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Misha Larkins [42]
2 years ago
11

Henry and 3 friends went to Lake Tahoe for a winter weekend. Henry made 19 cups of hot chocolate. Everyone, including, Henry, wa

nts an equal amount of all the hot chocolate. How much hot chocolate should each person get?
Mathematics
1 answer:
r-ruslan [8.4K]2 years ago
4 0
19 cups of hot coco for four friends, (Henry plus the 3 friends) 19 divided by 4 is 4.75
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Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form\[
Butoxors [25]

9514 1404 393

Answer:

  57

Step-by-step explanation:

Apparently, you want to simplify ...

  \displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}

so the denominator is rational. It looks like the form you want is ...

  \dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}

And you want to know the sum A+B+C+D+E+F.

__

We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

  \displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}

Comparing this to the desired form we have ...

  A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

  A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

3 0
2 years ago
Please someone help <br> I need this
Sunny_sXe [5.5K]

Answer:

the triangle

Step-by-step explanation:

The perimeter is the sum of the all sides of the shape.

Triangle:

3√147+2√108+2√48+3√75+ 6√12

147=49•3, 108=36•3, 48=16•3, 75=25•3, 12=4•3 that means

√147=7√3, √108=6√3, √48=4√3, √75=5√3, √12=2√3

perimeter=3•7√3+2•6√3+2•4 √3+3•5√3+6•2√3=68√3

Square:

4•1/3•√63=4/3•√9•√7=4√7

Rectangle:

2•1/4√100+2(2√48+4√75)=

5+2(8√3+20√3)=5+56√3

Now, if you use a calculator, you will find that the greatest perimeter is for the triangle shape.

8 0
3 years ago
A car travels 106 miles on 4 gallons of gas. How far can it go on a full tank of 12 gallons?
tino4ka555 [31]
106*3=318

106/4=x/12

the answer is 318
7 0
3 years ago
Read 2 more answers
Your math teacher gives you an extra credit problem to figure out her age. Half of her age three years
MatroZZZ [7]

Answer:

Teacher is 27 years old

Step-by-step explanation:

(1/2)(t - 3) = (1/3)(t + 9)

multiply by 6 to clear the fraction

3(t - 3) = 2(t + 9)

Distribute

3t - 9 = 2t + 18

Subtract 2t from both sides

t - 9 = 18

Add 9 to both sides

t = 27

Teacher is 27 years old

6 0
3 years ago
PLS PLS PLS HELP ME WITH THIS!!!!!!
nlexa [21]

Answer:

720

Step-by-step explanation:

8 0
2 years ago
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