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4 years ago

Which expression is equivalent to x + y + x + y + 3(y + 5)?

Mathematics

1 answer:

Taya2010 [7]4 years ago

3 0

Answer:

2x+5y+15

Step-by-step explanation:

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In segments JM, HK and LI are medians of triangle JHL, what is the name of point N?

FinnZ [79.3K]

Answer: Centroid

<u>Step-by-step explanation:</u>

Medians intersect at the CENTROID

Altitudes intersect at the Orthocenter

Perpendicular bisectors intersect at the Circumcenter

Angle bisectors intersect at the Incenter

8 0

3 years ago

A cylindrical can, open at the top, is to hold 840 cm3 of liquid. Find the height and radius that minimize the amount of materia

ycow [4]

Answer:

the radius of the base is equal to $x=2\sqrt[3]{\frac{105}{\pi } }$

And the height is equal to:

$y=\frac{840}{\pi(2\sqrt[3]{\frac{105}{\pi}})^{2} }$

Step-by-step explanation:

We write the volume function

$f(x,y)=840=\pi x^{2} y$ where x is the radius of the base and y is the height of the cylinder

$y=\frac{840}{\pi x^{2} }$

The surface of a cylinder is given by

$S(x)=\pi x^{2} +2\pi xy=\pi x^{2} +\frac{1680}{x}$ on the interval from 0 to infinity

We now determine the critical values by differentiating and making the equation equal to 0

$f'(x)=2\pi*x- \frac{1680}{x^{2}} =\frac{2\pi x^{3}-1680}{x^{2} } =0$

This equation have 2 complex solutions and one real solution

$x=2\sqrt[3]{\frac{105}{\pi } }$

For x=0 and infinity the equation goes to infinity also so the radius of the base is equal to $x=2\sqrt[3]{\frac{105}{\pi } }$

And the height is equal to:

$y=\frac{840}{\pi (2\sqrt[3]{\frac{105}{\pi } })^{2} }$

$y=\frac{840}{\pi(2\sqrt[3]{\frac{105}{\pi}})^{2} }$

7 0

3 years ago

Need help with these proofs asap i have a 58 in geometry cuz of proofs ;c

shutvik [7]

Sucks for you. nerdddddddddddddddddddddddddd

6 0

3 years ago

The sides of a triangle have lengths 2x + 2, 4x, and 5x + 1. The longest side of the triangle has a length of 5x + 1. For what v

Savatey [412]

Answer:

Step-by-step explanation:

(5x+1)²>(2x+2)²+(4x)²

25x²+10x+1>4x²+8x+4+16x²

5x²+2x-3>0

5x²+5x-3x-3>0

5x(x+1)-3(x+1)>0

(x+1)(5x-3)>0

x+1=0,gives x=-1

5x-3=0,gives x=3/5

x >0(because 4x should be >0)

side is always positive.

so x>3/5

again 5x+1<2x+2+4x

5x-6x<2-1

-x<1

x>-1

x=all real values >3/5

4 0

4 years ago

Find the absolute value of each rational number |3.7|

Aloiza [94]

$|a|=a \hbox{ if } a \geq 0 \\
|a|=-a \hbox{ if } a \leq 0 \\ \\
|3.7|=3.7$

6 0

3 years ago

Read 2 more answers