how to turn x+7y=20 into y=mx+b

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

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Answer:

undefined

Step-by-step explanation:

Answer:

4.6 feet (explanation of division)

Answer:

The length of each piece is 4.6 feet

Step-by-step explanation:

The number of books the library holds before it received the grant is 17,312 books

Let the original number of books in the library be x

If the collection  now is five times more than the original number of books, then;

x + 69,248 = 5x

5x - x = 69,248

4x = 69,248

x = 69,248 /4

x = 17,312

Hence the number of books the library holds before it received the grant is 17,312 books

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Answer:

-4

Step-by-step explanation:

That's the answer above

Answer:

true

Step-by-step explanation:

the less than or equal to sign (≤) means that -4 is a solution. if it was the less than sign (<) then -4 would not be included

Answer:

i believe it would be true

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Answer:

3/4 or 0.75

Step-by-step explanation:

When dividing- quotient- fractions, remember keep, change, flip

Keep- keep the first fraction

Change- change the division sign into a multiplication sign

Flip- flip the second fraction

So your problem really is:

[tex]\frac{1}{6} *\frac{9}{2}[/tex]

Which is: 9/12 or 3/4

Answer:

question 3 is $9.99

question 4 I believe is the third option

The y intercept is the y value when x is 0 which is shown on the graph as (0,4) making the y intercept is 4

The next point given is (1,8) which shows for every 1 increase in x (1-0 = 1) the y value increases by a multiple of 2 (4 x2 = 8)

The equation would be f(x) = 4 * (2)^x

The answer is B

Answer:3,312.50

Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 2500 is 100%, so we can write it down as 2500=100%.

4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.

5. Now we have two simple equations:

1) 2500=100%

2) x=3.25%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

2500/x=100%/3.25%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

y= -4x-5 you can find this by seeing how far it goes up/down and where it starts:)

Answer:

x = 1

y = 30°

Step-by-step explanation:

is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':

20x-3 = 5x+12

15x = 15

x = 1

we also know that RS intersecting with TU creates a 90° angle

if 3y = 90 then y = 30

Answer:

domain will be ( -∞, ∞)

Step-by-step explanation:

The given functions are f(x) = x² - 1 and g(x) = 2x - 3

We have to find domain of (fog)(x)

We will find the function (fg)(x) first.

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

         = (2x - 3)²

         = 4x² + 9 - 12x - 1

        = 4x² - 12x + 8

       = 4 (x² - 3x + 2)

The given function is defined for all values of x.

Therefore, domain will be ( -∞, ∞)

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Answer:  Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size.

Step-by-step explanation: pls give brainlist

Answer:

Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)

Answer:

3

Step-by-step explanation:

The pattern is dividing 4 each time.

192/4=48

48/4=12

12/4=3

Hope this helps! Plz give brainliest!

Answer:

B and A

Step-by-step explanation:

What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).

The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…

I hope this helps :)!

we have that

Y - 5 = 0.5x2 + 6x - 3--------------- > y=0.5x2 + 6x -3+5=0.5x2 + 6x+2

y=0.5x2 + 6x +2

using a graphic tool

see the attached figure

the graph have two x-intercepts----------> (-11.657,0) and (0.343,0)

Answer:

[tex]\sqrt{49 - x^{2}}[/tex]

Step-by-step explanation:

Pythagorean theorem  [tex]c^{2} = a^{2} + b^{2}[/tex] Then:

[tex]7^{2} = x^{2} + y^{2}\\y^{2} = 7^{2} - x^{2}\\y^{2} = 49 - x^{2}\\y = \sqrt{49 - x^{2}}[/tex]

the lenght of the third side = [tex]\sqrt{49 - x^{2}}[/tex]

Ф = [tex]sin^{-1} (\frac{x}{7} )[/tex]

Ф = [tex]cos^{-1} (\frac{y}{7} )[/tex]

Ф = [tex]tan^{-1} (\frac{x}{y} )[/tex]

Answer:

Step-by-step explanation:

Answer:

25.5

Step-by-step explanation:

There are 12 inches in a foot and therefore...

306/12=25.5

306 inches is 25.5 feet

Answer:

C

Step-by-step explanation:

It does what the equation says. It multiplies x by 36

I hope this helps!

Answer:

No. The correct answer would be C.

Step-by-step explanation:

AAS: The side cannot be in between the two angles.

ASA: The side is in between the two angles.

Answer:

(y-7) +25

Step-by-step explanation:

( y-7 ) +25

25 is added after the difference. so that's only the answer.

Answer:

I think the answer is D please forgive me if I'm wrong

Answer:

That is the answer

The answer is

Answer:

A’ (6, -4)

B’ (-2, -1)

C’ (-5, 0)

Step-by-step explanation:

When reflecting anything across the x, the x values stay the same and the y values become opposites. When reflecting anything across the y, the x values become the opposites and the y values stay the same.

The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Reflection is the flipping of a figure. If a point A(x, y) is reflected across the y axis, the new point is at A'(x, -y). Given the vertices of the triangle at A(6,4), B(-2,1) and C(5,0).

The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).

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Answer:

  1 in : 50 mi

Step-by-step explanation:

You can eliminate the choices that don't make any sense by comparing the given numbers to the offered choices:

  given:

  15 in : 750 mi

__

A. 1 in : 50 mi . . . . . . . . equivalent to dividing the given ratio numbers by 15

B. 15 in : 100 mi . . . . . . same inches, wrong miles

C. 1 in : 750 mi . . . . . . . wrong inches, same miles

D. 1 mi : 50 in . . . . . . . . both inches and miles are wrong (the ratio has the units swapped)

__

In the given ratio, the numerical number of miles (750) is 50 times the numerical number of inches (15). This is the ratio you're looking for among the answer choices. You need to pay attention to both the numerical values and their associated units.

Answer:

Point B is

Step-by-step explanation:

Answer:

B (-2,-4)

Step-by-step explanation: