:
When n = 1, we have;
T₁ = [tex]\frac{(-1)^{1+1}(1)}{2^1} = \frac{1}{2}[/tex] = 0.50000
When n = 2, we have;
T₂ = [tex]\frac{(-1)^{2+1}(2)}{2^2} = \frac{-2}{4} = \frac{-1}{2}[/tex] = -0.50000
When n = 3, we have;
T₃ = [tex]\frac{(-1)^{3+1}(3)}{2^3} = \frac{3}{8}[/tex] = 0.37500
When n = 4, we have;
T₄ = [tex]\frac{(-1)^{4+1}(4)}{2^4} = \frac{-1}{4}[/tex] = -0.25000
When n = 5, we have;
T₅ = [tex]\frac{(-1)^{5+1}(5)}{2^5} = \frac{5}{32}[/tex] = 0.15625
When n = 6, we have;
T₆ = [tex]\frac{(-1)^{6+1}(6)}{2^6} = \frac{-6}{64} = \frac{-3}{32}[/tex] = -0.09375
Therefore, the approximate sum of the series using the sum of the first six terms is
=> T₁ + T₂ + T₃ + T₄ + T₅ + T₆
=> 0.50000 + -0.50000 + 0.37500 + -0.25000 + 0.15625 + -0.09375
=> 0.1875
Graph y=-1/3x+5. Plsss help hurry
add or subtract
7 + 3 + (-7)
Answer: 3
Step-by-step explanation: you add 7+3 which is 10 - 7 =3
Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 + 1 f(x) = sigma^infinity_n = 0 (-1)^n x^2n+1 6^n Determine the interval of convergence. (Enter your answer using interval notation.)
Looks like your function is
[tex]f(x)=\dfrac x{6x^2+1}[/tex]
Rewrite it as
[tex]f(x)=\dfrac x{1-(-6x^2)}[/tex]
Recall that for [tex]|x|<1[/tex], we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
If we replace [tex]x[/tex] with [tex]-6x^2[/tex], we get
[tex]f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}[/tex]
By the ratio test, the series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2<1[/tex]
Solving for [tex]x[/tex] gives the interval of convergence,
[tex]|x|^2<\dfrac16\implies|x|<\dfrac1{\sqrt6}\implies -\dfrac1{\sqrt 6}<x<\dfrac1{\sqrt 6}[/tex]
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.
The interval of the convergence is (-1/√6 < x < 1/√6). We can confirm that the interval is open by checking for convergence at the endpoints.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The given function is
[tex]\rm f(x) = \dfrac{x}{6x^2 + 1} \\\\or \\\\f(x) = \dfrac{x}{1 - (-6x^2)}[/tex]
For |x| < 1, we have
[tex]\rm \dfrac{1}{1-x} = \Sigma_{n=0}^{\infty} \ x^n[/tex]
If x is replaced with -6x², then we have
[tex]\rm f(x)= \Sigma_{n=0}^{\infty} (-6x^2 )^n = \Sigma_{n=0}^{\infty} (-6)^n x^{2n+1}[/tex]
Then by the ratio test, the series converges if
[tex]\displaystyle \lim_{n \to \infty} \left| \dfrac{(-6)^{n+1}x^{2(n+1)+1}}{(-6)^{n}x^{2n+1}} \right|=6|x^{2}| \displaystyle \lim_{n \to \infty }1=6|x^{2}| < 1[/tex]
Solving for x, the interval of convergence will be
[tex]|x^2| < \dfrac{1}{6} \\\\|x| < \dfrac{1}{\sqrt6} \\\\-\dfrac{1}{\sqrt6} < x < \dfrac{1}{\sqrt6}[/tex]
We can confirm that the interval is open by checking for convergence at the endpoints.
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True or false: If you re-word what an author says in your own work, you do not have to provide a citation. * 1 point True False
Answer:
False
Step-by-step explanation:
In an essay, you have to cite every source you use because
a) the teacher needs to KNOW you didn't copy
b) the teacher needs to know if you got your info from a reliable source
c) the teacher needs to see your ability to use info from a source to put into your essay
This may be different for books, but citation is always a rule of thumb for essays in school, so don't forget unless you want points to be taken off of your score.
f(x)=g(x)? What is the solution
Answer:
The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
;)
Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).
Answer: the real solution: x = - 2
Find the attached file for the remaining solution
Step-by-step explanation:
The equation given is:
x3 - 5x2 + 28 = 0
Let assume that -2 is one of the root of the equation. Substitute -2 for x
(-2)^3 - 5(-2)^2 + 28
-8 - 20 + 28 = 0
Therefore, -2 is one of the root of the equation since the equation tend to zero.
If x = -2, then x+2 is one of the factors of the equation. Therefore, the real solution is x = -2
Please find the attached file for the remaining solution.
Carly solved a quadratic equation by completing the square, but her work has errors. Identify the first error in Carly's work.
Answer:
D. She added the wrong value to both sides of the equation to complete the square.
Step-by-step explanation:
Got it right on plato
The first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given equation is x(x+4)=117.
Here, x²+4x=117
Now, b/2 =4/2 =2
So, add 2² to both the sides of an equation, we get
x²+4x+2²=117+2²
⇒ x²+4x+4=117+4
⇒ (x+2)²=121
⇒ x+2=±√121
⇒ x+2=±11
⇒ x=±11-2
⇒ x=11-2=9 and x=-11-2=-13
The solution for the given a quadratic equation is x=9 and x=-13. Therefore, the first error in Carly's work is instead adding 2² on both the side of an equation, she added 4².
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Find an equation of a line with slope -7 and y-intercept 2. y=
Answer:
y = -7x + 2
Step-by-step explanation:
Use the slope-intercept form y = mx + b.
Substitute -7 for m, 0 for x and 2 for y. Then
2 = (-7)(0) + b, so b must be 2.
The desired equation is y = -7x + 2.
Translate into an equation: y is 37% of x.
Answer:
soln,
y=37/100×x
or, 100y=37x.....is the answer
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equation of y is 37% of x is
y = 0.37x
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
2 + 3 - 4 is an expression.
2x4 + 4x = 4 is an expression.
We have,
y is 37% of x.
This can be written as,
y = 37/100 of x
y = 0.37x
Thus,
The equation of y is 37% of x is
y = 0.37x
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Algebraic expressions
Evaluate
The dog is 4 years older than the cat. The cat is 7 years old. How old is the dog?
Answer:
11 years old
Step-by-step explanation:
Because the dog is 4 years older, add 7+4
Determine if the following table represents a quadratic function. X 1 2 3 4 5 Y 13 22 37 58 85
Answer:
Yes, the table represents quadratic function.
[tex]Y = 3X^2+10[/tex]
Step-by-step explanation:
Given that table of values:
[tex]\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}[/tex]
To find:
Whether the given table represents a quadratic?
Solution:
First of all, let us plot the given values on the coordinate xy plane.
Kindly refer to the attached image for the graph of given values.
The graph seems parabolic in nature which is the graph of a quadratic equation.
Now, let us try to find the equation from the given set of values from hit and trial.
Let Quadratic equation be:
[tex]y=ax^{2} +b[/tex]
If the coefficient a = 1
[tex]f(1) = 13 = 1^2+12[/tex]
[tex]f(2) = 22 = 2^2+18[/tex]
[tex]f(3) = 37= 3^2+28[/tex]
[tex]f(4) = 58 = 4^2+42[/tex]
[tex]f(5) = 85 = 5^2+60[/tex]
value of b is not same in each case.
Now, let us try coefficient a = 3
[tex]f(1) = 13 = 3 \times 1^2+10[/tex]
[tex]f(2) = 22 = 3\times 2^2+10[/tex]
[tex]f(3) = 37= 3\times 3^2+10[/tex]
[tex]f(4) = 58 = 3\times 4^2+10[/tex]
[tex]f(5) = 85 =3\times 5^2+10[/tex]
Value of b = 10
So, we can clearly say that the given table represents a quadratic equation.
and the quadratic equation is:
[tex]Y = 3X^2+10[/tex]
What are the attributes of the boundary line of this inequality? -3x − 2y < 6
Answer:
D. The line is dashed with a y-intercept at (0,-3) and slope of -.
Step-by-step explanation:
If you rearrange the inequality -3x-2y<6 to y=mx+b form you should get y>-3/2x-3
The slope would be mx or -3/2
The Y intercept would be b or -3
I hope this helps :)
The line with an inequality equation -3x - 2y < 6 when plotted on the graph, occupies a region with a dashed boundary line with the attributes, the slope m = -3/2, and the y-intercept c = -3.
What is an inequality equation of a line?An inequality equation for a line is the equation that is true for certain values of its variables. The inequality symbols are ' <, >, ≤, ≥ '.
How do graph an inequality?When inequality is graphed,
The region of values for which the inequality becomes true is shaded.If the inequality has < or > symbols, then the boundary of that region is represented with the dashed line. If the inequality has ≤ or ≥ symbols, then the boundary of that region is represented with the solid line (no breaks).Writing the given inequality in the slope-intercept form of a line:The inequality equation is re-arranged in the slope-intercept form to know the attributes of the line such as the slope of the line and the y-intercept of the line.
The given inequality is -3x - 2y < 6
Step 1: Rewriting the equation into the slope-intercept form:
-3x - 2y < 6
To change the sign, change the inequality symbol also.
⇒ 3x + 2y > 6
⇒ 2y > 6 - 3x
⇒ y > -3/2x - 3
Therefore, the obtained equation is in the slope-intercept form.
So, m = -3/2 and c = -3
Step 2: Graphing the inequality:
To graph the line, we need coordinates.
So, consider x = 0 inorder to get y-coordinate
On substituting,
-3(0) -2y = 6
y = -3
∴ (0, -3) is one of the coordinates of the line
Then, consider y = 0 inorder to get x-coordinate
On substituting,
-3x - 2(0) = 6
x = -2
∴ (-2, 0) is one of the coordinates of the line
These points are plotted in the graph and a line is drawn from these points.
Step 3: Observations from the graph:
Since the inequality is -3x -2y < 6 ( < ), the region above the line is shaded ( the values that satisfies the inequality). The line is represented as a dashed line that indicates the boundary for the inequality region.This means the line is excluded from the solution set of the given inequality.Therefore, the attributes of the boundary line (dashed line) are slope -3/2 and y-intercept -3.
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( 6m + 3 )( m - 2 ) A) 4m 2 - 2m - 20 B) 4m 2 - 20 C) 4m 2 + 18m + 20 D) 6m 2 - 9m - 6
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex](6m+3)(m-2)[/tex]
Use the distributive property and distribute:
[tex]=(6m+3)(m)+(6m+3)(-2)[/tex]
Distribute:
[tex]=(6m^2+3m)+(-12m-6)[/tex]
Combine like terms:
[tex]=6m^2+3m-12m-6\\=6m^2-9m-6[/tex]
The correct answer is D
Edit: Typo
Match the vocabvulary
Answer: The answers are in the steps I numbered it as a question from 1 to 12 hopes it helps.Read it carefully.
Step-by-step explanation:
(1) Answer is RATIONAL NUMBERS.
(2) Answer is Fraction
(3) Answer is Terminating decimal
(4) Answer is Decimal
(5) Answer is Integer
(6) Answer is Repeating Decimal
(7) Answer is Perfect Square
(8) Answer is CLASSIFY
(9) Answer is Real Numbers
(10) Answer is Percent
(11) Answer Whole numbers
(12) Answer is Irrational numbers
What is the sum of the three solutions? (find the values for x, y, and z, then add the answers)
2x + 3y − z = 5
x − 3y + 2z = −6
3x + y − 4z = −8
Answer:
Once we got
[tex]x=-1[/tex]
[tex]y=3[/tex]
[tex]z=2[/tex]
[tex]\boxed{\text{The sum is 4}}[/tex]
Step-by-step explanation:
Given the linear system:
[tex]\begin{cases} 2x + 3y-z = 5 \\ x- 3y + 2z = -6 \\ 3x + y - 4z = -8 \end{cases}[/tex]
Let's solve it using matrices. I will use Cramer's rule
[tex]M=\left[\begin{array}{ccc}2&3&-1\\1&-3&2\\3&1&-4\end{array}\right][/tex]
Considering determinant as D.
[tex]D=\begin{vmatrix}2&3&-1\\1&-3&2\\3&1&-4\\\end{vmatrix}=40[/tex]
[tex]M_x = \left[\begin{array}{ccc}5&3&-1\\-6&-3&2\\-8&1&-4\end{array}\right] \implies D_x = \begin{vmatrix}5&3&-1\\-6&-3&2\\-8&1&-4\\\end{vmatrix}=-40[/tex]
[tex]M_y = \left[\begin{array}{ccc}2&5&-1\\1&-6&2\\3&-8&-4\end{array}\right] \implies D_y = \begin{vmatrix}2&5&-1\\1&-6&2\\3&-8&-4\\\end{vmatrix}=120[/tex]
[tex]M_z = \left[\begin{array}{ccc}2&3&5\\1&-3&-6\\3&1&-8\end{array}\right] \implies D_z= \begin{vmatrix}2&3&5\\1&-3&-6\\3&1&-8\\\end{vmatrix}=80[/tex]
So, we have
[tex]$x=\frac{D_x}{D} =\frac{-40}{40}=-1 $[/tex]
[tex]$y=\frac{D_y}{D} =\frac{120}{40}=3$[/tex]
[tex]$z=\frac{D_z}{D} =\frac{80}{40}=2 $[/tex]
A vendor bought a supply of ice cream bars at three for 20 cents. He ate one and sold the remainder at 10 cents each. If he made $200.00, how many bars did he buy?
201 bars
Step-by-step explanation:Let the number of bars bought be x.
Cost of three bars is 20 cents.
Therefore, 1 bar will cost [tex]\frac{20}{3}[/tex] cents.
He ate one of the bars...
Therefore, remaining bars will be x - 1
... He sold the remainder at 10 cents each i.e
1 bar = 10 cents
(x - 1) bars = 10( x - 1) cents
...He made $200.00 from selling the remaining bars.
10( x - 1) cents = $200.00 ---------------(i)
Convert from dollars to cents
$1 = 10 cents
$200 = 200 x 10 cents = 2000 cents
From equation (i)
10(x - 1)cents = 2000 cents
=> 10( x - 1) = 2000 [divide both sides by 10]
=> x - 1 = 200
=> x = 200 + 1
=> x = 201
Therefore, he bought 201 bars of ice cream.
The sum of two of the angles of a heptagon is 200ᵒ. If the remaining angles are equal, find the value of each of the remaining angles.
Answer: 140°
Step-by-step explanation:
Heptagon is a seven-sided polygon. So heptagon has 7 angles.
As known the sum of the angles in poligon is
N=180°*(n-2)
So N(7)=180°*(7-2)=900°
if the sum of 2 angles are 200° then the sum of residual 5 angles is
900°-200°=700°
The remaining 5 angles are equal so each of them is
∠α=700°:5=140°
WY bisects UV at Y. If UV=x-7 and YV = 3x-29, find UV
Answer:
3.2 units
Step-by-step explanation:
Given that:
WY bisects UV at Y.
[tex]UV=x-7[/tex] and
[tex]YV = 3x-29[/tex],
To find: UV = ?
Solution:
First of all, let us draw the diagram of the given dimensions and bisector line WY of UV.
As UV is bisected i.e. divided in two equal parts at Y by the line WY
Therefore, UY = YV
UV = UY+YV
OR
UV = 2 YV
Now, let us put the given values to solve for [tex]x[/tex]:
[tex]x-7=2 \times (3x-29)\\\Rightarrow x-7=2 \times 3x-2 \times 29\\\Rightarrow x-7=6x-58\\\Rightarrow 6x-x=58-7\\\Rightarrow 5x=51\\\Rightarrow \bold{x =10.2 }[/tex]
Now, we are given that:
[tex]UV=x-7[/tex]
Putting value of [tex]x[/tex] as solved in above step to get the value of UV:
[tex]UV=10.2-7\\\Rightarrow \bold{UV=3.2}[/tex]
So, answer is UV = 3.2 units
the question is below, 20 is not the correct answer
Answer:
20
Step-by-step explanation:
Given:
m∠JKL = 3x + 5As per the picture:
m∠JKL = m∠JKM + m∠MKL = 45 + xComparing the two equations above:
3x+5 = 45 + x3x - x = 45 - 52x = 40x = 40/2x = 20x = 20 is the correct answer for this question
Otherwise something is wrong with the question.
I need help with this
Answer:
x = 16
Step-by-step explanation:
Step 1: We know DF - DE = EF
9x - 39 - 47 = EF
Step 2: Simplify
9x - 86 = EF
Step 3: Set the equation equal to 3x + 10
9x - 86 = 3x + 10
6x = 96
x = 16
Therefore x is equal to 16
Answer:
58
Step-by-step explanation:
DE + EF = DF
47+ 3x+10 = 9x-39
Combine like terms
57 +3x = 9x-39
Subtract 3x from each side
57+3x-3x = 9x-3x-39
57 = 6x-39
Add 39 to each side
57+39 = 6x-39+39
96 = 6x
Divide by 6
96/6 = 6x/6
16 =x
We want the length of EF
EF = 3x+10
= 3*16 +10
= 48+10
= 58
Two example that show two positive rational number is greater then either factor True?
Answer:
true
Step-by-step explanation:
Simplify (1-√3) (1÷3+√3) leaving your answer in the form p+q√3
Answer:
[tex]1-\dfrac{2}{3}\sqrt{3}[/tex]
Step-by-step explanation:
Maybe you want to simplify ...
[tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}[/tex]
Multiply numerator and denominator by the 'conjugate' of the denominator:
[tex](1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}[/tex]
the time difference between London and New York is -5 hours. The time difference New York and San Francisco is -3 hours. If it is 11:32 in London, what is the time in San Francisco
Answer:
found this on the web. hopefully it helps
Simplify 3x + 3 + 2.
3x + 5
5x + 3
8x
Answer:
3x + 5
Step-by-step explanation:
We are doing variables and simplifying.
You have two types of numbers here, you have a coefficient, and you have regular numbers. Now do keep in mind that you can never add a regular number to a coefficient. So the only thing in this problem you will add is 3 and 2. Because 3x is different
3x + (3 + 2)
3x + 5
The simplified form of the expression is 3x + 5.
Option A is the correct answer.
We have,
Expression:
3x + 3 + 2
Add like terms.
3x + (3 + 2)
3x + 5
This is the simplest simplified form of the expression.
Thus,
The simplified form of the expression is 3x + 5.
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PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Hello, please consider the following.
x is obviously different from 0 and then, dividing by x is legit.
For the first 105 miles the speed is x, so the time spent is
[tex]\dfrac{105}{x}[/tex]
For the second part, the speed is 1.4 x, so the time spent is
[tex]\dfrac{105}{1.4x}=\dfrac{75}{x}[/tex]
In total, the time she spent driving is
[tex]\dfrac{105}{x}+\dfrac{75}{x}\large \boxed{=\dfrac{180}{x}}[/tex]
Thank you.
when 1760 is divided into 14 equal parts the remainder is 10. what is a correct way to write the quotient
Answer:
125 10/14
Step-by-step explanation:
1,760/14 = 125 r10
- 125 x 14 + 10 = 1,760
You turn the remainder into a fraction using whatever number you divided the main number by. In this case that would be 14.
Suppose a ball is thrown upward to a height of h0 meters. Each time the ballâ bounces, it rebounds to a fraction r of its previous height. Let hn be the height after the nth bounce and let Sn be the total distance the ball has traveled at the moment of the nth bounce. Complete parts a. and b below. h0 = 9, r = o.4Find the first four terms of the sequence (Se).
Answer:What if you were asking this question? How would you explain it to yourself?
Step-by-step explanation:
Please help. I’ll mark you as brainliest if correct!
Answer:
-2°F
Step-by-step explanation:
So on Sunday night, the temperature was -10°F.
And by Monday morning, the temperature has increased by 8°F.
In other words, to find the temperature on Monday morning, we just have to add 8 to -10. Therefore:
[tex](-10)+(8)=-2[/tex]
The temperature on Monday morning is -2°F
Answer:
-2 degrees F.
If you have -10, you have to add positive 10 just to get to 0.
Dajia bought 5 shirts online, and in turn receives a 15% discount. She
must pay an additional 4.99 for shipping. Write an algebraic expression
to represent the total cost of the shirts with the discount, if x represents
the cost of each shirt.