The inequality - 15<-6 is given. Write the inequality you get when you perform the

a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation b

nikdorinn [45]

Answer:

Part 1)

The equation by factorization is

$x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))$

Both values of x are

$x1=-6+\sqrt{266}$

$x2=-6-\sqrt{266}$

Part 2) The dimensions of the cuboid are

$4\ cm$ , $(-5+\sqrt{266})\ cm$ and $(5+\sqrt{266})\ cm$

Step-by-step explanation:

step 1

we know that

The volume of the cuboid is equal to

$V=LWH$

substitute the given values

$V=4(x+1)(x+11)$

$V=924\ cm^{3}$

so

$4(x+1)(x+11)=924\\4(x^{2}+11x+x+11)=924\\ 4(x^{2}+12x+11)=924\\x^{2}+12x+11=231\\x^{2}+12x-230=0$

Complete the square

$x^{2}+12x-230=0$

$x^{2}+12x=230$

$x^{2}+12x+36=230+36$

$(x+6)^{2}=266$

square root both sides

$x+6=(+/-)\sqrt{266}$

$x=-6(+/-)\sqrt{266}$

so

$x1=-6+\sqrt{266}$

$x2=-6-\sqrt{266}$

therefore

The equation by factorization is

$x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))$

step 2

Find the dimensions of the cuboid

The dimensions are

$4\ cm$

$(x+1)\ cm -----> (-6+\sqrt{266}+1)=(-5+\sqrt{266})\ cm$

$(x+11)\ cm ----> (-6+\sqrt{266}+11)=(5+\sqrt{266})\ cm$

4 0

3 years ago

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5+5 PLZ help hardest question on my paper

Schach [20]

Answer: 10

Step-by-step explanation:

5+5=10

7 0

3 years ago

Each of the 4 children in a family drinks 24 ounces of milk every day. how much milk do the children drink in one week (7days)

olchik [2.2K]

Answer:

672

Step-by-step explanation:

8 0

3 years ago

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An open box is made from a 20-cm by 50-cm piece of tin by cutting a square from each corner and folding up the edges. The area

kipiarov [429]

Answer:

Therefore,

The length of the sides of the squares is

$x=7\ cm$

Step-by-step explanation:

Let "x" be the length of Cut Square,

As the tin size(Dimension) is

20 cm × 50 cm

So the size(Dimension) of box will be

(20 - 2x) × (50 - 2x)

Length = 50 - 2x

Width = 20 - 2x

Area of base of box = 216 cm²

To Find:

x = ?

Solution:

Area of Rectangular field is given by

$(Area\ of\ Rectangle(Box)) = Length\times Width$

Substituting the values we get

$216=(50-2x)(20-2x)$

Applying Distributive property we get

$216=1000-100x-40x+4x^{2}$

$4x^{2}-140x+784=0$

Dividing throughout by 4 we get

$x^{2}-35x+196=0$

On Factorizing we get

$x^{2}-28x-7x+196=0\\\\(x-7)(x-28)=0\\\\x-7=0\ or\ x-28=0\\\\x=7\ or\ x = 28$

As x cannot be 28 because tin size is 20 cm × 50 cm i.e longer than 20

Therefore,

$x=7\ cm$

Therefore,

The length of the sides of the squares is

$x=7\ cm$

5 0

4 years ago

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Need help with this, simple but I don't understand/remember how to do it.

Lorico [155]

By using definition of proportionality and Pythagorean theorem, the values of x and y associated with the geometrical system formed by two right triangles are 36 / 5 and 104 / 5, respectively.

<h3>How to analyze a geometrical system formed by two proportional right triangles</h3>

Herein we find a picture of a geometrical system formed by two proportional right triangles with two variables: {x, y} These variables can be found by using the definition of proportionality and the Pythagorean theorem:

5 / 8 = 12 / (12 + x) = 13 / y

Then, we proceed to solve the system formed by two equations:

(12 + x) / 12 = 8 / 5

12 + x = 96 / 5

x = 96 / 5 - 12

x = 36 / 5

y / 13 = 8 / 5

y = 104 / 5

By using definition of proportionality and Pythagorean theorem, the values of x and y associated with the geometrical system formed by two right triangles are 36 / 5 and 104 / 5, respectively.

To learn more on right triangles: brainly.com/question/6322314

#SPJ1

7 0

2 years ago