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3 years ago

Which equation is equivalent to

Mathematics

2 answers:

jeka57 [31]3 years ago

8 0

Answer:

The answer is option 2.

Step-by-step explanation:

In the question, 16 and 81 are perfect squares. So in order to find the equivalent equation, you have to factorize it :

APPLY,

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

So for this question :

$16 {x}^{4} - 81 = 0$

${(4 {x}^{2})}^{2} - {(9)}^{2}= 0$

$(4 {x}^{2} + 9)(4 {x}^{2} - 9) = 0$

Aleksandr [31]3 years ago

5 0

Answer:

(4x^2 +9)(4x^2-9) =0

Step-by-step explanation:

16x^4 - 18 = 0

Rewriting

(4x^2)^2 - 9^2 =0

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(4x^2 -9)(4x^2+9) =0

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prove that sin theta cos theta = cot theta is not a trigonometric identity by producing a counterexample

Zolol [24]

Answer:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Begin with the right hand side:

R.H.S = cot θ = $\frac{cos \ \theta}{sin \ \theta}$

L.H.S = sin θ cos θ

so, sin θ cos θ ≠ $\frac{cos \ \theta}{sin \ \theta}$

So, the equation is not a trigonometric identity.

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

<u>Anther solution:</u>

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R.H.S = cot θ = cot 45 = 1

So, L.H.S ≠ R.H.S

So, sin θ cos θ = cot θ is not a trigonometric identity.

5 0

3 years ago

Select the point that is a solution to the system of inequalities.<br> y≤2x-2<br> y≤ x²-3x

miss Akunina [59]

Both statements are true. Therefore (4,2) is a solution and option D is correct.

The given inequalities are $y\leq 2x-2$ and $y\leq x^{2} -3x$ .

We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).

<h3>What is an example of a system of inequalities in real life?</h3>

Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.

Any point is a solution to this system of inequality if it satisfies both inequalities.

Check the inequalities by each option.

For (-2, -1), $-1\leq 2(-2)-2 \implies -1\leq -6$ .

This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.

For (1, 3), $3\leq 2(1)-2 \implies 3\leq 0$

This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.

For (2,1), $1\leq 2(2)-2 \implies 1\leq 2$ .

$1\leq 2^{2} -3(2) \implies 1\leq -2$

This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.

For (4,2), $2\leq 2(4)-2 \implies 2\leq 6$

$2\leq 4^{2} -3(4) \implies 2\leq 4$

Both statements are true. Therefore (4,2) is a solution and option D is correct.

To learn more about inequalities visit:

brainly.com/question/20383699.

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2 years ago

Five cards are selected without replacement from a pack of 52 playing cards. What is the probability of exactly 3 hearts?

irga5000 [103]

There are 13 total hearts in the deck, which leaves 39 non-hearts. You're drawing a hand of five cards, so the probability of getting exactly 3 hearts is

$\dfrac{\binom{13}3\binom{39}2}{\binom{52}5}=\dfrac{2717}{33320}$

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3 years ago

Grace bought 6.9 ounces of chocolate. 0.7 ounces of it was milk chocolate and the rest was dark chocolate. How much dark chocola

goblinko [34]

6.2 you subtract the 0.7 from 6.9 because 0.7 of it is milk chocolate

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3 years ago

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When a single card is drawn from a shuffled deck of cards, find the odds in favor of getting a 10.?

sashaice [31]

4/52 because 4 of each number and 52 total.

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3 years ago