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3 years ago

Evaluate 4 + (-2)= PLEASE HELP IF YOU KNOW THE ANSWER PLEASE SHOW WORK!? THANK YOU!

Mathematics

1 answer:

Phoenix [80]3 years ago

8 0

Answer:

Step-by-step explanation:

4 + -2 = 2

HOPE THIS HELPED!

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What is the value of x?

zaharov [31]

Answer: around 47-49

Step-by-step explanation:

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2 years ago

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Which triangles are similar?

lara31 [8.8K]

I’m pretty sure it would be a and b

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3 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

Select all TRUE statements : A - Dilation always increase the length of shapes or line segments. B- Dilations of an angle are co

timurjin [86]

Hi!

A is FALSE - If you shrink a shape, it is not increased a shape, yet it is still dilating.

B is TRUE - When you dilate an angle, you're really just shortening or lengthening the sides, but the angle isn't changing.

C is FALSE - Explained above.

D is FALSE - Two triangles that are congruent are exactly the same, therefore if you dilate a triangle, you are changing the size so they are not the same.

E is TRUE - Similar shapes are always the same except for their size. When you dilate a shape, you only change the size, therefore they are equal in every other way and they are similar.

6 0

2 years ago

Show that each statement is true: Cos^4X-sin^4X=2cos^2X-1

Ivan

$cox^4x-sin^4x=2cos^2x-1\\\\
(cosx^2-sin^2x)(cosx^2x+sin^2x)=2cos^2x-1\\\\
cosx^2-sin^2x*1=2cos^2x-1\ \ \ | subtract\ 2cos^2x\\\\
-cosx^2-sin^2x=-1\ \ \ | multiply\ by\ -1\\\\
cosx^2+sin^2x=1\\\\
1=1$

4 0

2 years ago