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3 years ago

Transform both equations in each system of equations so that each coefficient is an integer.

Mathematics

1 answer:

inysia [295]3 years ago

4 0

For the first one multiply each term by the LCM of 4 and 6, which is 12:-

15x -36 = 2y..................(1)

and second multiply by 5:-

2x + y = 9..............(2)

solving:-
from equation (2) y = 9-2x, substitute in equation (1):-

15x - 36 = 2(9-2x) = 18 - 4x
19x = 54
x = 54/19 = 2.84

so y = 9 - 2(2.84) = 3.32

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We can see on this graph that the triangle has legs of x and 6 with a hypotenuse of 10 and we can use Pythagoreans theorem to find the unknown side.
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3 years ago

The height of a tennis ball tossed into the air is modeled by h(x) = 40x â€" 16x 2, where x is elapsed time in seconds. During w

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The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

Given that,

The height of a tennis ball tossed into the air is modeled by,

$\rm h(x) = 40x - 16x^2$

Where x is elapsed time in seconds.

We have to determine,

During what time interval will the tennis ball be at least 15 feet above the ground?

According to the question,

The height of a tennis ball tossed into the air is modeled by,

$\rm h(x) = 40x - 16x^2$

Where x is elapsed time in seconds.

Then,

When the tennis ball be at least 15 feet above the ground,

$h(x) = 15$

Substitute the value of h(x) in the equation,

$\rm h(x) = 40x - 16x^2\\\\ 15 = 40x - 16x^2\\\\ 16x^2-40x+15=0$

Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,

$\rm 16x^2-40x+15= 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2-4 \times 16 \times 15}}{2 \times 16}\\\\x = \dfrac{-(-40)\pm \sqrt{1600- 960}}{32}\\\\x = \dfrac{40\pm \sqrt{640}}{32}\\\\x = \dfrac{40 + 25.29}{32} \\\\x = \dfrac{40 + 25.29}{32} \ and \ x = \dfrac{40 - 25.29}{32}\\\\x = \dfrac{65.29}{32} \ and \ x = \dfrac{14.71}{32}\\\\x = 2.04 \ and \ x = 0.45$

Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.

For more details about Inequality refer to the link given below.

brainly.com/question/17177510

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