Social studies class is 4 more than two times the length of recess, in minutes.

1 answer:

8 0

Since there are no numbers, i will assume that the length of recess is 1 minute, or x. if social studies is 4 more than 2 times the length of recess, we can use the equation x*2+4 to solve the problem. the end result will be 6 minutes. Social studies is 6 minutes longer than recess

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Prove the statement holds for all positive integers:<br><br> 2 + 4 + 6 + ... + 2n = n² + n

crimeas [40]

Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.

The relation 2+4+6+...+2n = n^2+n has to be proved.

If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2

Assume that the relation holds for any value of n.

2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)

= n^2 + n + 2n + 2

= n^2 + 2n + 1 + n + 1

= (n + 1)^2 + (n + 1)

This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.

<span>By mathematical induction the relation is true for any value of n.</span>

6 0

3 years ago

Now consider just the second sentence of the multistep word problem. Sentence 2: If four times the brother's age is subtracted f

Natalka [10]

Answer:

4b - 3s = 40

4b = 40 + 3s

b = 40 - 3s/4

4b - 3s = 40

4b - 40 =3s

4b - 40 /3 = s

8 0

4 years ago

Distribute and simplify <br> √3 (-2+√20)

LiRa [457]

Answer:

Step-by-step explanation:

√3 (-2+√20) = √3×(-2) + √3×√20

= -2√3 + √3×√(4×5)

= -2√3 + √3×√4×√5

= -2√3 + √3×2×√5

= -2√3 + 2√15

5 0

4 years ago

Quick question if I had a problem that was sin x = 18.9/20 =.945 how would I inverse sin of both sides ?

galben [10]

Answer:

The result is about 70.9 degrees

Step-by-step explanation:

Easy for a calculator. If you're not using a calculator, it's much more tedious!

There is an inverse sine key on your calculator, but you may have to press a key (likely labeled 2nd or INV) first. The attached image shows a TI-83 display. To get the inverse sine, I first pressed the yellow 2nd key, then the sin key.

Check MODE first to make sure you're measuring angles in degrees (if that's what you want!). Some calculators display angle mode with a small letter at the top of the display, D, R, or G usually.

The left side of the equation produces just x.

$\sin{x}=.945\\\\\sin^{-1}(\sin{x})=\sin^{-1}(.945)\\x=\sin^{-1}(.945) \approx 70.9^\circ$