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3 years ago

Answer to the question

Mathematics

1 answer:

Zepler [3.9K]3 years ago

7 0

Answer:

x = 23

Step-by-step explanation:

AE = EC

so, 5x + 3 = 118

5x + 3 = 118

Bring +3 to the other side so -3

5x = 118 - 3

5x = 115

Bring 5 to the other side so:

x = 115 ÷ 5

x = 65

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How many square feet of glass is used to create the window

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Answer:108

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Step-by-step explanation:8 pieces of glass uses 1 sqft. glass window. 864 sqin. required = = 108 pieces. Number of pieces required for 864 sq.inches = 108 pieces.

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2 years ago

What is the x angle?

Troyanec [42]

Answer: 35

Step-by-step explanation:

180-145=35

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3 years ago

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If:

PSYCHO15rus [73]

Take some trinomial expansions to find some useful expressions and their values.

• 2nd degree expansion

$x + y + z = 7 \\\\ \implies (x+y+z)^2 = x^2+y^2+z^2+2(xy+xz+yz) = 7^2 \\\\ \implies xy+xz+yz = \dfrac{49-33}2 = 8$

• 3rd degree expansion

$x+y+z=7 \implies (x+y+z)^3 = 7^3 \\\\ \implies \\ 243 = x^3+y^3+z^3+3(x^2y+x^2z+xy^2+y^2z+xz^2+yz^2) + 6xyz \\\\ \implies \\ x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 + 2xyz = \dfrac{343 - 145}3 = 66$

• 4th degree expansion

$x+y+z=7 \implies (x+y+z)^4 = 7^4 \\\\ \implies \\ 2401 = x^4+y^4+z^4+4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~+ 6(x^2y^2+x^2z^2+y^2z^2) + 12(x^2yz+xy^2z+xyz^2) \\\\ \implies \\\\ x^4+y^4+z^4 = 2401 - 4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~~~~~~~~~~~- 6(x^2y^2+x^2z^2+y^2z^2) - 12(x^2yz+xy^2z+xyz^2)$

Simplify:

$x^3y+x^3z+xy^3+y^3z+xz^3+yz^3 \\\\ ~~~~ = x^2 (xy+xz) + y^2 (xy+yz) + z^2 (xz + yz) \\\\ ~~~~ = x^2 (xy+xz+yz) + y^2 (xy+xz+yz) + z^2 (xy + xz + yz) - (x^2yz + xy^2z + xyz^2) \\\\ ~~~~ = (x^2+y^2+z^2) (xy+xz+yz) - xyz (x+y+z) \\\\ ~~~~ = 264 - 7xyz$

$x^2y^2+x^2z^2+y^2z^2 \\\\ ~~~~ = xy\cdot xy + xz \cdot xz + yz \cdot yz \\\\ ~~~~ = xy(xy+xz+yz) + xz(xy+xz+yz) + yz(xy+xz+yz) - 2(x^2yz+xy^2z+xyz^2) \\\\ ~~~~ = (xy+xz+yz)^2 - 2xyz(x+y+z) \\\\ ~~~~ = 64 - 14xyz$

$x^2yz+xy^2z+xyz^2 = xyz (x + y + z) = 7xyz$

Then the equation we got from the 4th degree expansion reduces to

$x^4+y^4+z^4 = 2401 - 4(264-7xyz) - 6(64-14xyz) - 12(7xyz) \\\\ ~~~~~~~~~~~~~~~~~= 961 + 28xyz$

and all we need now is the value of $xyz$ .

In the 3rd degree expansion, we have

$x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 \\\\ ~~~~ = x(xy + xz) + y(xy + yz) + z(xz + yz) \\\\ ~~~~ = x(xy+xz+yz) + y(xy+xz+yz) + z(xy+xz+yz) - 3xyz \\\\ ~~~~ = (x+y+z)(xy+xz+yz) - 3xyz \\\\ ~~~~ = 56 - 3xyz \\\\ \implies (56 - 3xyz) + 2xyz = 66 \\\\ \implies xyz = -10$

So, we end up with

$x^4+y^4+z^4 = 961 - 280 = \boxed{681}$

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1 year ago

A cone-shaped popcorn cup has a radius of 5 centimeters and a height of 9 centimeters. How many cubic centimeters of popcorn can

guajiro [1.7K]

Answer:

The cup can hold 235.5 cubic cm of popcorn.

Step-by-step explanation:

A cone shaped popcorn cup has a radius of 5 cm and a height of 9 cm.

Use 3.14 as an approximation for pi.

Now, to find cubic cm of popcorn the cup can hold.

Radius (r)= 5 cm

Height (h)= 9 cm

$\pi$ = 3.14 (as per question).

So, to get the cubic cm of popcorn the cup can hold we put formula of volume:

Volume= $\pi$ r $x^{2}$ h $\frac{x}{y}$ 3

Volume= 3.14 x 5 $x^{2}$ × 9 $\frac{x}{y}$ 3

Volume= 3x14 x 25 x 3

Volume= 235.5 cubic cm.

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3 years ago

If a circle is inscribed in a triangle which of the following must be true

KatRina [158]

A, C, E

B false because triangle is confirmed larger if the circle is fit inside of it.

D false because circle on the inside.

A true because triangle on outside

C true because it is a property of inscribed/circumscribed circles/triangles

E true because of inverse relationship

3 0

3 years ago

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