Answer:
i can help u just give me the work
Step-by-step explanation:
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
What is the slope of the line shown below?
Answer:
2
Step-by-step explanation:
Given two points on the line, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 7 - -3)/(3 - -2)
= (7+3)/(3+2)
= 10/5
=2
1. Prove the following identity:
—> sin^2 theta (1+ 1/tan^2 theta) =1
9514 1404 393
Explanation:
[tex]\sin^2(\theta)\times\left(1+\dfrac{1}{\tan^2(\theta)}\right)=\\\\\sin^2(\theta)\times\left(1+\dfrac{\cos^2(\theta)}{\sin^2(\theta)}\right)=\\\\\dfrac{\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta))}{\sin^2(\theta)}=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}[/tex]
D
6
5
F
5.5
к.
6.6
What additional information must be known to prove the triangles similar by SSS?
A) No additional information is needed.
B) 2D = LJ
C) The lengths of DG and JL
D) .F.LK
Answer:
C) the length of DG and JL
Salma invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $1400. As a percentage, what was the annual interest rate of her investment? If necessary, refer to the list of financial formulas.
Answer: I don’t know lol maybe 1460
Step-by-step explanation:
it takes engineer 3 hrs to drive to his brother's house at an average of 50 miles per hour. if he takes same route home, but his average speed of 60 miles per hour, what is the time, in hours, that it takes him to drive home?
Answer:
t2 = 2.5 hours.
Step-by-step explanation:
The distance is the same.
d = r * t
The rates and times are different so
t1 = 3 hours
t2 = X
r1 = 50 mph
r2 = 60 mph
r1 * t1 = r2*t2
50 * 3 = 60 * t2
150 = 60 * t2
150 / 60 = t2
t2 = 2.5
Answer:
Answer: Travel Time is 2 hours & 30 minutes
Step-by-step explanation:
Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles
Original Distance is 150 miles, New Speed is 60 mph.
Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph
- Mariah is looking at her bank account and sees that she is in debt $40. She plans to buy dinner
for several friends on Friday at $5 per meal. On Monday she earns $30.25 babysitting and
$25.75 for tutoring several younger students. On Tuesday, she cleans the apartment for her
mom and earns $11 dollars. She spends $2 of those dollars on a candy bar. How many friends
can she buy dinner for on Friday?
Answer: 5 friends
Note: if Mariah pays for her own meal, then it would drop to 4 friends.
===========================================================
Explanation:
Add up the amount she earns:
30.25+25.75+11 = 67
Now add up the amounts that she's either in debt or that she spends money on. Ignore the dinner portion for now.
40+2 = 42
She earns $67 total and has to spend $42, without including the dinner portion just yet. That means Mariah has 67-42 = 25 dollars left over.
-------------------
Let x be the number of $5 meals she can buy
So she can spend a total of 5x dollars here. Set this equal to 25 (the amount left over) and solve for x.
5x = 25
x = 25/5
x = 5
She can buy dinner for 5 friends. Or if Mariah is paying for herself as well, then she can buy dinner for 4 friends. It's not clear which scenario your teacher is after, but I'll assume the first scenario.
You start savings a $250 a month for the next 22 years to give us a gift to your daughter when she graduates college if you put the money into a long-term savings account that receives 3.5 interest how much money will you be able to give your daughter
Answer:
$376,475.71
Step-by-step explanation:
FVA Due = P * [(1 + r)n – 1] * (1 + r) / r
FVA Due = 250 * [(1.2916)264 – 1] * (1.2916) / .2916
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
What is the product? (–3s + 2t)(4s – t)
Answer:
[tex] - 12 {s}^{2} + 11st - 2 {t}^{2}[/tex]Step-by-step explanation:
(–3s + 2t)(4s – t)
= -3s (4s - t) + 2t(4s - t)
[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]
[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]
Answer: -12s^2 + 11st -2t^2
Step-by-step explanation:
= (-3s + 2t)(4s - t)
= -12s^2 + 3st + 8st -2t^2
= -12s^2 + 11st -2t^2
Answer Provided by GauthMath please heart and comment thanks if you like.
If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 11 cm. (Round your answer to three decimal places.)
Answer:
Step-by-step explanation:
I'm going to go through this as I would when teaching it to my students for the first time. This is a super simple one, so it shouldn't be too hard. Begin with what you know:
A snowball is a sphere. Since we are told that the surface area is changing (decreasing, to be exact), it would make sense to know the formula for the surface area of a sphere:
[tex]S=4\pi r^2[/tex] where r is the radius. Let's take the derivative of this using implicit differentiation to see what it is we need to solve this:
[tex]\frac{dS}{dt}=4\pi*2r\frac{dr}{dt}[/tex], where dr/dt is the rate at which the radius is changing. If we look at the problem, we are looking for the rate at which the DIAMETER is changing. So instead of using the radius in the original formula, we need to write it in terms of the diameter. We know that
d = 2r so
[tex]r=\frac{d}{2}[/tex] and we will put that into the formula for r to get:
[tex]S=4\pi(\frac{d}{2})^2[/tex] and simplify a bit:
[tex]S=4\pi(\frac{d^2}{4})[/tex] and the 4's cancel each other out, leaving us with simply:
[tex]S=\pi d^2[/tex] Now let's take the derivative:
[tex]\frac{dS}{dt} =\pi 2d\frac{dD}{dt}[/tex] where the rate of the surface area is -8 ("decreasing" rate makes this number a negative) when the diameter is 11. Filling in:
[tex]-8=\pi(2)(11)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]\frac{dD}{dt}=-\frac{8}{22\pi}[/tex] , which rounds to
[tex]\frac{dD}{dt}=-1.142\frac{cm}{min}[/tex] and again, the negative means that the diameter is decreasing.
write your answer in simplest radical form
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
Whoever gets this problem right with proper work shown will get brainliest
Answer:
100 % or 1
Step-by-step explanation:
There are two dice
Each dice has a possible roll of 1,2,3,4,5,6
The possible sums are 2,3,4,5,6,7,8,9,10,11,12
The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1
$9500 is invested, part of it at 11% and part of it at 8%. For a certain year, the total yield is $937.00. How much was invested at each rate
Answer:
5900 at 11%
3600 at 8%
Step-by-step explanation:
x= invested at 11%
y= invested at 8%
x+y=9500
.11x+.08y=937
Mulitply the first equation by .11
.11x+.11y= 1045
Subtract this and the second equation
(.11x+.11y)-(.11x+.08y)=1045-937
.03y=108
y=3600
SOlve for x
x+3600=9500
x=5900
Are the two figures similar? if they are, solve for the missing side.
Answer:
They are not similar.
Step-by-step explanation:
26 / 13 = 2
24 / 11 = 2.18
They are not proportional which means that they don't have a scale factor and cannot be answered.
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
how all work.
A) What is the average rate of change of the function g(x) = 14x + 6 over the interval [0, 5]?
B) What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,5]?
C) How does this compare to your Answers for Problem 4?
Answer:
Here we can only answer A and B.
For a given function f(x), the average rate of change in a given interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(14*5 + 6) - (14*0 + 6)}{5} = \frac{14*5}{5} = 14[/tex]
The average rate of change is 14.
B) We have g(x) = 3*(2x) - 6
we can rewrite this as:
g(x) = 3*2*x - 6 = 6x - 6
And we want to find the rate of change in the interval [0, 5]
is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(6*5 - 6) - (6*0 - 6)}{5} = 6[/tex]
Consider the series ∑n=1∞5n2+n.
The general formula for the sum of the first n terms is Sn=
. Your answer should be in terms of n.
The sum of a series is defined as the limit of the sequence of partial sums, which means
∑n=1∞5n2+n=limn→∞(
)=
.
Select all true statements (there may be more than one correct answer):
A. Most of the terms in each partial sum cancel out.
B. The series converges.
C. The series is a p-series.
D. The series is a telescoping series (i.e., it is like a collapsible telescope).
E. The series is a geometric series.
(a) Decompose the summand into partial fractions:
[tex]\dfrac5{n^2+n} = \dfrac5{n(n+1)} = \dfrac an+\dfrac b{n+1}[/tex]
[tex]\implies 5=a(n+1)+bn=(a+b)n+a[/tex]
[tex]\implies a+b=0\text{ and }a=5 \implies b=-5[/tex]
[tex]\implies\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = 5\sum_{n=1}^\infty\left(\frac1n-\frac1{n+1}\right)[/tex]
The n-th partial sum for the series is
[tex]S_n = 5\displaystyle\sum_{k=1}^n\left(\frac1k-\frac1{k+1}\right)[/tex]
which can be simplified significantly by examinging consective terms in the sum:
[tex]\displaystyle S_n = 5\left(1-\frac12\right) + 5\left(\frac12-\frac13\right) + 5\left(\frac13-\frac14\right) + \cdots + 5\left(\frac1{n-1}-\frac1n\right) + 5\left(\frac1n-\frac1{n+1}\right)[/tex]
[tex]\implies S_n = \boxed{5\left(1-\dfrac1{n+1}\right)}[/tex]
(b) Using the result of (a), you then get
[tex]\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = \lim_{n\to\infty}\boxed{5\left(1-\frac1{n+1}\right)} = \boxed{5}[/tex]
(c) As shown in (a), the partial sum is simplified because of the reasons given in options A and D, and the result of (b) says that B is also correct.
Answer:
Part a. [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]
Part b. [tex]\displaystyle \lim_{n \to \infty} (5 - \frac{5}{n + 1}) = 5[/tex]
Part c. A, B, and D
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringPre-Calculus
Partial Fraction DecompositionCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]Sequences
Series
Definition of a convergent or divergent seriesTelescoping Series: [tex]\displaystyle \sum^\infty_{n = 1} (b_n - b_{n + 1}) = (b_1 - b_2) + (b_2 - b_3) + (b_3 - b_4) + ... + (b_n - b_{n + 1}) + ...[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n}[/tex]
Step 2: Rewrite Sum
Factor: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \frac{5}{n(n + 1)}[/tex]Break up [Partial Fraction Decomposition]: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{A}{n} + \frac{B}{n + 1}[/tex]Simplify [Common Denominator]: [tex]\displaystyle 5 = A(n + 1) + Bn[/tex][Decomp] Substitute in n = 0: [tex]\displaystyle 5 = A(0 + 1) + B(0)[/tex]Simplify: [tex]\displaystyle 5 = A[/tex][Decomp] Substitute in n = -1: [tex]\displaystyle 5 = A(-1 + 1) + B(-1)[/tex]Simplify: [tex]\displaystyle 5 = -B[/tex]Solve: [tex]\displaystyle B = -5[/tex][Decomp] Substitute in variables: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} + \frac{-5}{n + 1}[/tex]Simplify: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} - \frac{5}{n + 1}[/tex]Substitute in decomp [Sum]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg)[/tex]Step 3: Find Sum
Find Sₙ terms: [tex]\displaystyle \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg) = (5 - \frac{5}{2}) + (\frac{5}{2} - \frac{5}{3}) + (\frac{5}{3} - \frac{5}{4}) + (\frac{5}{4} - 1) + ... + ( \frac{5}{n} - \frac{5}{n + 1}) + ...[/tex]Find general Sₙ formula: [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]Find Sum [Take limit]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \lim_{n \to \infty} S_n[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5 + 0[/tex]Simplify: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5[/tex]∴ the sum converges by the Telescoping Series.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)
9514 1404 393
Answer:
common denominator: (x² -4)simplified complex fraction: (2x +1)/(9 -2x)Step-by-step explanation:
It is helpful to remember the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
__
Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.
It looks like you want to simplify ...
[tex]\dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}[/tex]
Answer:
c
Step-by-step explanation:
(x+2)^2(x-2)
A cube has an edge of 2.25 feet. The edge is increasing at the rate of 1.25 feet per hour. Express the volume of the cube as a function of h, the number of hours elapsed.
Answer:
[tex]V(h)=(1.25h+2.25)^3[/tex]
Step-by-step explanation:
Recall that the volume of a cube is given by:
[tex]\displaystyle V = s^3[/tex]
Where s is the side length of the cube.
The edges of the cube has an original length of 2.25 feet. It increases by 1.25 feet per hour. In other words, the length s after h hours can be modeled by the equation:
[tex]s=1.25h+2.25[/tex]
Substitute. Hence, our function is:
[tex]V(h)=(1.25h+2.25)^3[/tex]
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation:
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
The function ƒ(x) = x−−√3 is translated 3 units in the negative y-direction and 8 units in the negative x- direction. Select the correct equation for the resulting function.
Answer:
[tex]f(x)=\sqrt[3]{x}[/tex] [tex]3~units\: down[/tex]
[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]
[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]
----------------------------
Hope it helps..
Have a great day!!
Answer:
its not B that what i put and i missed it
Step-by-step explanation:
A particular fruit's weights are normally distributed, with a mean of 344 grams and a standard deviation of 10 grams. If you pick 10 fruit at random, what is the probability that their mean weight will be between 334 grams and 354 grams
Answer:
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 344 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 344, \sigma = 10[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{10}{\sqrt{10}}[/tex]
What is the probability that their mean weight will be between 334 grams and 354 grams?
This is the p-value of Z when X = 354 subtracted by the p-value of Z when X = 334.
X = 354
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{354 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
X = 334
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{334 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = -3.16[/tex]
[tex]Z = -3.16[/tex] has a p-value of 0.0008.
0.9992 - 0.0008 = 0.9984
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
please help me with this question.
The line parallel to y = -3x + 4 that passes through (9,-6)
Answer:
y=−3x+21
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
Anyone willing to help on this worksheet?
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
Please help me thank you!!!
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point
Answer:
Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.
