Which graph shows a linear function?

8x^3 − 125y^3/(2x + 5y)3 ÷ 4x^2 + 10xy + 25y^2/4x^2 + 20xy + 25y^2

To divide by a fraction, multiply by its reciprocal.

8x^3 − 125y^3/(2x + 5y)^3  ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Simplify the numerator.

Rewrite 8x^3 as (2x)^3.

(2x)^3 − 125y^3/(2x + 5y)^3 ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2  

Rewrite 125y^3 as (5y)^3.

(2x)^3 − (5y)^3/(2x + 5y)^3  ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Since both terms are perfect cubes, factor using the difference of cubes formula,

a^3 − b^3 = (a − b) (a^2 + ab + b^2) where a = 2x and b = 5y.

(2x − (5y)) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3  ⋅ 4x + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2

Multiply 5 by −1.

(2x − 5y) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3   ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2  

Apply the product rule to 2x.  

(2x − 5y) (22x^2 + 2x (5y) + (5y)^2)/(2x + 5y)3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y2

Raise 2 to the power of 2.

(2x − 5y) (4x^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3    ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Rewrite using the commutative property of multiplication.

(2x − 5y) (4x^2 + 2 ⋅ 5xy + (5y)^2)/(2x + 5y)^3      ⋅   4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Multiply 2 by 5.

(2x − 5y) (4x^2 + 10xy + (5y)^2)/(2x + 5y)^3  ⋅ 4x^2 + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2

Apply the product rule to 5y.

(2x − 5y) (4x^2 + 10xy + 52y^2)/(2x + 5y)^3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Raise 5 to the power of 2.

(2x − 5y) (4x^2 + 10xy + 25y^2)/(2x + 5y)^3    ⋅  4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2

Cancel the common factor of 4x^2 + 10xy + 25y^2.

((2x − 5y)/(2x + 5y)^3) (4x^2 + 20xy + 25y^2)

Multiply

(2x − 5y) (4x^2 + 20xy + 25y^2)/ (2x + 5y)^3

Factor using the perfect square rule.

Rewrite 4x^2 as (2x)^2.

(2x − 5y) ((2x)^2 + 20xy + 25y^2)/ (2x + 5y)^3

Rewrite 25y^2 as (5y)^2.

(2x − 5y) ((2x)^2 + 20xy + (5y)^2)/ (2x + 5y)^3

Check that the middle term is two times the product of the numbers being squared in the first

term and third term.

20xy = 2 ⋅ (2x) ⋅ (5y)

Rewrite the polynomial.

(2x − 5y) ((2x)2 + 2 ⋅ (2x) ⋅ (5y) + (5y)2)/(2x + 5y)^3

Factor using the perfect square trinomial rule a^2 + 2ab + b^2 = (a + b)^2, where a = 2x and  b = 5y.

(2x − 5y) (2x + 5y)^2/ (2x + 5y)^3

Cancel the common factor of (2x + 5y)^2 and (2x + 5y)^3.

Factor (2x + 5y)^2 out of (2x − 5y) (2x + 5y)^2.

(2x + 5y)^2 (2x − 5y) / (2x + 5y)^3

Cancel the common factors.

 2x − 5y / 2x + 5y

Answer:

This may be wrong but: (2x - 5y) ((2x)^2 + 10xy + (5y)^2) over (2x + 5y) (4x^2 + 10xy + 25y^2)

Step-by-step explanation:

Complete question

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)

Answer:

[tex]\frac{dx}{dt}=11.94m/min[/tex]

Step-by-step explanation:

From the question we are told that

Slant height [tex]z=29m[/tex]

Change in Vertical height  [tex]\triangle y=7m/s[/tex]

Horizontal length [tex]x=21[/tex]

Generally in finding the distance form the  top to the bottom of the wall it is mathematically given by

 [tex]x^2+y^2=z^2[/tex]

 [tex]21^2+y^2=29^2[/tex]

 [tex]y^2=29^2+21^2[/tex]

 [tex]y=35.81[/tex]

Generally solving for the differential equation is mathematically represented as

 [tex]x^2+y^2=29^2[/tex]

 [tex]2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0[/tex]

 [tex]x*\frac{dx}{dt} +y*\frac{dy}{dt} =0[/tex]

 [tex](21)*\frac{dx}{dt} +(35.81)*(-7) =0[/tex]

 [tex](21)*\frac{dx}{dt} -250.64 =0[/tex]

 [tex]\frac{dx}{dt}=\frac{250.64}{21}[/tex]

 [tex]\frac{dx}{dt}=11.94m/min[/tex]

The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.

So, A right angle triangle is formed.

Since, the bottom of the ladder is 21 meters from the wall.

So,    [tex]y=21[/tex]

Applying Pythagoras theorem,

                         [tex]x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20[/tex]

Given that,   the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.

                           [tex]\frac{dx}{dt}=-7meter/min[/tex]

Differentiate below equation with respect to time.

                     [tex]x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.[/tex]

Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Learn more about Differentiation here:

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Answer:

Parallel

Step-by-step explanation:

2x + 3y = 15

3y = -2x + 15

y = -2/3x + 5 (slope = -2/3)

4x + 6y = -48

6y = -4x - 48

y = -2/3x - 8 (slope = -2/3)

Since the slopes are the same, they are parallel.

Step-by-step explanation:

Hey there!

Given equations are;

2x+3y = 15...............(i)

4x+6y = -48…………(ii)

From eqaution (i)

2x+3y = 15

Slope (m1) = (-coefficient of x)/(coefficient of y)

Slope (m2) = (-2)/(3)

Therefore, slope (m1) = -2/3.

From eqaution (ii).

4x+6y= -48

Slope (m1) = (-coefficient of x)/(coefficient of y)

Slope (m2) = (-4)/6

Therefore, slope (m2) = -2/3.

Now;

Condition of parallel lines: m1=m2

-2/3 = -2/3

So, they are parallel.

Hope it helps....

Answer:

Answer:

Slope: -7

y-intercept: (0,12)

Answer:

here give my friend the brainliest ^^;

Step-by-step explanation:

Answer:

=8m

Step-by-step explanation:

=5m+3m

=m+m+m+m+m+m+m+m

=8m

Answer:

8m

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

5m + 3m

Step 2: Simplify

Answer:

x=56

Step-by-step explanation:

16 x 7= x * 2

[tex]x=\frac{16 x7}{2}[/tex]

x=56

Hope this helps :)

Answer:

18 (a)

Step-by-step explanation:

but I hope it works

Answer:

On the side length of the triangle

Step-by-step explanation:

On the side length of the triangle

Answer:

17 w  +  35

Step-by-step explanation:

You get this answer by using PEMDAS.

i think its 50 im not completley for sure though

Answer: y=-4x+9

Step-by-step explanation:

m= -4

b=9

Answer:

the slope is 4

y-intercept is -2

and the equation is

y=4x -2

Answer:

no

Step-by-step explanation:

Answer:

true for sure it \s pretty easy to do but hard to explain

Answer:

the answer is false I think

Hey there!

The answer to your question is $240.87

First we need to find how much he earned:

9.75 x 30

292.50

Now, we find the amount of all the deductions:

292.50(0.1 + 0.062 + 0.0145)

51.63

Now, we take this off the total pay:

292.50 - 51.63

240.87

The amount of pay after deductions was 240.87

Hope it helps and have an amazing day!

Answer:

$243.34425 round it up to the nearest 100th place

Step-by-step explanation:

9.75*30

=$295.5

=$295.5*10/100

for Federal income tax is $29.55

$295.5*6.2/100

Social Security tax $18.321 round it up $18/32

$295.5*1.45/100

Medicare tax is $4.28475 round it up to the nearest 100ths place $4.28

add all of them

$29.55+$18.321+4.28475= $52.15575 round it up = $52.16

sutract the amount you got paid

$295.5-$52.16=$243.34425

or you could have done

add all the %

10+6.2+1.45=17.65*295.5/100

=52.15575

hope it helped

Answer:

53

Step-by-step explanation:

You need the perimeter, which is all sides added together

Answer:

53

Step-by-step explanation:

Perimeter= w+w+h+h

w=width

h=height

w=14.5

h=12

12+12=24

14.5+14.5=29

29+24=53

Answer:

0.2% of the people had mid allergic reaction.

Step-by-step explanation:

Given that:

Number of people tested for a new shampoo = 9000

Number of people who had allergic reaction = 18

Percent of people = [tex]\frac{People\ who\ have\ reaction}{Total\ number}*100[/tex]

Percent of people = [tex]\frac{18}{9000}*100[/tex]

Percent of people = 0.002 * 100

Percent of people = 0.2%

Hence,

0.2% of the people had mid allergic reaction.

Answer:

B. y = 2x + 1

Step-by-step explanation:

Substitute the information into the point-slope form equation.

y - y₁ = m(x - x₁)

y - (-5) = 2(x - (-3)

y + 5 = 2(x + 3)

y + 5 = 2x + 6

y = 2x + 1

Answer:

c!

Step-by-step explanation:

Answer:

(x-3)(x-5)

Step-by-step explanation:

Answer:

x = 3 or x= 5

Step-by-step explanation:

Δ = (-8)² - 4×15

   = 64- 60

   =4

and 4≥0

so x = (8 - √4 )÷2 = 3

or  x= (8 + √4 )÷2 = 5

so P(x) = (x-3) (x-5)

Answer:

Real numbers = 39 and 9

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0

Given the following data;

a = 1

b = -43

c = 306

Quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the equation, we have;

[tex] x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1} [/tex]

[tex] x = \frac {43 \pm \sqrt {1849 - 1224}}{2} [/tex]

[tex] x = \frac {43 \pm \sqrt {625}}{2} [/tex]

[tex] x = \frac {43 \pm 25}{2} [/tex]

[tex] x_{1} = \frac {43 + 25}{2} [/tex]

[tex] x_{1} = \frac {68}{2} [/tex]

[tex] x_{1} = 39 [/tex]

[tex] x_{2} = \frac {43 - 25}{2} [/tex]

[tex] x_{2} = \frac {18}{2} [/tex]

[tex] x_{2} = 9 [/tex]

Therefore, the two real numbers are 39 and 9.

The quadratic equation now becomes;

x² - 43x + 306 = (x - 39)(x - 9) = 0

Answer:

96.0 or 96.01499407

Step-by-step explanation:

r = C / (pi x 2)

Answer:

r = 6

Step-by-step explanation:

V(cyl) = π · r² · h

144π =  π · r² · 4

144 = r² · 4

144 = r²

 4

r = [tex]\sqrt{144}[/tex] ÷ [tex]\sqrt{4}[/tex]

r = 12/2

r = 6

Answer:

Because the teacher told him  to take a seat.

Answer:

Lol. Because the teacher told him to take a seat.

Answer:

It's C

Step-by-step explanation:

I got a 100% on edge, have a delightful day Chicos y chicas!

Answer: A

Step-by-step explanation:

Answer:

whats this supposed to be?

Step-by-step explanation:

Answer: 1.C 2.B

Step-by-step explanation:

Answer:

440 square inches

Step-by-step explanation:

5 x 8 x 11 = 440

Answer:

Choice C

Step-by-step explanation:

The line is a linear line because it's straight exponential lines are more like an arch.

Next the line is increasing because it's going up not down if it was down it would be decreasing.

C) Linear increasing is the category of the graph.

The line is a linear line because its straight exponential lines are more like an arch. Next, the line is increasing because it's going up not down if it was down it would be decreasing.

If a linear graph is growing then its gradient is superb, for the reason that while x will increase by using 1, y adjustments through an advantageous quantity. If a linear graph is lowering, the gradient is a terrible range.

The key difference between linear and exponential increases is the slope of the curves (this is, the rate of an exchange over the years). A linear boom function has an advantageous constant slope, while an exponential increase feature has a high-quality slope that is continually growing.

Despite the fact that you're probably really familiar with growth, any increase that reasons the output Y to be larger than the enter X is known as a non-linear boom. In standard, the outputs of human interest grow in a non-linear style.

Learn more about Linear increasing here: https://brainly.com/question/4025726

#SPJ2

Answer:

Choice C

Step-by-step explanation:

A geometric sequence is usually one that multiply or divide to get to the next number in the sequence. So let's go through them to see which one gets multiplied since all of the choices are increasing.

Choice A:

[tex]1^{+3},4^{+1},5^{+4},9^{+5},14[/tex]

Nope that's not what we're looking for.

Choice B:

[tex]3^{+3},6^{+3},9^{+3},12^{+3},15[/tex]

This would be a perfect arithmetic sequence but not the type of sequence we are looking for.

Choice C:

[tex]6^{*3},18^{*3},54^{*3},162[/tex]

Yes! See how this one is multiplying by 3 and not adding or subtracting.

Choice D:

[tex]3^{+2},5^{+3},8^{+5},13^{+7},21[/tex]

Nope this is not it either.