Find the factors in the expression: 3x( x +4)
A 3x, x and 4
B 3x and ( x + 4)
C 3, x and (x + 4)
D 3, X, X, and 4

Answer:

[tex]\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]

Step-by-step explanation:

So we want to find the derivative of the rational equation:

[tex]y=\frac{x^2-2x}{x^3+3}[/tex]

First, recall the quotient rule:

[tex](\frac{f}{g})'=\frac{f'g-fg'}{g^2}[/tex]

Let f be x^2-2x and let g be x^3+3.

Calculate the derivatives of each:

[tex]f=x^2-2x\\f'=2x-2[/tex]

[tex]g=x^3+3\\g=3x^2[/tex]

So:

[tex]\frac{dy}{dx}=(\frac{x^2-2x}{x^3+3})'[/tex]

Use the above format:

[tex]\frac{dy}{dx}=\frac{f'g-fg'}{g^2}\\\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]

And that's our answer :)

(If you want to, you can also expand. However, no terms will be canceled.)

Answer:

x < ( 8 - 2b ) / -a

Step-by-step explanation:

For this problem, we simply will solve the inequality for x.

-ax + 2b > 8

-ax > 8 - 2b

x < ( 8 - 2b ) / -a

Note, the comparison is flipped since a negative multiplicand was used to isolate x.

Cheers.

Answer:

Part A:

[tex]7n + 5[/tex]

Part B:

15 people

Step-by-step explanation:

Each person gets one club sandwich and two regular sandwiches. There is one additional Dagwood sandwich.

If a club sandwich has 3 slices, then the total amount of slices needed for [tex]n[/tex] people will be [tex]3n[/tex], since each person has 3 slices.

If a regular sandwich has 2 slices and everybody gets 2 regular sandwiches, then it's represented as [tex]4n[/tex], since everyone has 4 slices each.

Additionally, we have one Dagwood sandwich, which can be represented as 5,, since a Dagwood sandwich has 5 slices.

Combining these terms we get [tex]3n + 4n + 5[/tex]. Combining like terms gets us the expression [tex]7n + 5[/tex].

To solve for  [tex]7n + 5[/tex], we have to make it an equation. Using the information in Part B, the Deli ends up receiving 110 slices of bread. So, the equation is

[tex]7n + 5=110[/tex]

We want to isolate n on one side, to do this we have to subtract 5 then divide by 7.

[tex]7n + 5 - 5= 110-5\\\\7n = 105\\\\7n\div7 = 105\div7\\\\n = 15[/tex]

So 15 people are going to the picnic.

Hope this helped!

Answer:

[tex]\huge \boxed{h= \displaystyle \frac{SA}{2\pi r} -r}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]SA=2\pi r^2 +2\pi rh[/tex]

Subtracting [tex]2\pi r^2[/tex] from both sides:

[tex]SA-2\pi r^2 =2\pi rh[/tex]

Dividing both sides by [tex]2\pi r[/tex]:

[tex]\displaystyle \frac{SA-2\pi r^2}{2\pi r} =h[/tex]

Simplifying the equation:

[tex]\displaystyle \frac{SA}{2\pi r} -r=h[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = -12

Step-by-step explanation:

Let x be the number.

The product of 5 and x increased by 9 is equal to 15 less than 3 times x.

5x + 9 = 3x - 15.

We can isolate x, getting (5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

The required number is -12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The product of five and a number, increased by 9 is equal to fifteen less than three times then number.

Let x be the number.

Establishing the equation,

5x + 9 = 3x - 15.

(5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

Hence, the number is -12

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Answer:

Step-by-step explanation:

A). If a function 'f' is inverse of another function 'g',

Then f[g(x)] = x = g[f(x)]

In this question the given functions are,

f(x) = [tex]\frac{1}{x-3}[/tex] and g(x) = [tex]\frac{3x+1}{x}[/tex]

Then, f[g(x)] = [tex]\frac{1}{\frac{3x+1}{x}-3}[/tex]

                    = [tex]\frac{x}{3x+1-3x}[/tex]

                    = x

Similarly, g[f(x)] = [tex]\frac{(\frac{3}{x-3})+1}{\frac{1}{x-3} }[/tex]

                         = [tex]\frac{3+x-3}{1}[/tex]

                         = x

Therefore, Both the functions are inverse of each other.

B). Domain of the compositions of these functions will be a set of all real numbers, (-∞, ∞)

Answer:

Answer of 15(i) is the picture . 15(ii) and 17 are solved

Step-by-step explanation:∆ABC where B=90°

→D is mod point of BC so CD=BD

To Prove:

→BC^2=4(AD^2-AB^2)

PROOF:--

In ∆ABD by pythagorus theorem we get,

AD^2=AB^2+BD^2

SO

➡️BD^2= AD^2-AB^2. (1)

NOW ,

BC= BD+CD

BC= 2BD (AS D IS MID POINT)

SQUAREING BOTH SIDES

BC^2= 4BD^2

BY EQUATION 1 WE GOT BD^2 = AD^2-AB^2

Putting this value

➡️BC^2= 4(AD^2-AB^2)

HENCE PROVED

-------------------------------------------------------------------------

17.

Construction : Draw AE ⊥ BC

Proof : In ∆ABE and ∆ACE, we have

AB = AC [given]

AE = AE [common]

and ∠AEB = ∠AEC [90°]

Therefore, by using RH congruent condition

∆ABE ~ ∆ACE

⇒ BE = CE

In right triangle ABE.

AB2 = AE2 + BE2 ...(i)

[Using Pythagoras theorem]

In right triangle ADE,

AD2 = AE2 + DE2

[Using Pythagoras theorem]

Subtracting (ii) from (i), we get

AB2 - AD2 = (AE2 + BE2) - (AE2 + DE2)

AB2 - AD2 = AE2 + BE2 - AE2 - DE2

⇒ AB2 - AD2 = BE2 - DE2

⇒ AB2 - AD2 (BE + DE) (BE - DE)

But BE = CE [Proved above]

⇒ AB2 - AD2 = (CE + DE) (BE - DE)

= CD.BD

⇒ AB2 - AD2 = BD.CD

Hence Proved.

A

Step-by-step explanation:

Answer:

the answer is 14. hope this helps :)

Step-by-step explanation:

Answer:

A. 2.27 kg

B. 61.23 kg

Step-by-step explanation:

A. 31.75 - 29.48 = 2.27

B. 31.75 + 29.48  = 61.23

Answer:hi

Step-by-step explanation:Let me first warn you that I CANNOT get the denominators of this problem to go underneath the numerators. It looks good on my answer page but when I click "preview your answer" the denominators are ALL over the place. Grrrrr.

I think the weirdly placed denominators make this explanation hard to understand but you give this a go and see if you understand things. If it is too hard to see, maybe this website will let you instant message me or email me. If so, then I will send you the solution via email. I'm very sorry the denominators are SO scattered.

See what you think of the explanations below but it might help if you write down my answer on paper, so that you can move the number to rest more closely under their proper numerators. :-)

Ok then......

Let's start with your first problem. A quick way to do this work is to cross multiply. Here's what I mean:

__3___ = __6___

r - 1 r + 2

Ok, so you can cross multiply:

3(r + 2) = 6(r - 1) (cross multiply)

3r + 6 = 6r - 6 (use the distributive property)

Now you will have to put the "r" variables on the left side of the equal sign and numbers without variables on the right side of the equal sign. To get 6r from the right side to the left, you can subtract 6r from the right side. If you subtract it from the right, you must subtract it from the left.....

To get 6 from the left side to the right, you can subtract it from the left. If you subtract it from the left, you must subtract it on the right.....

So now you have:

3r - 6r = -6 - 6 This becomes.........

- 3r = -12

Now to solve for "r" you will have to divide by -3. Why? Well, -3r is really saying: -3 times r. The -3 and the r are actually being multiplied together so to isolate the "r" you have to sort of "undo" the multiplication. What is the opposite of multiplication? It's DIVISION. Soooo, you must divide by -3 on both sides. SO you have:

- 3r = -12

r = 4 (-12 divided by -3 is a positive 4)

Now you know "r" equals 4. If we "plug" 4 back into the original equation, we can see the answer is correct. Check this out:

__3___ = __6___ (original equation)

r - 1 r + 2

__3___ = __6___ (substitute "4" in for "r"

4 - 1 4 + 2

__3___ = __6___ (do the math in the denominator area)

3 6

1 = 1 (3/3 equals 1 and 6/6 also equals 1, so our

solution that r = 4 is correct!) :-)

Now to your 2nd problem..........

4/2x-5 = 24/2x

___4___ = __24___

2x � 5 2x

Let's cross multiply again:

4(2x) = 24(2x - 5)

8x = 48x - 120

8x - 48x = - 120

-40x = - 120

(divide both sides by -40)

x = 3

Now let's "plug" 3 in where we had the variable "x" in the original equation to see if we are correct.

___4___ = __24___ (original equation)

2x � 5 2x

___4___ = __24___ (substituted 3 for "x")

2(3) � 5 2(3)

___4___ = __24___

6 - 5 6

___4___ = __24___

1 6

4 = 4

SO once again we have found the correct answer. Yay for us! :-)

I hope this helps. :-)

Answer:

[tex]r=9[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-8(6-r)=24[/tex]

Divide both sides by -8:

[tex]6-r=-3[/tex]

Subtract 6 from both sides:

[tex]-r=-9[/tex]

Divide both sides by -1:

[tex]r=9[/tex]

And we're done!

Answer:

[tex]JL=56[/tex]       [tex]JK=39[/tex]        [tex]KL=17[/tex]

Step-by-step explanation:

Your question is not well presented/formatted; however, I can deduce that the question requires that you calculate the following lengths;

JK, KL and JL

Given that

[tex]JL=5x-9[/tex]

[tex]JK=3x[/tex]

[tex]KL=1x+4[/tex]

The relationship between the given parameters is:

[tex]JL = JK + KL[/tex]

Substitute 5x - 9 for JL; 3x for JK and 1x + 4 for KL

[tex]5x - 9 = 3x + 1x + 4[/tex]

Collect Like Terms

[tex]5x - 3x - 1x = 9 + 4[/tex]

[tex]x = 13[/tex]

Now that the value of x has been solved, we can easily get the numeric values of JK, KL and JL by substituting 13 for x

So;

[tex]JL=5x-9[/tex]

[tex]JL=5*13-9[/tex]

[tex]JL=65 - 9[/tex]

[tex]JL=56[/tex]

[tex]JK=3x[/tex]

[tex]JK=3 * 13[/tex]

[tex]JK=39[/tex]

[tex]KL=1x+4[/tex]

[tex]KL=1 * 13+4[/tex]

[tex]KL=13+4[/tex]

[tex]KL=17[/tex]

Hence;

[tex]JL=56[/tex]       [tex]JK=39[/tex]        [tex]KL=17[/tex]

The speed of the object in feet per minute to nearest whole number is 164feet/min

Speed is the ratio of the distance to the time of an object. Mathematically;

Speed = Distance/Time

Given the following

Speed = 3km/hr

Using the conversion ratio

1km = 3280.84feet

3km = x

Cross multiply

x = 3 * 3280.84

x = 9,842.52feet

Convert 1 hour to minute

1 hour = 60minutes

Get the speed in feet per minutes

Speed in feet/minutes = [tex]\frac{9,842.52}{60}[/tex]

Speed in feet/minutes = 164.042 feet/minutes

Hence the speed of the object in feet per minute to nearest whole number  is 164feet/min

Learn more here: https://brainly.com/question/1462592

The speed in feet per  minute is 164.

Given the following data:

In this exercise, you're required to convert the value of the speed given in kilometers per hour to feet per minute.

Conversion:

1 kilometer = 3280.84 feet

3 kilometer = X feet

Cross-multiplying, we have;

X [tex]= 3280.84[/tex] × [tex]3[/tex]

X = 9842.50 feet

Since we know that one (1) hour is equal to sixty (60) minutes, we would divide the value of X by 60 in order to convert it to feet per minute.

[tex]X = \frac{9842.50}{60}[/tex]

X = 164.042 feet per minute.

To the nearest whole number;

X = 164 feet per minute

Therefore, the speed in feet per  minute is 164.

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Answer:

M=-49

Step-by-step explanation:

-7=M/7

-7*7=M

-49=M

Answer:

-7= -49/7

Step-by-step explanation:

you're just creating an equal expression so think of it as -7/1 = -49/7. your just multiplying the first ratio by 7 but when you simplify the two ratios theyu are equal

Answer :1,2,4,8

Step-by-step explanation:

Answer:

Factors  Multiples

1, 2, 3, 6 6 60

1, 7 7 70

1, 2, 4, 8 8 80

1, 3, 9 9 90

Step-by-step explanation:

factors of 8 are numbers between -8 and 8 because all of these numbers are between 8 and -8 it has to have split between two numbers thats how you get factors of 8.

Answer:

2.7 [tex]g/mL[/tex]

Step-by-step explanation:

The density of an object will be its mass over volume.

We know that the mass of this rock is 54 grams because it took 54 grams of gram stackers to balance the scale. If we have a balanced scale, that means the amount of weight on either side is equal. So the mass is 54 grams.

Also, we can tell that the volume of the rock is 20 mL. This is because, according to Archimedes principle, if you put an object in water, the amount of water displacement will be it's volume. So the amount of water displacement is [tex]60-40=20[/tex] mL.

Density is mass over volume, so the density is [tex]54\div20 = 2.7[/tex]. Density is measure in mass over volume, so [tex]g/mL[/tex].

So 2.7  [tex]g/mL[/tex] is the density of the rock.

Hope this helped!

Answer:

8/15

Step-by-step explanation:

1 hour = 60 minutes

32 minutes / 60 minutes

Divide top and bottom by 4

8/15

Answer:

y=-35

Step-by-step explanation:

Steps

$\frac{y}{5}-=-7$

$\mathrm{Subtract\:}-\mathrm{\:from\:both\:sides}$

$\frac{y}{5}=-7$

$\mathrm{Simplify}$

$\frac{y}{5}=-7$

$\mathrm{Multiply\:both\:sides\:by\:}5$

$\frac{5y}{5}=5\left(-7\right)$

$\mathrm{Simplify}$

$y=-35$

Answer:

y = 35

Step-by-step explanation:

    multiply by -5 on both sides

    -5 and -5 cancel out

    -5 times -7 is 35

    y = 35

Answer:

it IS b

Step-by-step explanation:

Answer:

D) systematic

Step-by-step explanation:

Systematic sampling. With systematic random sampling, one creates a list of every member of the population, and from the list, one can randomly select the first sample element from the first Nth elements on the population list. Thereafter, we select every Nth element on the list. Selection is done according to a random starting point but with a fixed, periodic interval. This interval, which is called the sampling interval, is calculated by dividing the population size by the desired sample size.

The individuals in this data set are B) Compression bandage styles

The style tags in the first column is what Alex is surveying.

====================================================

This data set contains A) 3 variables, 1 of which is categorical

The three variables are

The first two are quantitative data. We can do math on them such as finding the average. The last variable is categorical. We cannot apply the average as the average color doesn't really make sense. We simply have a list of labels, so this data is nominal. It is not ordinal because we cannot sort the colors.

Answer:

compression bandages styles

3 variables, 1 of which is categorical

Answer:

The number is 270

Step-by-step explanation:

Let the number be 'x'

3/5 of x = 162

[tex]\frac{3}{5}*x = 162\\\\x=162*\frac{5}{3}\\\\x=54 * 5\\\\x = 270[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{270}}}}}[/tex]

Step-by-step explanation:

Let the number be 'x'

[tex] \sf{ \frac{3}{5 } \: \: of \: x \: = 162}[/tex]

⇒[tex] \sf{ \frac{3x}{5} = 162}[/tex]

Apply cross product property

⇒[tex] \sf{3x = 162 \times 5}[/tex]

Multiply the numbers

⇒[tex] \sf{3x = 810}[/tex]

Divide both sides of the equation by 3

⇒[tex] \sf{ \frac{3x}{3} = \frac{810}{3} }[/tex]

Calculate

⇒[tex] \sf{x = 270}[/tex]

Hope I helped!

Best regards!!

=============================================

Work Shown:

Solve 5m^2 = 45 for m to get

5m^2 = 45

m^2 = 45/5

m^2 = 9

m = sqrt(9)

m = 3

I'm making m to be positive so that way the expression 12m is not negative. Otherwise, sqrt(12m) would not be a real number result.

--------------

Plug m = 3 into the expression we want to evaluate

m^3 + sqrt(12m)

3^3 + sqrt(12*3)

27 + sqrt(36)

27 + 6

33

Answer: 9 energy drinks and 18 granola bars.

Step-by-step explanation:

Price per granola bar = $0.50

Price per energy drink = $2.

We can define G as the number of granola bars that she bought, and D as the number of drinks that she bought.

Then

"She buys twice as many granola bars as energy drinks."

G = 2*D

" If she spends $27 in total"

G*$0.50 + D*$2 = $27

So we have a system of equations:

G = 2*D

G*$0.50 + D*$2 = $27

The first step will be to replace the first equation into the second one, and solve it for D.

(2D)*$0.50 + D*$2 = $27

D*(2*$0.50) + D*$2 = $27

D*$1 + D*$2 = $27

D*$3 = $27

D = $27/$3 = 9.

So she bought 9 energy drinks, and we know that:

G = 2*D

G = 2*9 = 18

She bought 18 granola bars.

Answer:

ok lets do it..

Step-by-step explanation:

You simply multiply out each factor.

So you start by multiplying the a in (a+b) to each term in (a−2b).

You will get a2−2ab as the first portion of the answer.

So now you will do the same with the b in (a+b).

Then you get −2b2+ab.

Now you add a2−2ab and −2b2+ab to get a2−2b2−ab .

i hope it will work....

Answer:

a² + ab - 2b²

Step-by-step explanation:

Given

(a - b)(a + 2b)

Each term in the second factor is multiplied by each term in the first factor, that is

a(a + 2b) - b(a + 2b) ← distribute both parenthesis

= a² + 2ab - ab - 2b² ← collect like terms

= a² + ab - 2b²

Answer:

D. 424 m³

Step-by-step explanation:

Use the formula for the volume of a cylinder

V = [tex]\pi[/tex]r²h

Plug in the values we know

V = (3.14)(3²)(15)

V = 423.9 m³

This is closest to answer choice D, 424 m³

So, D is correct

Answer:

x^2 +6x -15

Step-by-step explanation:

(3x^2 +2x -8) - (2x^2 -4x+7)

Distribute the minus sign

(3x^2 +2x -8) - 2x^2 +4x-7

Combine like terms

x^2 +6x -15

Answer:

x²+6x-15

Step-by-step explanation:

We are given this expression:

[tex](3x^2+2x-8) - ( 2x^2-4x+7)[/tex]

We want to simplify the expression. First, distribute the negative sign in front of the second set of parentheses. Multiply each term inside the parentheses by -1.

[tex](3x^2+2x-8) + (-1*2x^2) + (-1*-4x) + (-1*7)[/tex]

[tex](3x^2+2x-8) -2x^2+ 4x -7[/tex]

Next, combine like terms. The 2 terms with an x² can be combined, just like the two terms with an x, and the two terms without a variable.

[tex](3x^2-2x^2) + (2x+4x) + (-8-7)[/tex]

[tex]x^2+(2x+4x)+(-8-7)[/tex]

[tex]x^2+6x+(-8-7)[/tex]

[tex]x^2+6x-15[/tex]

The expression x²+6x-15 is equivalent to (3x²+2x-8)-(2x²-4x+7)

Answer:

By scoring 240 in the sixth game, Marlon can maintain this exact average

Step-by-step explanation:

The first thing to do here is to calculate the average for the first 5 games.

Mathematically, the average can be calculated by adding all the scores in the games and dividing by 5;

= (210 + 225 + 254 + 231 + 280)/5 = 1200/5 = 240

Now to maintain this average score of 240, we want to know the score she must have in the 6th game.

Let the score be x;

By adding x to the previous total of 1200 before and dividing by the new count of 6, we can work our way to get x.

Mathematically, what we are saying is;

(1200 + x)/6 = 240

6 * 240 = 1200 + x

1440 = 1200 + x

x = 1440 -1200

x = 240

Answer:

80 -14=66 and 66-80=52 if we check the 66-52 the difference will be 14