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2 years ago

Competition time!

Mathematics

1 answer:

Fofino [41]2 years ago

6 0

Answer:

For each sandwich, spread 2 tablespoons peanut butter onto 1 slice of bread. Spread 1 tablespoon jelly onto another slice of bread.

Heat 12-inch skillet or griddle over medium heat.

Place 2 sandwiches into skillet. Cook, turning once, 4-6 minutes or until golden brown and peanut butter is melted.

Step-by-step explanation:

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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

Use complete sentences to describe the similarities and differences between an expression and an equation.

nirvana33 [79]

Which class ques is this

3 0

3 years ago

Look at the proof. Name the postulate you would use to prove the two triangles are congruent.

vovikov84 [41]

Answer:

Option A, SSS Postulate

Step-by-step explanation:

<em>Since it gives you three sides, that means that it is a SSS.</em>

There are no angles given which eliminates 2 options.

Answer: Option A, SSS Postulate

3 0

2 years ago

Kevin built a deck in his backyard. The length of the deck was x feet and the width of the deck was 3 feet longer than the lengt

Triss [41]

Answer:

4x + 6 feet

Step-by-step explanation:

The deck is the shape of a rectangle

Hence, the perimeter of a rectangle is:

P = 2L + 2W

Where

L = Length = x feet

The width of the deck was 3 feet longer than the length.

W = Width = 3 + x feet

Hence:

Perimeter = 2(x ) + 2(3 + x)

Perimeter = 2x + 6 + 2x

Perimeter = 4x + 6 feet

Hence, the expression for the Perimeter of the deck is given as:

4x + 6 feet

3 0

2 years ago

What times what equals 52

hoa [83]

4 times 13 is equal to 52

4 0

3 years ago

Read 2 more answers