the domain of f/g consists of numbers x for which g(x)........0 that are in the domain of both.....and......

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

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]

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.

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

Answer:

C) the length of DG and JL

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

Answer:

y=−3x+21

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

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

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.

Answer: I don’t know lol maybe 1460

Step-by-step explanation:

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

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.

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:

Answer:

train A=38mph train B=44mph

Step-by-step explanation:

Setting up a table:

         s            t           d

A     x            190/x    190

B    x+6      220/x+6  220

Train A was 6mph slower as shown in the table, so to make it easier, train a is identified as x, train b would be x+6

Their distances are put in their respective column.

You find time from distance divided by speed.

So time would be written as such.

Since you know they take the same amount of time, for the equation, you connect them with an equal sign. Cross multiply to something like:

190(x+6)=220x

190x+1140=220x

1140=30x

x=38

You plug this in and get the speed for train A as 38, and train B as 44.

Hope this helps ^^

Answer: 90° counterclockwise

Step-by-step explanation:

Answer:

D. 3.2

Step-by-step explanation:

Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.

Based on this theorem, we have: TV = ½(RS)

TV = 3n - 2

RS = n + 12

Substitute

3n - 2 = ½(n + 12)

Multiply both sides by 2

2(3n - 2) = (n + 12)

6n - 4 = n + 12

Collect like terms

6n - n = 4 + 12

5n = 16

Divide both sides by 5

5n/5 = 16/5

n = 3.2

Step-by-step explanation:

1. 12/18/3 = 4/6....!!!

Answer:

6

Step-by-step explanation:

I would first simplify the fraction on the left:

12/18 = 2/3

Then:

2/3 = 4/x

2x/3 = 4

2x = 4*3

x = 4*3/2

x = 12/2

x = 6

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.

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]

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.

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.

9514 1404 393

Answer:

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)

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

Answer:

35/45 or 7/9

Step-by-step explanation:

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

(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

Pre-Calculus

Calculus

Limits

Sequences

Series

Telescoping 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

Step 3: Find Sum

∴ 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

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

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:

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.