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The value of constant of variation is, 5.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

⇒ p varies jointly as q and the cube of r.

Since, p varies jointly as q and the cube of r.

Hence, We can formulate;

⇒ p = k × q × r²

Where, k is constant of variation.

Here, p = 270 when q = 6 and r = 3.

Substitute all the values, we get;

⇒ p = k × q × r²

⇒ 270 = k × 6 × 3²

⇒ 270 = 54k

⇒ k = 270 / 54

⇒ k = 5

Learn more about the proportion visit:

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Answer:

Step-by-step explanation:

Given

Need to complete square on the left side of equation

The square should be in the form of:

We see a = x therefore

So the missing constant term is 9/64

Answer:

Step-by-step explanation:

Divide the numbers

12+153⋅6−412+153⋅x6−412+315​⋅x6−412+56−412+5x6−4 12+5x6−4

Answer:

0

Step-by-step explanation:

Answer:

1785

Step-by-step explanation:

Answer:

(2, 5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y - 3x = 1

2y - x = 12

Step 2: Rewrite Systems

y - 3x = 1

Step 3: Redefine Systems

y = 3x + 1

2y - x = 12

Step 4: Solve for x

Substitution

Step 5: Solve for y

Answer: First you have to take 20% and make it into a fraction 1/5.

Then you multiply 46.5 and multiply it by 1/5 and get 9.3

Add $46.50 and $9.30 and get $55.80

Step-by-step explanation: Hope this helps!! <3

Answer:

19

Step-by-step explanation:

228/12=19

Answer:

0.064

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

HII do the parentheses first then carry on if you need more help i suggest you go to caculatorsoup  and search mixed number caculator and it should help u its a web

Answer:

you mean 2.5?????? in two quart????

Answer:

Step-by-step explanation:

Answer:

Yes they are equivalent

Step-by-step explanation:

Because 24/6=4

And 72/18= 4

Hope this helps, have a good day

Answer:

the correct graph is B

Step-by-step explanation:

to check, you can see that my graph and graph in answer B both intersects at (-1,2)

Answer:

Step-by-step explanation:

x^2 - 11x + 30 = (x - 6)(x - 5)

x^2 - 4 = (x + 2)(x - 2)

x^2 + 3x - 40 = (x + 8)(x - 5)

x - 2 = x - 2

Invert and multiply the right fraction.

(x - 6)(x - 5)           (x - 2)

===========   x   =======

(x - 2)(x + 2)          (x + 8)(x - 5)

x - 5 on the top cancels with x - 5 on the bottom

x - 2 on the top  cancels with x - 2 on the bottom left

So what's left?

(x - 6)

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

(x + 2)(x + 8)

This is likely the answer.

Answer:

[tex]\frac{x-6}{x^{2} +10x+16}[/tex]

Step-by-step explanation:

to much to explain

Answer:

45

Step-by-step explanation:

6² + 3²

36 + 9

45

Follow me please

Answer:

Root of polynomial synonyms: zero, x-intercept

Step-by-step explanation:

Technically in calculus we also call roots critical points of f, but I'm not sure of the obvious 3rd word. Maybe horizontal intercept?

Answer:

the answer is A,

P(x) = -0.4x³+100x²-900x+500

Step-by-step explanation:

monthly cost:

[tex]c(x) = 600x {}^{2} + 300x[/tex]

monthly revenue:

[tex]r(x) = - 0.4 {}^{3} + 700x {}^{2} - 600x + 500[/tex]

profit function:

[tex]p(x) = r(x) - c(x)[/tex]

[tex]p(x) = ( - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500) - (600x {}^{2} + 300x)[/tex]

i) remove the first bracket

[tex]p(x) = - 0.4x {}^{3} + 700x {}^{2} - 600x + 500 - (600 {x}^{2} + 300x)[/tex]

ii) there is a negative sign, '-' in front of the second bracket. so, change the sign of each term of the expression inside the bracket

[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500 - 600x {}^{2} - 300x[/tex]

iii) collect like terms

[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600 {x}^{2} - 600x - 300x + 500[/tex]

iv) simply the like terms

[tex]p(x) = - 0. 4{x}^{3} + 100 {x}^{2} - 900x + 500 [/tex]

Answer:

2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0

-----

4sin(x)cos(x) - 2sin(x) + 2sqrt(3)cos(x) - sqrt(3) = 0

-----

Factor:

2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0

-----

[2cos(x)-1][2sin(x)+sqrt(3)] = 0

Solve:

2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0

cos(x) = 1/2 or sin(x) = -sqrt(3)/2

x = +/-pi/3 or x = -pi/3 or (4/3)pi

hope this helps!

Answer:

x = +/-pi/3 or x = -pi/3 or (4/3)pi

Step-by-step explanation:

2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0

4sinxcosx - 2sinx + 2sqrt(3)cosx - sqrt(3) = 0

2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0

[2cos(x)-1][2sin(x)+sqrt(3)] = 0

2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0

cos(x) = 1/2 or sin(x) = -sqrt(3)/2

x = +/-pi/3 or x = -pi/3 or (4/3)pi

Answer:

Good for Lily.

Step-by-step explanation:

Answer:

y=-4x+10

Step-by-step explanation:

you subtract 4x on both sides

Answer:

If you were to get a different piece of paper and trace the same shape and flip it over to the same position that one of them is in it will be the exact same measurements!

Answer:

1 lb

Step-by-step explanation:

Picked up 3/5 and 4/5.

Used 3/8.

Amount now:

3/5 + 4/5 - 3/8 =

= 7/5 - 3/8

= 56/40 - 15/40

= 41/40

Answer: 1 lb

Answer:

[tex]y = \frac{224}{15}[/tex]

Step-by-step explanation:

Given

[tex]y = 7x + 14[/tex]

[tex]2x + 4y = 60[/tex]

Required

Find y

First, substitute 7x + 14 for y in the second equation:

[tex]2x + 4y = 60[/tex] becomes

[tex]2x + 4(7x + 14) =60[/tex]

Open bracket

[tex]2x + 28x + 56 = 60[/tex]

[tex]30x = 60 - 56[/tex]

[tex]30x = 4[/tex]

Solve for x

[tex]x = \frac{4}{30}[/tex]

[tex]x = \frac{2}{15}[/tex]

[tex]y = 7x + 14[/tex] becomes

[tex]y = 7 * \frac{2}{15} + 14[/tex]

[tex]y = \frac{14}{15} + 14[/tex]

[tex]y = \frac{210+14}{15}[/tex]

[tex]y = \frac{224}{15}[/tex]

Hence:

[tex]y = \frac{224}{15}[/tex]

Answer:

is it g(x) = 350(1.04)x − 1

or is it this- > g(x) = 350[(1.04)x − 1]

Step-by-step explanation:

well 350 is the initial quantity and we can write the expression like this- g(x)=350(1+0.4)x−1 so here g(x) is the amount received after x years 350 is the original amount 0.4 corresponds to rate of increment

Answer:

The correct answer is option 2: 32 cm

Step-by-step explanation:

Let l be the length of the picture frame and w be the width

Then according to given statements, the system of equations will be

[tex]2l+2w = 100\ \ \ Eqn\ 1\\w = 2l-4\ \ \ Eqn\ 2[/tex]

Putting w = 2l-4 in equation 1

[tex]2l+2(2l-4) = 100\\2l+4l-8=100\\6l-8 = 100\\6l = 100+8\\6l=108\\\frac{6l}{6}=\frac{108}{6}\\l = 18[/tex]

Putting the value of l in equation 2

[tex]w = 2(18)-4\\w = 36-4\\w = 32[/tex]

The width is 32 cm

Hence,

The correct answer is option 2: 32 cm

Answer:

[tex]-2a^3+a^2-14a +8[/tex]

Step-by-step explanation:

Given

[tex]6a^3+2a^2-8a-9-8a^3-a^2-6a+1[/tex]

Required

Simplify

[tex]6a^3+2a^2-8a-9-8a^3-a^2-6a+1[/tex]

Collect Like Terms

[tex]-8a^3+6a^3-a^2+2a^2-8a-6a-9+1[/tex]

[tex]-2a^3+a^2-14a +8[/tex]