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laiz [17]
3 years ago
14

The table shows the cost of concessions at a concert. Evan spent $31.50

Mathematics
1 answer:
REY [17]3 years ago
8 0

p= popcorn

x=number of kids in class

c= cost

Plug in data:

c = px

31.5=1.5x

Divide both sides by 1.5:

21= x

There are 21 kids in the class.

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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 help
denpristay [2]

9514 1404 393

Answer:

  • 260 miles
  • $73.80

Step-by-step explanation:

The cost of each plan (y) is the sum of the initial fee and the product of the mileage charge and the number of miles (x).

First Plan: y = 40 +0.13x

Second Plan: y = 53 +0.08x

__

We can find when the costs are the same by solving this system of equations. A way to do that is to subtract the second equation from the first:

  (y) -(y) = (40 +0.13x) -(53 +0.08x)

  0 = -13 +0.05x

Multiplying by 20 gives ...

  0 = -260 +x

Adding 260, we have ...

  x = 260

The plans cost the same for 260 miles of driving.

__

The cost of the plans for that distance is ...

  y = 40 +0.13x = 40 +0.13(260) = 40 +33.80

  y = 73.80

The cost when the two plans cost the same is $73.80.

8 0
2 years ago
Help plss (find the perimeter) thx
LiRa [457]

Answer:

64 units

Step-by-step explanation:

divide the shape into two shapes:

first one: 15+15+4+4=38

second shape:7+7+6+6=26

pweimwter for the whole shape: 38+26=64 units

3 0
2 years ago
One kilogram is 2.2 pounds. If i had 1 pound would that be 0.45 kilograms why or why not?
prisoha [69]

Step-by-step explanation:

1 kg = 2.2 pounds

0.45 kg = 1 pounds to see whether it's correct or not we can cross multiply the given equations

multiply 1 kg with 1 pounds and 0.45 kg with 2.2 pounds then check if they are equal

1 × 1 = 2.2 × 0.45

1 = 0.99 as you can see this is not an equality therefore the statement is wrong.

3 0
3 years ago
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Helen [10]

Answer:

1 is B

2 is B

3 is stream line body and fluke both help in swimming and both are independent envolved that is their ancestors don't match

Step-by-step explanation:

8 0
2 years ago
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