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3 years ago

Calculate the distance between Points A and B. A.4.5 B.7.1 C.7.8 D.9.2

Mathematics

1 answer:

storchak [24]3 years ago

4 0

Answer:

7.8 units separate the points A and B.

Step-by-step explanation:

Going from B to A, x increases by 6 (this is the horizontal side of the triangle formed by vertices A and B), and y increases by 5. Applying the Pythagorean Theorem, we get

d = √(6² + 5²), or √(61, which is approximately 7.8, the desired distance.

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Laws of sines!!!!! find c. round to the nearest tenth!!!

Mrac [35]

Answer:

c = 0.5 cm

Step-by-step explanation:

Law of sines:

sin (15) / c = sin(105) / 2

0.2588 / c = 0.9659 / 2

c = 0.2588 * 2 / 0.9659

c = 0.5 cm

5 0

3 years ago

Read 2 more answers

There are 50 runners in a race. How many ways can the runners finish first, second, and third?

Dmitrij [34]

Number of ways can the runners finish first, second, and third is 1,17,600 .

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

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is : $P(n,r) = \frac{n!}{(n-r)!}$ where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n = 50 , r= 3

⇒ $P(n,r) = \frac{n!}{(n-r)!}$

⇒ $P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}$

⇒ $P(50,3) = 50(49)(48)$

⇒ $P(50,3) = 1,17,600$

∴ Number of ways can the runners finish first, second, and third is 1,17,600 .

8 0

3 years ago

Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)

Rom4ik [11]

Answer:

Step-by-step explanation:

Given : $p(x)=x^{3} +6x^{2} -7x-60$

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, $\text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Since constant term = -60

Leading coefficient = 1

$\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}$

$\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}$

Thus the possible roots are $\pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60$

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is $x^{2} +x-12$