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Darya [45]
3 years ago
10

Write 243 as a product of primes.

Mathematics
1 answer:
shtirl [24]3 years ago
6 0

Answer:

243 = 3⁵

Step-by-step explanation:

Firstly we will find the factors of 243. On calculating it see that the factors of 243 are 3 x 3 x 3 x 3 x 3.

or

243 = 9 x 9 x 3

We need to write 243 as the product of primes.

The number that divides itself or 1 are prime numbers.

3 is the only prime number here such that,

243 = 3⁵

Hence, this is the required solution.

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Which of the following are the coordinates of the vertex of y = −x2 + 2x + 1? (2, 1) (1, –2) (1, 2) (–2, 1)
IceJOKER [234]

Answer:

C

Step-by-step explanation:

We want to determine the vertex of the quadratic equation:

\displaystyle y = -x^2 + 2x + 1

Recall that the vertex is given by the formulas:

\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

In this case, <em>a</em> = -1, <em>b</em> = 2, and <em>c</em> = 1.

Determine the <em>x-</em>coordinate of the vertex:

\displaystyle x = -\frac{(2)}{2(-1)} = 1

To determine the <em>y-</em>coordinate, evaluate the function at <em>x</em> = 1:

\displaystyle \begin{aligned} y(1)&= -(1)^2 + 2(1) + 1 \\ &= 2\end{aligned}

In conclusion, the vertex of the quadratic equation is (1, 2).

Hence, our answer is C.

3 0
2 years ago
Help with these math problems above!
dimulka [17.4K]
The answers to the questions

6 0
3 years ago
Can someone please help as I'm not sure how to tackle this step by step? Especially question b, d, g, j, k, l. Not how sure to d
Arisa [49]

Step-by-step explanation:

√a = 1√a so we can solve them easily:

b) 3√7 -√7= 3√7 - 1√7 =( 3-1)√7= 2√7

d) 5√6 - 2√6+√6= (5-2+1)√6 = 4√6

g) √2+2√2= 3√2

j) √5+5√5 - 3√5 = 3√5

k) 2√3 + √3 - 5√3= -2√3

I) 5√11 + 7√11 - √11 = 11√11

7 0
2 years ago
6) A standard deck has 52 cards, and contains 13 cards of each of the four suits: diamonds, spades, hearts, and clubs. What is t
Crazy boy [7]

Answer:

\dfrac{12}{51}\cong\dfrac{4}{17}

Step-by-step explanation:

You have 52 cards in a deck and 13 cards of each suit.

The probability of picking a diamond in a complete deck of cards is:

\dfrac {13}{52}

Or the probability is 13 put of 52.

Since you took out 1 diamond card already there would be only 51 cards left and 12 diamond cards left. So you would have a probability of:

\dfrac{12}{51}

If we simplify it you will have a probability of:

\dfrac{4}{17}

6 0
2 years ago
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Ugo [173]
1. 90°
2. 5.74
3. 90°
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4 0
3 years ago
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