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Dennis_Churaev [7]

3 years ago

13

Lin,Mac, and star spend 6$ on supplies to set up a lemonade stand they sell 21$ worth of lemonade they are going to share the mo

ney equally evaluate the expression (21-6) divided by 3 to find how much money each one will make.

1 answer:

sukhopar [10]3 years ago

8 0

Each person will make $5.00.

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Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number

jeka94

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any <u>nonzero</u> rational number", then his statement would be correct that the result is irrational.

----------------------------------------------

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.

7 0

3 years ago

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

<u>At, </u>

<u>n = 2</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

<u>At, </u>

<u>n = 3</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

<u>At, </u>

<u>n = 4</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER.

elixir [45]

Answer:

20 degrees

Step-by-step explanation:

8 0

2 years ago

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Through: (6, 2), perpendicular to<br> y = -x-5 <br> in slope intercept form

True [87]

Answer:

y = x-4

Step-by-step explanation:

y = -x-5

Slope of line is -1.

Slope of perpendicular to line is 1.

Point-slope equation for line of slope 1 that passes through (6,2):

y-2 = 1(x-6)

Rearrange equation to slope-intercept form:

y = 1(x-6) + 2

y = x-4

6 0

2 years ago

Show that angle a+ angle b is equal to angle d

mr_godi [17]

sum of two angles of triangle are equal to the exterior angle of triangle

8 0

2 years ago

Read 2 more answers