Please help me answer all of these questions. Its a chance to get 100 points please help me. Whoever does all of them I will mark brainlest. :) Please help.
Answers
Answer:
Step-by-step explanation:
Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.
1.
a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.
b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].
2.
a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]
b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]
c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n
d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.
Related Questions
Write a proof
given: angle 1 and angle 3 are supplementary
prove: m is parallel to n
Answers
sorry just wanted to see if the bold thing works
What is the L.C.M of: 6(a+b)+3
Answers
Answer:
I hope this is the right answer
Write an expression for cotA
Answers
Answer:
[tex]cotA=\frac{2x}{5}[/tex]
Step-by-step explanation:
Answer:
[tex]\text{cotA} =\frac{2x}{5}[/tex]
Step-by-step explanation:
cotA = (Adjacent side) ÷ (Opposite side)
The measure of the Adjacent side = 2x
The measure of the Opposite side = 5
Then
[tex]\text{cotA} =\frac{2x}{5}[/tex]
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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32.For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
32. (2, 4) and (4, 10)
Answers
Answer:
The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2
Step-by-step explanation:
Two points are given in question, (2,4) and (4,10).
It is required to find out a linear equation satisfying the points (2,4) and (4,10).
To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]
Step 1 of 3
The slope of a line passing through the points (2,4) and (4,10) is given by
[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$$[/tex]
Step 2 of 3
Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-4)=3(x-2)$$[/tex]
Distribute 3 ,
[tex]$$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$$[/tex]
Step 3 of 3
This linear function can be written in the slope-intercept form by adding 4 on both sides,
[tex]$$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$$[/tex]
So, this is the required linear equation.
Find the product of (x − 5)2. (1 point) Group of answer choices x2 + 10x + 25 x2 − 10x + 25 x2 − 25 x2 + 25
Answers
Answer:
[tex]x^2 - 10x + 25[/tex]
Step-by-step explanation:
Hello!
Expand the square using the Distributive Property.
Expand[tex](x - 5)^2[/tex][tex](x - 5)(x-5)[/tex]Distributive x - 5 to each factor
[tex]x(x - 5) -5 (x - 5)[/tex][tex]x^2 - 5x - 5x+25[/tex][tex]x^2 - 10x + 25[/tex]The answer is [tex]x^2 - 10x + 25[/tex].
We can also use a special binomial product formula.
Formula: [tex](a - b)^2 = a^2 - 2ab + b^2[/tex]
[tex](x - 5)^2 = x^2 - 2(x)(5) + 5^2[/tex][tex](x - 5)^2 = x^2 - 10x + 25[/tex]We get the same answer both ways.
Taseem’s loose change consists of dimes and quarters. When you ask her how many of each type of coin she has, she gives you the following clues: 0.1x+0.25y=19.9 and x+y=100 What can you conclude? Select all that apply.
Answers
The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
0.1x + 0.25y = 19.9 and
x + y = 100
Let x = number of dimes
y = number of quarters
After solving the above system of equations by substitution method.
[tex]\rm \dfrac{398-5y}{2}+y=100[/tex]
y = 66
[tex]\rm x=\dfrac{398-5\cdot \:66}{2}[/tex]
x = 34
Thus, the statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
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I need help pls WILL GIVE BRAINLIEST
Answers
Answer: (3,-2)
Step-by-step explanation:
[tex]-3x-7y=5\\15x+6y=33[/tex]
[tex]5(-3x-7y)=5(5)\\-15x-35y=25[/tex]
new system:
[tex]-15x-35y=25\\15x+6y=33[/tex]
add.
[tex]-29y=58\\y=-2[/tex]
plug in -2 for y
[tex]-3x-7(-2)=5\\-3x+14=5\\-3x=-9\\x=3[/tex]
system:
[tex](3,-2)[/tex]
Answer:
(3, - 2 )
Step-by-step explanation:
- 3x - 7y = 5 → (1)
15x + 6y = 33 → (2)
multiplying (1) by 5 and adding to (2) will eliminate x
- 15x - 35y = 25 → (3)
add (2) and (3) term by term to eliminate x
0 - 29y = 58
- 29y = 58 ( divide both sides by - 29 )
y = - 2
substitute y = - 2 into either of the 2 equations and solve for x
substituting into (2)
15x + 6(- 2) = 33
15x - 12 = 33 ( add 12 to both sides )
15x = 45 ( divide both sides by 15 )
x = 3
solution is (3, - 2 )
On a coordinate plane, parallelogram A B C D, parallelogram A prime B prime C prime D prime, and parallelogram A double prime, B double prime, C double prime, D double prime are on the graph.
In the pre-image of the parallelogram, the slope of AD is −3 and the slope of BC is −3. The image is translated down 7 units and then reflected over the y−axis.
The slope of A"D" is
.
The slope of B"C" is
.
What can you determine about the line segments A"D" and B"C"?
Answers
Using translation concepts, we have that:
The slope of A"D" is of 3.The slope of B"C" is 3.The lines are parallel.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
When the function is translated down, the slope remains constant, while when the function is reflected over the y-axis, the slope is multiplied by -1, hence both lines will have a slope of 3, and since they have the same slope, they are parallel.
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is 7.666 a rational number
Answers
Answer:
Yes, it's a rational number
Step-by-step explanation:
solve the inequality
8x - 3 ≥6x + 4
Answers
Answer:
Hello! The answer is x ≥ [tex]\frac{7}{2}[/tex].
Step-by-step explanation:
To solve this inequality, we have to get x by itself. To do so, we will rearrange the inequality. To do so, we will subtract 6x from both sides and add 3 to both sides:
8x - 3 ≥ 6x + 4
-6x +3 -6x +3
----------------------
2x ≥ 7
Now, we have to get x by itself and divide both sides by 2 to do so:
2x ≥ 7
-- --
2 2
This leaves us with:
x ≥ [tex]\frac{7}{2}[/tex]
The required solution to the inequality 8x - 3 ≥6x + 4 is x ≥ 3.5.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To solve the inequality, we want to isolate the variable x on one side of the inequality symbol.
8x - 3 ≥ 6x + 4
Subtract 6x from both sides:
2x - 3 ≥ 4
Add 3 to both sides:
2x ≥ 7
Divide both sides by 2:
x ≥ 7/2
Therefore, the solution to the inequality is x ≥ 3.5.
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2. A person takes a loan of Rs 100 000 at an interest rate of 4.2% compounded annually and deposits it in a bank that pays 8% interest compounded annually. What is the profit of his investment after 2 years?
Answers
The profit of his investment after 2 years is $8,063.60.
What is the profit of his investment?The profit earned is the difference between the amount he earned from the deposit at the bank and the interest paid on the loan.
Total value of the loan in 2 years : 100,000 x (1.042²) = 108,576.40
Total value of the amount deposited in 2 years : 100,000 x (1.08²) = 116,640
Difference = 116,640 - 108,576.40 = $8,063.60
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A cheerleading team plans to sell t-shirts as a fundraiser. The team's
goal is to make a profit of at least $1248. The profit on each t-shirt sold
is $6.50. The team's goal is written as the inequality shown below.
6.50t ≥1248 where t=number of t-shirts sold
Which graph represents the solution to this inequality?
Answers
Answer:
You didn't include any choices.....see below
Step-by-step explanation:
Pls help solve i will mark branliest
Answers
Answer:
1.875 liters
Step-by-step explanation:
x=1.25×32=3.752=1.875 liters
Given: A, C, and F are collinear
Prove: measure of angle s= measure of angle x+measure of angle y
Answers
m∠x+m∠r+m∠y=180° (angles in a triangle add to 180°)
m∠r+m∠s=180° (angles that form a linear pair add to 180°)
m∠x+m∠r+m∠y=m∠r+m∠s (Transitive property of equality)
m∠x+m∠y=m∠s (subtraction property of equality)
m∠s=m∠x+m∠y (symmetric property of equality)
Is this a function?
yes
no
Answers
Bryan is asked to write an inequality to represent the graph.
A number line going from negative 16 to negative 10. An open circle is at negative 14. Everything to the right of the circle is shaded.
He writes Negative 14 less-than-or-equal-to x.
Which error did Bryan make?
Bryan must write the inequality with the variable on the left side of the relation symbol.
Bryan chose a relation symbol that does not point in the same direction as the ray.
Bryan included –14 in his solution set.
Bryan used the wrong number in his inequality.
Answers
The error that Bryan has done in this inequality is that he included –14 in his solution set.
How to point out the mistake madeWhat Bryan has to do would be to write this inequality in such a way that the variable would appear on the left.
But the symbol that he has chosen does not move in this same direction as the graph.
The -14 should not be inclusive in the graph because it is not a part of the graph solution.
He used the wrong number in this inequality.
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Answer:
its c
Step-by-step explanation:
on edge
Question is in the picture, please help me out!!
Answers
The arithmetic sequences are as follow:
What is Arithmetic Sequence?An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.
1) t(n) = 5n + 4
t(1) = 9, t(2) = 14, t(3) = 19
So,
9,14,19,...
d= 14-9 = 5
d= 19-14 =5
Hence, it is an AP
2) 1, 2, 4, 8 , 16
Hence, it is not an AP
3) 3, 6, 9 ,...
It is an AP
4)It is given that it is an AP
5) tn = 2*3^n
t1= 6, t2= 18, t3= 54
So, 6, 18, 54,...
Hence, it is not an AP
6) 3 , 1, 1/3,...
It is not an AP
7) t(n+1)= 6*t(n)
t(1) = -1
t(2)=-6
t(3)= -36
Hence, it is not an AP
8) -3, 1, 5, 9
Hence, it is an AP.
9) 1, 4, 9,...
Hence, it not an AP
10) 2,1,0,1,2,...
It is not an AP
11) t(n)= -2n-5
t(1)= -7, t(2)= -9, t(3)= -11
Hence, it is an AP
12) tn= (1/2)^n
t1= 1/2, t2= 1/4, t3= 1/8
It is not an AP
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If you vertically stretch the exponential function f(x) = 2* by a factor of 4, what
is the equation of the new function?
A. g(x) = 2.4*
OB. g(x) = 24x
OC. g(x)=1.2*
OD. g(x)=4-2*
Answers
If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x
Vertical stretch of a functionExponential function is written in standard form as y= ab^x
where
a is the base
x is the exponent
Given the following exponential function f(x) = 2^x. If the function is vertically stretched by 4, the resulting function will be g(x) = 4(2)^x
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Simplify
50(x^2+7x+6)
Answers
Distribute [tex]50[/tex] to every term inside the parentheses.
[tex]50\cdotx^2+50\cdot7x+50\cdot6[/tex]
Simplify with multiplication.
[tex]\huge\boxed{50^2+350x+300}[/tex]
You can't simplify further by adding, so leave the answer as-is.
Answer:
50x^2 + 350x + 300
Step-by-step explanation:
Original Equation:
50(x^2+7x+6)
Distribute 50 to all 3 #'s:
50x^2 + 350x + 300
What is the approximate total length of iron edging needed to create the square frame and the two diagonals? 43.5 inches 50.9 inches 54.0 inches 61.5 inches
Answers
Total length of iron edging needed to create the square frame is 43.5 inches
Important properties of square:
All four interior angles are equal to 90°
All four sides of the square are congruent or equal to each other.
The opposite sides of the square are parallel to each other.
The diagonals of the square bisect each other at 90°
The two diagonals of the square are equal to each other.
Diagonal of square = [tex]\sqrt{2}[/tex]a
9 = [tex]\sqrt{2}[/tex]a
a = [tex]\frac{9}{\sqrt{2}}[/tex]
a = 6.36 inches
Iron edging needed to create the square frame = 4*6.36 = 25.44 inches
iron edging needed to create two diagonals = 2*9 = 18 inches
total length = 18 + 25.44
= 43.44 ~ 43.5 inches
Thus, Total length required is 43.5 inches
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The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
Answers
The percentage given shows that the amount is decreasing by 8%.
How to illustrate the information?From the information given, the function is f(x) = 9,628(0.92)x. This illustrates that the amount is decreasing by 8% she compared to the previous year. This was computed as:
= 1 - 0.92
= 0.08
= 8%
For part B, the percentage change will be:
= (8,972 - 8,074.80)/8972 × 10
= 10%
Therefore, the account recorded a greater percentage change in amount of money over the previous year is account B as 20% is lore than 8%.
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which coordinate pair is a solution of the linear equation below -3x+4y=19
Answers
The coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)
How to determine the ordered pair?The linear equation is given as:
-3x + 4y= 19
Set x = 0
So, we have:
-3(0) + 4y = 19
Evaluate
4y = 19
Divide by 4
y = 19/4
Hence, the coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)
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The sum of two numbers is 79. Three times the first number added to 5 times the second number is 283. What are the two numbers?
Answers
Answer:
The two numbers are 56 and 23.
Step-by-step explanation:
Let the two numbers be A and B.
We are told that:
A+B = 79, and
2) 3A + 5B = 283
Rearrange the first expression to isolate A:
A = 79-B
Now use this value of B in the second expression:
3A + 5B = 283
3(79-B) + 5B = 283
237-3B + 5B = 283
2B = 46
B = 23
If B=23, we can find A from (1):
A+B = 79
A+23 = 79
A = 56
CHECK:
Does A+B = 79?
56 + 23 = 79? YES
Does 3A + 5B = 283?
3(56) + 5(23) = 283?
168 + 115 = 283? YES
What is the asymptote of the function g(x) = 5•2^3x + 4 shown on the graph?
A: y=4
B: y=5
C: y=0
D: y = 3
Answers
Hope this helps :)
Help please I'll mark you as brainlist if the answer is correct
if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p
Answers
Answer:
factor polynomial is x+q so x=-q
putting the value of x in both equations
eqn 1)a^2+p(-a)+q=0
a^2 -ap+q=0
eqn 2)a^2+m(-a)+n=0
a^2-am+n=0
Since both are equal to zero,we can write:
a^2-ap+q=a^2-am+n
-ap+am=n-q
a(-p+m)=n-q
a=(n-q)/(m-p)
Explanation:
Since (x + a) is a factor of the two polynomials, when x = -a, the polynomials should both equal 0 (this is known as the factor theorem).
• First equation:
[tex]x^{2} + px + q[/tex]
When x = -a:
[tex](-a)^{2} + p(-a) + q = 0\\\\a^{2} -pa + q = 0[/tex]
• Second equation:
[tex]x^{2} + mx + n[/tex]
When x = -a:
[tex](-a)^{2} + m(-a) + n = 0\\\\a^{2} -ma + n = 0[/tex]
• As both equations equal 0, we can equate them:
[tex]a^{2} -pa + q = a^{2} -ma + n \\\\-pa + ma = n - q\\\\a(m - p) =n -q\\\\a = (n - q)/ (m - n)[/tex][proven]
Which statement is not true about the data shown by the box plot below?
a.The range is 67.
b. The data point 5 lies outside the range of the data.
c. Three fourths of the data is less than 68.
d. Half the data lies between 51 and 68.
Answers
based on the options given, one thing that isn't true of the box plot is that d. Half the data lies between 51 and 68.
what is false about the box plot?the box plot has a range of 67:
= 90 - 23
= 67
the data point 5 lies outside the data set.
3/4 of the data is less than 68 which is the 3rd quartile.
this means that the false statement is that half of the data is between 57 and 68.
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2. On Friday, the Lee family had dinner at a
restaurant. They ordered 12 cheeseburgers and
4 chili bowls for $19.40. The following Friday,
the Lee family went back to the same restaurant.
They ordered 8 cheeseburgers and 6 chili bowls
for $16.60. How much does a cheeseburger
cost?
Answers
Answer:
cheeseburger costs $1.25
Step-by-step explanation:
let x be the cost of a cheeseburger and y the cost of chilli and set up 2 simultaneous equations, that is
12x + 4y = 19.4 → (1)
8x + 6y = 16.6 → (2)
multiplying (1) by 6 and (2) by - 4 and adding the result will eliminate y
72x + 24y = 116.4 → (3)
- 32x - 24y = - 66.4 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 50
40x = 50 ( divide both sides by 40 )
x = 1.25
the cost of a cheeseburger is $1.25
Simplify the radical. What is the number under the radical sign when it is simplified? Do not rationalize the denominator. ∛-27/81. Please help asap^^
Answers
Answer:
[tex]-\frac{1}{\sqrt[3]{3}}[/tex]
Step-by-step explanation:
To do this we can ask ourselves "What number multiplied three times by itself is _____?" In this case we have -27 and 81. We see that -3*-3*-3=-27. We also see that 3*3*3*3=81. This means that [tex]\sqrt[3]{-27}=-3,[/tex] and [tex]\sqrt[3]{81} = 3\sqrt[3]{3}.[/tex]
The fraction we get is [tex]\frac{-3}{3\sqrt[3]{3} }[/tex], and we can simplify to get [tex]-\frac{1}{\sqrt[3]{3}}[/tex].
in triangle abc and triangle def angle a=angle d and angle b= angle e and ab=ef. will the 2 triangles be congruent ? justify your answer
Answers
Answer:
Step-by-step explanation:
no, you don't have the measure of at least one side, so having the same angles is similar but not congruent