Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][(2 × 5) + 2(n - 1) ]
= [tex]\frac{n}{2}[/tex](10 + 2n - 2)
= [tex]\frac{n}{2}[/tex](2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
The sum of n terms for the arithmetic series is:
[tex]S_n=\frac{n}{2}[8+2n ][/tex]
The value of n for which the series has sum 165 is 11
The given series is:
5 + 7 + 9 +.......
The first value, a = 5
The common difference, d = 7 - 5
d = 2
The sum of the first n terms of an arithmetic series is given by the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d ][/tex]
Substituting a = 5, and d = 2 into the sum of the series, we have:
[tex]S_n=\frac{n}{2}[2(5)+(n-1)(2) ]\\\\S_n=\frac{n}{2}[10+2n-2 ]\\\\S_n=\frac{n}{2}[8+2n ][/tex]
To determine the value of n for which the series has sum 165, substitute [tex]S_n=165[/tex] into the sum above
[tex]S_n=\frac{n}{2}[8+2n ]\\\\165=\frac{n}{2}[8+2n ]\\\\2(165)=n(8+2n)\\\\2n^2+8n-330=0\\\\n^2+4n-165=0\\\\n^2-11n+15n-165=0\\\\n(n-11)+15(n-11)=0\\\\(n-11)(n+15)=0\\\\n=11, n=-15[/tex]
The value of n for which the series has sum 165 is 11
Learn more on Arithmetic Progression here: https://brainly.com/question/24205483
I AM GIVING 15 POINTS TO WHOMEVER ANSWERS THIS!!!
Compare 6 x 10^5 and 3 x 10^4.
A) 6 x 105 is 20 times larger than 3 x 104
B) 6 x 105 is 15 times larger than 3 x 104
C) 6 x 105 is 10 times larger larger than 3 x 104
D) 6 x 105 is 5 times larger than 3 x 104
Answer:
20
Step-by-step explanation:
To find how many times 6 x 10^5 power is greater tan 3 x 10^4 power, we divide the first number by the second. Write an equation!
(6 x 10^5)/(3 x 10^4)=
To divide them, we simply subtract the exponents. 5-4=1.
(6 x 10^1)/(3 x 10^1)
60/30=20
Your answer is 20.
Hope this helps!
Answer:
Your answer would be A)6x105 is 20 times larger than 3x104
All u have to do is get your answer from 6x10^5(which is 600,000) and 3x10^4(which is 30,000) and divide it by each other So it would be 600,000/30,000=20 =^.^=
Step-by-step explanation:
The table below gives the dimensions of a statue and a scale drawing of the statue.
Find the scale factor of the drawing to the real statue.
Write your answer as a fraction in simplest form.
Answer:
1/6 is the scale factor
Step-by-step explanation:
If two figures are similar, then we can relate different characteristics of the figure by using the scale factor. The scale factor is a measure of proportion with the original figure.
Obviously only similar figures can be compared using a scale factor. We know that similar figures are proportional and constant of proportionality of different dimensions in linear form such as length, height, width, perimeter etc is called scale factor.
If scale factor >1 then there is dilation of enlargement otherwise shrink
Here drawing is having dimensions as 9x7 instead of original 54x42
Proportion is the same as 1/6
So scale factor = 1/6
Answer: [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
The formula to find the scale factor(k) :
[tex]k=\dfrac{\text{length of side in image}}{\text{length of corresponding side in pre-image}}[/tex]
From the given table, the height of statue of drawing = 9 inches
The height of statue of real statue = 54 inches
Then, the scale factor : [tex]k=\dfrac{9}{54}=\dfrac{1}{6}[/tex]
Similarly for length , the scale factor = [tex]k=\dfrac{7}{42}=\dfrac{1}{6}[/tex]
Hence, the scale factor of the drawing to the real statue = [tex]\dfrac{1}{6}[/tex]
Write an equation in slope-intercept
A slope of 0 and passes through (0,-3)
If the line has a slope = 0, then it's a horizontal line
with the equation y = constant.
The line passes through (0, -3) → y= -3
Answer: y = -3Find ab , bc , and ac .. HELPPPP ( all parts )
At the product store you can buy four bags of bananas for 2084 how much would it cost if you were to buy 3 bags
Answer:
1563
Step-by-step explanation:
x= 1 bag of bananas
so, 4x=2084
Divide 2084 by 4 to find how much 1 bag of bananas would cost. 2084/4= 521.
To find how much 3 bags of bananas would cost, multiply 521 (the price of one bag) by 3. 521x3= 1563
3 bags of bananas are $1563
PLEASE HELP AND EXPLAIN!
The table below shows how much it costs to use a music website. How much will it cost you to use website for 6 months?
Month Cost
First Month .................. Free
Second month .............. $8.50
Each additional month .... $5.25
Answer:
$29.50
Step-by-step explanation:
please help!!! MAX POINTS I CAN DO//// it’s in math because i trust the math people more
i can help you with points if you would like
pls consider it i have alot
translate each of the following into a variable expression
the product of mask (m) and acceleration(a)
use the graph to find the value of y = sin theta for the value of theta.
1/4pi radians
a. -0.7
b. 0.7
c. -0.9
d. 0.9
Answer:
y ≈ 0.7
Step-by-step explanation:
locate [tex]\frac{\pi }{4}[/tex] on the x-axis, move up the vertical line until meeting the graph then the horizontal reading gives y ≈ 0.7
what is the square root of 120
Answer: [tex]2\sqrt{30}[/tex]
Step-by-step explanation:
120
∧
12 10
∧ ∧
3 4 2 5
∧
2 2
[tex]\sqrt{120}[/tex]
= [tex]\sqrt{2*2*2*3*5}[/tex]
= [tex]2\sqrt{2*3*5}[/tex]
= [tex]2\sqrt{30}[/tex]
what is indicated by arrowheads on a line?
Arrows on a line mean that the line continues forever in that direction. If there are two arrows in both directions along a line, then you have a geometric line. If you only have one arrow, then it is a ray. Having no arrows indicates a segment.
Helena is purchasing a house for $210000
The question requires understanding of real estate value, equity, and mortgage calculations related to buying a house. Freda's equity is the entire value of her house at $250,000. Ben has paid off a portion of his loan and has an equity of $100,000 in his home.
Explanation:The question provided deals with the financial aspects of purchasing a house and understanding real estate value, equity, and mortgage calculations. Helena purchasing a house for $210,000 would fall under the mathematics or business subject area as it involves financial calculations.
Freda's house situation, where she bought a house for $150,000 in cash and its current value is $250,000, tells us that her equity in the property would be the entire value of the house, which is $250,000, since she owes nothing to the bank.
As for Ben, he initially purchased his house for $100,000 and made a 20% down payment. He took a loan from the bank to cover the remaining 80%, later paid off $20,000 of it, and his house value has increased to $160,000. Ben's remaining loan balance would be the original borrowed amount minus what he has already paid back. Since he had taken 80% of $100,000, that would have been $80,000 initially, minus the $20,000 paid, leaves him with a $60,000 debt. The equity that Ben has in his house is the current market value minus the debt, which is $160,000 - $60,000, giving him an equity of $100,000.
In another scenario provided, Joanna is looking to determine how much she can afford in terms of a house loan with yearly payments of $12,000 at an interest rate of 4.2% over a 30-year period. She would need to apply the formula for calculating a mortgage payment and the total amount paid over the course of the loan.
Helena's total monthly payments are approximately $2,361.17. The closest answer choice is C. $2330.20.
Principal and Interest:
Down payment = 5% of $210,000 = $10,500
Loan amount = $210,000 - $10,500 = $199,500
Using a mortgage calculator, the monthly principal and interest payment for a 15-year loan at 4.5% interest on $199,500 is $1595.54.
PMI (Private Mortgage Insurance):
Loan-to-value ratio (LTV) = $199,500 / $200,000 = 99.75%
Based on the table, the PMI premium for a 15-year fixed-rate loan with an LTV of 95.01% to 97% is 0.79%.
Annual PMI premium = 0.79% of $199,500 = $1575.05
Monthly PMI premium = $1575.05 / 12 = $131.25
Property Taxes:
Annual property taxes = 3.5% of $200,000 = $7000
Monthly property taxes = $7000 / 12 = $583.33
Homeowners Insurance:
Monthly homeowners insurance = $600 / 12 = $50
Total Monthly Payments:
Principal and Interest: $1595.54
PMI: $131.25
Property Taxes: $583.33
Homeowners Insurance: $50 Total: $2350.12
Complete Question:
Helena is purchasing a house for $210,000, with a 15 -year fixed-rate mortgage at 4.5% interest. She has made a 5% down payment. The house is valued at $200,000, and the local tax rate is 3.5%. Her homeowners insurance is $600 per year. What are her total monthly payments? (Use the table below to calculate PMI premiums.)
[tex]\begin{tabular}{lcccl} Base-To-Loan\% & \multicolumn{2}{c}{ Fixed Rate Loan } & \multicolumn{2}{c}{ ARM 2\%+1 Year Cap } \\& $30 {yrs}$ & $15 {yrs}$ & $30 {yrs}$ & $15 {yrs}$ \\$95.01 \%$ to $97 \%$ & $0.90 \%$ & $0.79 \%$ & ${n} / {a}$ & ${n} / {a}$ \\$90.01 \%$ to $95 \%$ & $0.78 \%$ & $0.26 \%$ & $0.92 \%$ & $0.81 \%$ \\$85.01 \%$ to $90 \%$ & $0.52 \%$ & $0.23 \%$ & $0.65 \%$ & $0.54 \%$ \\$85 \%$ and Under & $0.32 \%$ & $0.19 \%$ & $0.37 \%$ & $0.26 \%$\end{tabular}[/tex]
A. 2654.23
B. 2894.71
C. 2330.20
D. 2202.72
The parabola has a focus at (−3, 0) and directrix y = 3. What is the correct equation for the parabola? x2 = −12y x2 = 3y y2 = 3x y2 = −12x
Answer:
[tex]x^2+6x+6y=0[/tex]
Step-by-step explanation:
The distance between the parabola focus and the directrix is 3, then
[tex]p=3.[/tex]
Parabola vertex is placed on the perpendicular line to the directrix and this perpendicular line passes trough the focus. Its equation is x=-3 and parabola vertex coordinates are (-3,1.5).
Branches of the parabola go in negative y-direction, then the equation of the parabola is
[tex](x-(-3))^2=-2\cdot 3(y-1.5),\\ \\(x+3)^2=-6(y-1.5),\\ \\x^2+6x+9=-6y+9,\\ \\x^2+6x+6y=0.[/tex]
Answer:
y2=-12x
Step-by-step explanation:
AM I CORRECT??? thanks for checking my answer
Translate the sentence into an equation.
Three times the sum of a number and 9 is 4.
Use the variable b for the unknown number.
Answer:
3* (b+9) = 4
Step-by-step explanation:
b is the unknown number
Three times the sum of a number and 9 is 4.
3* (b+9) = 4
To translate 'Three times the sum of a number and 9 is 4' into an equation, you represent the unknown number by 'b' and write the equation as 3(b + 9) = 4. Solve for 'b' by distributing the 3 and then isolating 'b' to get b = -23/3.
Translating the sentence 'Three times the sum of a number and 9 is 4' into an equation involves identifying the phrases that represent mathematical operations and the variable represented by b. The sentence describes a two-step mathematical process: finding the sum of a number (b) and 9, and then multiplying that sum by 3 to get 4. This can be written as an equation: 3(b + 9) = 4.
To solve for the unknown, which in this case is b, we first distribute the 3 inside the parentheses: 3b + 27 = 4. Then we isolate the b on one side by subtracting 27 from both sides of the equation: 3b = 4 - 27, which simplifies to 3b = -23. Finally, we divide both sides by 3 to get b on its own: b = -23/3.
the artist goes to the store to buy brushes and small cans of paint. he pays $94. he buys 8 brushes that cost $5 each. the rest of the money is used for the 6 cans of paint. each can of paint cost the same amount. how much does each can of paint cost?
Answer:
$9
Step-by-step explanation:
The artist buys 8 brushes that cost $5 each, then all brushes cost
[tex]\$5\cdot 8=\$40.[/tex]
He pays $94 for all brushes and cans of paint, then all cans of paint cost
[tex]\$94-\$40=\$54.[/tex]
If he buys 6 cans of paint, then one can of paint costs
[tex]\$54:6=\$9.[/tex]
Please Help Quick!!!
Answer:0.16 and 6%
Step-by-step explanation:
In a parking lot of 240 red and blue cars, the ratio of red cars to blue is 3:5
How many red cars are there?
Answer:
There would be 144 red cars.
Step-by-step explanation:
3:5 is equal to 3/5
240 * (3/5) = 144
Answer:
90 red cars
Step-by-step explanation:
sum the parts of the ratio 3 + 5 = 8 parts
divide 240 by 8 to find one part of the ratio
240 ÷ 8 = 30 ← 1 part of the ratio
3 parts = 3 × 30 = 90 ← number of red cars
5 parts = 5 × 30 = 150 ← number of blue cars
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLPPPPPPPPPPPPP
The system results in a false statement
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?
a. y= -1/5x+1
b. y= 1/5x+3
c. y= -5x-23
d. y= 5x+27
Answer:
a. y= -1/5x+1
Step-by-step explanation:
If we have 2 points , we can find the slope using the formula
m = (y2-y1)/(x2-x1)
= (-1-2)/(10--5)
=(-1-2)/(10+5)
= -3/15
= -1/5
The slope if -1/5
We can use the point slope form of a line to write an equation
y-y1= m(x-x1)
y-2 = -1/5(x--5)
y-2 =-1/5(x+5)
Distribute the -1/5
y-2=-1/5x -1
Add 2 to each side
y-2+2 = -1/5x -1+2
y = -1/5x+1
Step-by-step explanation:
Use this formula: Y2 - Y1
X2 -X1
Then, use point slope form: y - Y1 = m (x - X1)
m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineFinally, it'll reveal your answer!!! :)
Given X(4, -7). What are the coordinates of X" if
X"=R----
A. (-4, 7)
B. (0,9)
C.(-4,9)
D.(0,-7)
B. (0, 9)
Step-by-step explanation:Reflection across x=a is represented by the transformation ...
... (x, y) ⇒(2a-x, y)
Reflection across y=b is represented by the transformation ...
... (x, y) ⇒ (x, 2b-y)
The double reflection, across x=2, y=1 will result in the transformation ...
... (x, y) ⇒ (2·2-x, y) ⇒ (4-x, 2·1-y) ⇒ (4-x, 2-y)
For (x, y) = X(4, -7), the transformed point is ...
... X''(4-4, 2-(-7)) = X''(0, 9)
The double reflection across x=2 and y=1 transforms the point X(4, -7) to X''(0, 9), illustrating the sequential application of reflection transformations (4-x, 2-y).
The correct answer is option B.
A reflection across the vertical line x=a is represented by the transformation (x, y) ⇒ (2a-x, y). Similarly, a reflection across the horizontal line y=b is represented by the transformation (x, y) ⇒ (x, 2b-y). The double reflection, across x=2 and y=1, can be expressed by applying these transformations sequentially.
Starting with the point (x, y), the first reflection across x=2 yields (2·2-x, y), and then, the reflection across y=1 gives (4-x, 2·1-y). Combining these transformations, the double reflection is represented by the transformation (x, y) ⇒ (4-x, 2-y).
Now, applying this double reflection to the given point X(4, -7), we get X''(4-4, 2-(-7)) = X''(0, 9). Therefore, the transformed point after the double reflection is X''(0, 9) making option B the correct option.
Learn more about Transformations here:
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BRAINLIEST FOR U! answer in 5 mins
Which of the following methods separates a homogeneous solution by spinning the solution very fast?
ik its not 'D' i got it wrong on my test
a. Evaporation and distillation
b. Filtration
c. Centrifuge
d. Magnetism
Answer:
I would say the answer is c
Answer: the best answer is c
A wood stove burns 4 same-sized logs in 2 hours.How many logs does the stove burn in 8 hours?
Answer:
16 logs
Step-by-step explanation:
4 logs in 2 hours
8 logs in 4 hours
12 logs in 6 hours
16 logs in 8 hours
Answer:
16
Step-by-step explanation:
16 Because 2 divided by 8 equals 4 then 4x4=16
What is the sum 1/8 plus 1/4
Answer:
3/8
Step-by-step explanation:
1/8 + 1/4 =
We need to get a common denominator of 8
1/8 + 1/4 * 2/2
1/8 + 2/8
3/8
A water park offers a season pass for $64 per person which includes free
admission and free parking. Admission for the water park is $14.50 per person. Parking is normally $5 for those without a season pass.
a. How many visits to the water park would you have to use for
the season
pass to be a better deal?
b. What would the total cost be for 3 visits with and without a season pass?
Answer:
Part a) The number of visits mus be greater than or equal to [tex]4[/tex]
Part b)
with season pass
The total cost is [tex]\$64[/tex]
without season pass
The total cost is [tex]\$58.5[/tex]
Step-by-step explanation:
Let
x---> the number of visit to the water park
y---> the total cost to visit the water park per person
we know that
[tex]y=(14.50+5)x=19.5x[/tex]
so
Part a) How many visits to the water park would you have to use for the season pass to be a better deal?
For [tex]y=\$64[/tex]
Substitute the value of y in the equation and solve for x
[tex]64=19.5x[/tex]
[tex]x=64/19.5=3.28\ visits[/tex]
therefore
The number of visits mus be greater than or equal to [tex]4[/tex]
Part b) What would the total cost be for 3 visits with and without a season pass?
with season pass
The total cost is [tex]\$64[/tex]
without season pass
The total cost for [tex]x=3\ visits[/tex] is
[tex]y==19.5(3)=\$58.5[/tex]
your network wants to cut your expenses per episode. thry have given you a budget of $85,134 for the next 6 episode. how much do you have to spend per episode?
Q3. What is the quotient? −218÷114 Enter your answer as a mixed number, in simplified form, in the box.
Edit: This is very hard, so please help with these as well...?
Q4. What is the quotient?
158÷(−135)
Enter your answer as a mixed number, in simplified form, in the box.
Q5. Divide.
−834÷216
Options:
A. −4/18
B. −4/126
C. −3/2526
D. −3/18
(Please answer in detail)
Thank you! ^-^
Answer:
3. - 1 52/57
4. -1 23/135
5. -3 31/36
Step-by-step explanation:
3. Note the answer will be a negative number because one of the numbers is negative and the other is positive. When we do the division use positive numbers . Then we can just plug in the negative.
It looks like 114 will only divide once into 218 because 2*114 = 228 .
So the whole number part is 1. Now subtract 114 from 218 we get 104.
So we have the mixed number 1 104/114. These numbers in the fraction are positive so we divide by 2 to simplify.
This gives us 1 52/57
Finally plug in the negative and we have -1 52/57 (answer)
Q4. In a similar fashion to the above 158 / 135 = 1 and the fraction part is (158-135) / 135 = 23/135,so the answer is -1 23/135 ( note its negative because of the -135).
Q5.
-834 / 216
216 divides 3 times into 834 and the remainder is 834 - 3 * 216
= 834 - 648 = 186
so the mixed number is -3 186/216
Now simplify 186/216:-
divide each number by 2 , we get 93/108
3 will divide into 93 and 108 giving 31/36
Now plug in the negative.
So the answer is -3 31/36
Answer:
3. [tex]-1\tfrac{52}{57}[/tex]
4. [tex]-1\tfrac{23}{135}[/tex]
5. [tex]-3 \tfrac{31}{36}[/tex]
Step-by-step explanation:
3.
To find : the quotient when we divide -218 by 114
Solution : As in −218÷114 one of the numbers is negative and the other is positive, quotient must be negative .
[tex]\frac{-218}{114}=\frac{-109}{57}=-1\tfrac{52}{57}[/tex] ( mxed fraction )
( see fig (i) )
4.
To find : the quotient when we divide 158 by 135
Solution: As in 158÷(−135) one of the numbers is negative and the other is positive, quotient must be negative .
[tex]\frac{158}{-135}=-1\tfrac{23}{135}[/tex] ( mixed fraction )
( see fig (ii) )
5.
To find : −834÷216
Solution :
As in −834÷216 one of the numbers is negative and the other is positive, quotient must be negative .
[tex]\frac{-834}{216}=\frac{-417}{108}=\frac{-139}{36}=-3 \tfrac{31}{36}[/tex]
( see fig iii )
what the simplified of 2/3 dived by 2/9
Answer:
3
Step-by-step explanation:
2/3 divided by 2/9
flip 2/9 to 9/2
2/3 mutilplied by 9/2
2 cancels 2 and 9 divides 3
equals 3
Melinda starts with $22 and saves $10 each week. George starts with $10 and saves $13 each week. After how many weeks will they have the same amount saved?
Answer: 4
Step-by-step explanation:
Melinda: y = 10x + 22
George: y = 13x + 10
13x + 10 = 10x + 22
-10x -10x
3x + 10 = 22
-10 -10
3x = 12
÷3 ÷3
x = 4
Lets say Y is the amount they will save.
So Melinda's savings could be described by the equation Y=22+10X, where X is the number of weeks. The same goes to George, but his equation would be Y=10+13X.
To save the same amount, their equations must match:
22+10X = 10+13X
Solving this, one gets
12 = 3x
=> 4=x
So the answer is 4 weeks.
Solve 3[-x + (2x +1)] =x-1
Answer:
x=-2
Step-by-step explanation:
Remove parenthesis 3(-x+(2x+1))=x-1
Collect the like terms 3(-x+2x+1)=x-1
Multiply parenthesis by 3 3(x+1)=x-1
Move terms 3x+3=x-1
Collect the like terms and calculate 3x-x=-1-3
Divide both sides by 2 2x=-4
Answer: x=-2
Step-by-step explanation: