Helppp ..

9. Given that P = (-1,16) and Q = (1, 9), find the component form and

Olenka [21]

To find the component form, u only need to know how to substitute figures for letters. What do I mean by this?

If initial side is (x1,y1)
Then x1 = -1, and y 1 = 16
If the terminal side is x2, y2
Then x2 =1 and y2 =9

This component from p is x2-x1 y2-y1
In this case <[1-(-1)], (9-16)
Which give us
2,-7

If p = x ,y using Pythagorean’s theorem
2(2) + (-7)(7)
4+49
53
Square root of 53 is
7.28010988928
7.3

7 0

2 years ago

Flori’s Flower shop contains fewer than 150 flowers. All the flowers are purple, yellow, red or white. The ratio of purple flowe

alexgriva [62]

Flori's Flower Shop have 48 white flowers, 40 red flowers, 30 yellow flowers and 15 purple flowers, whose sum equals 133 flowers, which is fewer than 150 flowers.

<h3>How to determine the quantity of flowers in a flower shop</h3>

Flori's Flower shop owns a quantity less than 150 flowers, in which there are four kinds of flowers according to color: (purple - p, yellow - y, red - r, white - w), each variable represents positive integers. Now we proceed to construct the system of equation that describes the situation:

z < 150 (1)

p + y + r + w = z (2)

p = y/2 (3)

y = 3 · r/4 (4)

r = 5 · w/6 (5)

By (1) and (3) in (2):

y/2 + y + r + w < 150

By (4):

3 · y/2 + r + w < 150

9 · r/8 + r + w < 150

17 · r/8 + w < 150

By (5):

85 · w/48 + w < 150

133 · w/48 < 150

133 · w < 7200

w < 54.135

Now we assume that w = 48, then we have the following solution for the flower shop: r = 40, y = 30, p = 15.

Flori's Flower Shop have 48 white flowers, 40 red flowers, 30 yellow flowers and 15 purple flowers, whose sum equals 133 flowers, which is fewer than 150 flowers. $\blacksquare$