A tennis ball machine serves a ball vertically into the air from a height of 2

Mathematics

1 answer:

k0ka [10]3 years ago

5 0

Answer:

Step-by-step explanation:

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Tina must select and answer in any order three of seven

Leno4ka [110]

Answer:

Tina can select and answer the essay questions on her test in 35 ways.

Step-by-step explanation:

The order in which she chooses the questions is not important. For example, choosing questions 1, 3 and 7 is the same as choosing 7, 3 and 1. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Three questions from a set of 7. So

$C_{7,3} = \frac{7!}{3!(7-4)!} = 35$

Tina can select and answer the essay questions on her test in 35 ways.

6 0

2 years ago

What is one of the solutions to the following system of equations? y2 x2 = 53 y − x = 5 (−10, −5) (−7, −2) (7, 2) (5, 10).

Aliun [14]

The solution of the system of equation is (-7, -2).

<h2>Given</h2>

The system of the equations;

$\rm y^2 + x^2 = 53 \\\\y -x = 5$

From equation 1

$\rm y -x=5\\\\y = 5+x$

Substitute the value of y in equation 1

$\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2$