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C is the midpoint of AB, D is the midpoint of AC, E is the midpoint of AD, F is the midpoint of ED, G is the midpoint of EF, and H is the midpoint of DB. If DC = 16, what is GH?

It would have helped if you drew it more accurately.

What fraction of AB is GF?

No one over-answer me, thank you.

That is great.

Also, the cube root of 54 is approx 3.8

This means that the smallest one has to be 3 or less.

Miss Minerva challenges her class to guess her secret positive integer. She gives them these clues:
1) The sum of the digits of this three-digit number is 14.
2) The tens digit is the cube of a prime number.
3) The units digit is one-fifth of the hundreds digit.
What is Miss Minerva's number?

Hello class from Miss Minerva!

$x+y+z=14\\ y\in\{{\mathbb{P}^3}\}\\ z=\frac{x}{5}$

$y\in\{{\mathbb{P}^3}\}=14-x-z\\ y\in\{{\mathbb{P}^3}\}=14-x-\frac{x}{5}\\ y\in\{{\mathbb{P}^3}\}=14-5-1$

$x=5\\ y=8\\ z=1$

  !

Help me find the value of x!

Hello Guest!

$180^{\circ}-147^{\circ}+x+180^{\circ}-4x=180^{\circ}\\ 3x=180^{\circ}-147^{\circ}$

$x=11^{\circ}$

  !

If the total surface area of cone is 704cm^2 and radius of its base is 7cm. Find the volume of cone​.

Hello Guest!

$S=\pi r^2+\pi rs=\pi r(r+s)\\ s=\frac{S}{\pi r}-r=\frac{704cm^2}{\pi \cdot7cm}-7cm$

$s=25cm$

$h=\sqrt{s^2-r^2}=\sqrt{(25^2-7^2)cm^2}$

$h=24cm$

$V=\frac{1}{3}\cdot \pi r^2h=\frac{1}{3}\cdot \pi \cdot 7^2cm^2\cdot 24cm$

$V=1231.5cm^3$

  !

∠ABD ≅ ∠DBC

3x = 6x - 30

- 3x = - 30  

-x = -10  | *-1

x = 10

Angles AOD and COB are congruent

2x + 30 = x + 90

x = 60 degrees

The distance between the points (x, 21) and (4, 7) is 10√2. Find the sum of all possible values of x.

10√2  is a hypotenuse of a right triangle, the longer leg is 14.                                                                                          The short leg     a = sqrt[(10√2)² - 14²] = 2

1/      x = 4 - a = 2

2/      x = 4 + a = 6

So, the sum of all possible values of x is 8 

P R O O F =5! / 2! = 60 Permutations as follows:

{F, O, O, P, R} | {F, O, O, R, P} | {F, O, P, O, R} | {F, O, P, R, O} | {F, O, R, O, P} | {F, O, R, P, O} | {F, P, O, O, R} | {F, P, O, R, O} | {F, P, R, O, O} | {F, R, O, O, P} | {F, R, O, P, O} | {F, R, P, O, O} | {O, F, O, P, R} | {O, F, O, R, P} | {O, F, P, O, R} | {O, F, P, R, O} | {O, F, R, O, P} | {O, F, R, P, O} | {O, O, F, P, R} | {O, O, F, R, P} | {O, O, P, F, R} | {O, O, P, R, F} | {O, O, R, F, P} | {O, O, R, P, F} | {O, P, F, O, R} | {O, P, F, R, O} | {O, P, O, F, R} | {O, P, O, R, F} | {O, P, R, F, O} | {O, P, R, O, F} | {O, R, F, O, P} | {O, R, F, P, O} | {O, R, O, F, P} | {O, R, O, P, F} | {O, R, P, F, O} | {O, R, P, O, F} | {P, F, O, O, R} | {P, F, O, R, O} | {P, F, R, O, O} | {P, O, F, O, R} | {P, O, F, R, O} | {P, O, O, F, R} | {P, O, O, R, F} | {P, O, R, F, O} | {P, O, R, O, F} | {P, R, F, O, O} | {P, R, O, F, O} | {P, R, O, O, F} | {R, F, O, O, P} | {R, F, O, P, O} | {R, F, P, O, O} | {R, O, F, O, P} | {R, O, F, P, O} | {R, O, O, F, P} | {R, O, O, P, F} | {R, O, P, F, O} | {R, O, P, O, F} | {R, P, F, O, O} | {R, P, O, F, O} | {R, P, O, O, F} (total: 60)

180 - 4x + x + 180 - 147 = 180

- 3x = 180 - 180 - 33

- 3x = - 33  | * -1

3x = 33

x = 11

The sum of all possible values of is 28.

Let his normal hourly rate = H

[2.5H * 5]  +  40 * H = 420, solve for H

H = $8.00 per hour - his normal hourly rate.

Mary gets an oil change for her car every 3750 miles and a tire rotation every 5000 miles. What is the mileage of the car at the first time she gets both an oil change and a tire rotation at the same time?     

3,750 x 4  =  15,000  

5,000 x 3  =  15,000  

_.

Just kiddin'

See here, I approve of this answer:

I learned this material in 6th grade, but I knew it since 3rd. This forum is free to anyone.

Is this forum for the third graders too???

Option 1: 

3 1/5 hrs

Option 2:

3 hrs

Option 2 is faster.

3x-5+2x-25=180

5x-30=180

5x=210

x=42

A / XYZ = 4/9  

Your sequence goes like this:

(1/(1/2+1), 1/(3/4+1), 1/(21/16+1), 1/(777/256 +1), 1/(802641 / 65536 + 1), 1/(696834455457 / 4294967296 +1)..........etc.

Just sum them up and you will see that it closer and close to 2 but never quite reaching it.

Let the number of cc of 17% concentration needed =S

Then, the number of cc of 7% concentration needed =350 - S

0.17S  +  0.07*[350 - S] =0.14 * 350, solve for S 

S = 245 cc of 17% concentration

350 - 245 =105 cc 0f 7% concenration.

NO!, not quite:

0.00175 = 1.75 x 10^-3 . Or: 1.75E-3

The surface area is 68 cm^2.