Answer:
2/7
Step-by-step explanation:
d=2n+3
[tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]
13(2n+3) -91 =8n - 16
26n+39 -91 = 8n-16
18n=36
n=2
d=7
Can someone help me solve this? Thanks!
9514 1404 393
Answer:
p(x) = x³ -3x²+4x -2
Step-by-step explanation:
When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.
Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...
p(x) = (x -1)(x -(1+i))(x -(1-i))
The last two factors can be recognized as the factors of the difference of squares:
((x -1) +i)((x -1) -i) = (x -1)² -i²
= (x² -2x +1) -(-1) = x² -2x +2
Now the whole polynomial can be seen to be ...
p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)
p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses
p(x) = x³ -3x²+4x -2
GET 95 POINTS Let f(x) = 1/x and g(x)=x² + 6x. What
two numbers are not in the domain of fᵒg?
Separate your answers with a comma.
Answer:
hey there hope this answer helps you out
Step-by-step explanation:
we have two functions f(x) and g(x) such that
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} + 6x[/tex]
solving for f ° g, we'll substitute the x in f(x) by the value of g(x)
[tex]fog = \frac{1}{g(x)} [/tex]
[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]
taking x common in denominator
[tex]fog = \frac{1}{x(x + 6)} [/tex]
for a function to exist it should not have 0 in its denominator
checking the values of x for which the denominator of f ° g becomes 0 :-
x = 0 and x = -6so the function doesn't exist at values x = 0, -6
So, 0, -6 cannot be in the domain of f°gTo find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x
Answer:
[tex]m = \frac{1}{12}[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (36,6)[/tex]
[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve
Required
The slope of f(x)
The slope (m) is calculated using:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex](x,y) = (36,6)[/tex] implies that:
[tex]a = 36; f(a) = 6[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]
If [tex]f(x) = \sqrt x[/tex]; then:
[tex]f(36 + h) = \sqrt{36 + h}[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]
Multiply by: [tex]\sqrt{36 + h} + 6[/tex]
[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]
Expand the numerator
[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]
Collect like terms
[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]
[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]
Cancel out h
[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]
[tex]h \to 0[/tex] implies that we substitute 0 for h;
So, we have:
[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]
[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]
[tex]m = \frac{1}{6 + 6}[/tex]
[tex]m = \frac{1}{12}[/tex]
Hence, the slope is 1/12
PLEASE ANYONE definition of a percent increase?
Answer:
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.
Step-by-step explanation:
I hope it helps
If a student walked 2 feet straight to the chalk board in 2 seconds and
then walked 2 feet back to his or her original position at his or her desk at
the same speed, what was the student's displacement at 2 seconds
compared to 0 seconds?
O 6 feet
O O feet
O2 feet
O 4 feet
Answer:
2 feet
Step-by-step explanation:
Displacement at 0 seconds is 0 feet.
Displacement at 2 seconds is 2 feet because it took them 2 seconds to walk 2 feet.
Write an addition or a subtraction equation (your choice!) to describe the diagram. Pls help
Answer:
Addition equation = -4-0) + [(-13)-(-4)]
Answer = -13
Step-by-step explanation:
For the small arrow in the diagram, the expression is (-4 - 0)
For the bog arrow, the expression will be -13 - (-4)
Adding both expressions
Addition = (-4-0) + [(-13)-(-4)]
Addition = (-4) + (-13+4)
Addition = -4 + (-9)
Addition = -4-9
Addition = -13
The following data was collected from a survey in which people identified their average salaries over the past ten years. Identify the number of classes in the histogram.
Answer:
nine 9 classes in the histogram
Find f(6), f(0), and f(-1)
f(x)=-7X
Answer:
f(6)=-42
f(0)=0
f(-1)=7
Step-by-step explanation:
since f(x) =-7x
it implies that f(6),f(0) and f(-1) are all equal to f(x)
which is equal to -7x .
so wherever you find x you out it in the
function
Choose ASA SAA or neither to describe this figure
Answer:
SAA
Step-by-step explanation:
HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.
Based on a sample survey, a company claims that 86% of their customers are satisfied with their products. Out of 1,100 customers, how many would you predict to be satisfied?
Answer:
946 people
Step-by-step explanation:
Find how many you would predict to be satisfied by multiplying 1,100 by 0.86:
1,100(0.86)
= 946
So, you could expect 946 people to be satisfied
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)
Answer:
there is a 64% chance that the student got both problems wrong
a 32% chance that they got only 1 correct
and a 4% chance that they got both correct
Step-by-step explanation:
There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.
[tex]25-9=16[/tex]
[tex]\frac{16}{25} =\frac{x}{100}[/tex]
[tex]\frac{64}{100}[/tex]
[tex]64[/tex]%
[tex]\frac{8}{25} =\frac{y}{100}[/tex]
[tex]\frac{32}{100}[/tex]
[tex]32[/tex]%
[tex]\frac{1}{25} =\frac{z}{100}[/tex]
[tex]\frac{4}{100}[/tex]
[tex]4[/tex]%
Question 4
Which term in the sequence given by n th term formula 7n - 50 has a value of 41?
th term
Answer:
13th term
Step-by-step explanation:
41 = 7n - 50
41 + 50 = 7n
91 = 7n
7n = 91
n = 91/7
n = 13
13th term has value 41
Answer:
n = 13
Step-by-step explanation:
7n - 50 = 41
Add 50 to both sides
7n = 41 + 50
7n = 91
Divide both sides by 7
n = 91/7
n = 13
Michael was 1.0 metres tall, and could
only reach up to the 1st floor lift button. .
From the 1st floor, he had to walk up 100
steps to reach the 6th floor.
Vinh was 1.4 metres tall, and could reach
the 5th floor button. He had to walk up
20 steps to reach the 6th floor.
Lucy was 1.1 metres tall. To reach the
6th floor, how many steps did she have to
walk up?
Answer:
Lucy must walk up 80 steps to reach the 6th floor.
Step-by-step explanation:
Since Michael was 1.0 meters tall, and could only reach up to the 1st floor lift button, and from the 1st floor, he had to walk up 100 steps to reach the 6th floor; while Vinh was 1.4 meters tall, and could reach the 5th floor button, and he had to walk up 20 steps to reach the 6th floor; If Lucy was 1.1 meters tall, to determine how many steps did she have to walk up to reach the 6th floor, the following calculation must be performed:
1 = 100
1.4 = 20
1.4 - 1 = 100 - 20
0.4 = 80
0.1 = X
0.1 x 80 / 0.4 = X
20 = X
100 - 20 = 80
Therefore, Lucy must walk up 80 steps to reach the 6th floor.
13. Given that
[tex] {x}^{2} + {y}^{2} + 10y + 16 = 0[/tex]
and
[tex] {(x - 3)}^{2} + {y}^{2} = 1[/tex] are two circles on the same plane. Find:
a) the coordinates of the center and the radius for each circle.
b) the equation of the straight line joining the center of both circles.
step by step explanation:
[tex]\mathfrak{x}^{2}+{y}^{2}+16=0[/tex]
=[x2+16=0x26]
=[2x{y}^2{16}~0]
=[4×{y}^0{16}]
=[32x{y}^x]
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
urdxvjok NCAA earth bno
Does the equation 3x-6y=0 represent a direct variation? *
Answer:
yes
Step-by-step explanation:
if you change it to standard form, it would be
y=1/2x
because it's in the format of y=ax then it is direct variation
Solve the equation −96=3(8x)^(5/3).
Answer:
x= - 1
Step-by-step explanation:
1. Find the exact value of sin( a−B), given that sin a=−4/5 and cos B=12/13, with a in quadrant III and B in quadrant IV.
2. Find all real numbers in the interval [0,2pi) that satisfy the equation.
3sec^2 x tan x =4tan x
3. Simplify the following trigonometric expressions, using identities as needed:
sin(x)/1−cos(x) + 1−cos(x)/sin(x)
(1) Recall that
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
sin²(x) + cos²(x) = 1
Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have
• sin(α) < 0 and cos(α) < 0
• sin(β) < 0 and cos(β) > 0
Solve for cos(α) and sin(β) :
cos(α) = -√(1 - sin²(α)) = -3/5
sin(β) = -√(1 - cos²(β)) = -5/13
Then
sin(α - β) = sin(α) cos(β) - cos(α) sin(β) = (-4/5) (12/13) - (-3/5) (-5/13)
==> sin(α - β) = -63/65
(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,
sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)
==> tan²(x) + 1 = sec²(x)
Rewrite the equation as
3 sec²(x) tan(x) = 4 tan(x)
3 (tan²(x) + 1) tan(x) = 4 tan(x)
3 tan³(x) + 3 tan(x) = 4 tan(x)
3 tan³(x) - tan(x) = 0
tan(x) (3 tan²(x) - 1) = 0
Solve for x :
tan(x) = 0 or 3 tan²(x) - 1 = 0
tan(x) = 0 or tan²(x) = 1/3
tan(x) = 0 or tan(x) = ±√(1/3)
x = arctan(0) + nπ or x = arctan(1/√3) + nπ or x = arctan(-1/√3) + nπ
x = nπ or x = π/6 + nπ or x = -π/6 + nπ
where n is any integer. In the interval [0, 2π), we get the solutions
x = 0, π/6, 5π/6, π, 7π/6, 11π/6
(3) You only need to rewrite the first term:
[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]
Then
[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Which sentence correctly compares the two numbers 5.395 and 5.385?
05.395 < 5.385
05.385 > 5.395
o 5.395 = 5.385
5.385 < 5.395
h
Submit
Pass
Don't know answer
Answer:
5.385 < 5.395
Step-by-step explanation:
Compare digits one by one starting form the left.
5.395 and 5.385
The 5s in the ones place are equal.
5.395 and 5.385
The 3s in the tenths place are equal.
5.395 and 5.385
The 9 in the hundredths place is greater than the 8 in the hundredths place, so the number with the 9 is grater than the number with the 8.
That makes the number with the 8 less than the number with the 9.
Answer: 5.385 < 5.395
I need help with this.
Answer:
A and b Are in quadrant 2. F and D are in quadrant 1. F is in quadrant 3 and C is in quadrant 4
Step-by-step explanation:
each quadrant is in the boxes and the question is asking what is each coordinate is in what quadrant
write the expression x^2+8x-5 and x^2-4x-2 in the form (x+a)^2 +b
Số táo của An Bình Chi là như nhau. An cho đi 17 quả, Chi cho đi 19 quả thì lúc đó số táo của Chi gấp 5 lần tổng số táo của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo?( Giải bài toán trên bằng phương trình hoặc hệ phương trình )
Answer:
please write in english i cannot understand
Step-by-step explanation:
You can afford a $950 per month mortgage payment. You've found a 30 year loan at 8% interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?
Answer:
129469.3194
342000
212530.6806
Step-by-step explanation:
Going to assume that the 8% is a nominal, montly rate
which means the effective monthly rate is .08/12= .006667
using the annuity immediate formula...
a.)
[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]
b.) we would pay 950*30*12= 342000
c.) the amount in interest would be 342000-129469.3194=212530.6806
a) The loan one can afford is $1,29,460.2
b) The total amount of money paid to the loan company over the life of the loan is $342,000.
c) $212539.8 of the total amount paid is interest.
To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:
[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual interest rate divided by 12),
and n is the total number of payments (number of years multiplied by 12).
Given:
Monthly payment (M) = $950
Loan term = 30 years
Interest rate = 8% per year
a) How big of a loan can you afford?
Let's calculate the principal loan amount (P):
First, we need to convert the annual interest rate to a monthly interest rate:
r = 0.08 / 12
= 0.00667
n = 30 years × 12 months
n= 360
Using the formula and plugging in the values we have:
[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]
[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]
[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]
[tex]950\times9.948 = 0.0730P[/tex]
Divide by 0.073:
Now we can solve for P:
[tex]P=\frac{9450.6}{0.0730}[/tex]
[tex]P = 1,29,460.2[/tex]
Therefore, you can afford a loan amount of $1,29,460.2
b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total amount = Monthly payment × Total number of payments
Total amount =[tex]$950 \times 360[/tex]
Total amount = [tex]342,000[/tex]
Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.
c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:
Interest = Total amount - Principal loan amount
Interest = [tex]342,000 - 129460.2[/tex]
=$212539.8
Therefore, $212539.8 of the total amount paid is interest.
To learn more on Simple Interest click:
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The length of a rectangle is 12 m and its diagonal is 15 m. find
the breadth and area of the rectangle.
Answer:
108 square metres
Step-by-step explanation:
A=√d square - l square
here
A = area
d= diagonal
l= length
Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)
Step-by-step explanation:
here is the answer. Feel free to ask for more.
In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3. Consider 1980 as the starting point (time zero) for this problem. Create an explicit exponential formula for the median age of the U.S. population t years after 1980, assuming the median age has exponential growth.
Answer: [tex]30e^{0.00813x}[/tex]
Step-by-step explanation:
Given
Median age in 1980 is [tex]30[/tex]
It is [tex]35.3[/tex] in year 2000
Suppose the median age follows the function [tex]ae^{bx}[/tex]. Consider 1980 as starting year. Write the equation for year 1980
[tex]\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a[/tex]
For year 2000
[tex]\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813[/tex]
After t years of 1980
[tex]\Rightarrow 30e^{0.00813x}[/tex]
How many flowers spaced every 4 inches are needed to surround a circular garden with a 15-foot radius? Round all circumference and area calculations to the nearest whole number.
Answer:
283 flowers
Step-by-step explanation:
c=2pi*r
c = 1130.973 =1131
1131/4
282.75 = 283
what is the value of c? enter your answer in the box. round only your final answer to the nearest whole number.
Answer:
c ≈ 21
Step-by-step explanation:
By applying cosine rule in the given triangle ABC,
c² = a² + b² - 2abcos(C)
c² = (17)² + (10)² - 2(17)(10)cos(98.8°)
c² = 289 + 100 - 340(-0.1530)
c² = 441.015
c = 21
c ≈ 21
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
Learn more about the Continuous Compounding here:
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sin4x - cosx
---------------- = f(x) f^1(π/4) what is the derivative?
tanx
I think you are asked to find the value of the first derivative of f(x) at π/4. Given
[tex]f(x) = \dfrac{\sin(4x)-\cos(x)}{\tan(x)}[/tex]
use the quotient to differentiate and you get
[tex]f'(x) = \dfrac{\tan(x)(4\cos(4x)+\sin(x))-(\sin(4x)-\cos(x))\sec^2(x)}{\tan^2(x)}[/tex]
Then at x = π/4, you have
tan(π/4) = 1
cos(4•π/4) = cos(π) = -1
sin(π/4) = 1/√2
sin(4•π/4) = sin(π) = 0
cos(π/4) = 1/√2
sec(π/4) = √2
==> f ' (π/4) = (1•(-4 + 1/√2) - (0 - 1/√2)•(√2)²) / 1² = -4 + 1/√2 + √2
