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2 years ago

Please help me solve this short problem guys

Mathematics

1 answer:

-BARSIC- [3]2 years ago

8 0

Answer:

Step-by-step explanation:

Given equation of the quadratic function is,

y = x² + 5x - 7

Convert this equation into vertex form,

y = x² + 2(2.5x) - 7

= x² + 2(2.5x) + (2.5)² - (2.5)² - 7

= (x + 2.5)²- 6.25 - 7

= (x + 2.5)² - 13.25

Therefore, vertex of the function is → (-2.5, -13.25)

For the solutions,

y = 0

(x + 2.5)² - 13.25 = 0

x = (±√13.25) - 2.5

x = (±3.64) - 2.5

x = 1.14, -6.14

Solutions → (-6.14, 0) and (1.14, 0)

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y=-4x-8

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The amount that the would be paid after 40% discount is $27

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Given Data

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2 years ago

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3 years ago

6. If you draw 35 lines on a piece of paper so that no two lines are parallel to each

umka2103 [35]

The point of intersection is the point where lines intersect.

There will be 595 intersections for 35 lines, where no 3 lines are concurrent.

Given

$n = 35$ --- the number of lines

$d = 3$ --- no three lines are concurrent

When no three line are concurrent, it means that no three lines meet at the same point.

So, the sequence of intersection is:

0 intersection for 1 line
1 intersection for 2 lines
3 intersections for 3 lines
6 intersections for 4 lines

Following the above sequence, the number of intersections for n lines is:

$n_k = \frac{n \times (n - 1)}{2}$

In this case, $n = 35.$

So, we have:

$n_k = \frac{35 \times (35 - 1)}{2}$

$n_k = \frac{35 \times 34}{2}$

$n_k = 35 \times 17$

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Hence, there will be 595 intersections for 35 lines, where no 3 lines are concurrent.

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