All four B points are equidistant from points A and C. Are they all midpoints of AC? Justify your answer.
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Answer:
Step-by-step explanation:
1) slope-interception form is: y=s*x+i, where 's' and 'i' are slope and interception;
2) according to the condition s= -5/4, then the required equation is: y= -5/4 *x +i, where i - interception;
3) if to substitute (-4;7) into the required equation y= -5/4 *x +i, it is possible to calculate 'i':
7= -5/4*(-4)+i; ⇒i=2, then
Flori's Flower Shop have 48 <em>white</em> flowers, 40 <em>red</em> flowers, 30 <em>yellow</em> flowers and 15 <em>purple</em> 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 - <em>p</em>, yellow - <em>y</em>, red - <em>r</em>, white - <em>w</em>), each variable represents <em>positive</em> 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 <em>w =</em> 48, then we have the following solution for the flower shop: <em>r =</em> 40, <em>y =</em> 30, <em>p =</em> 15.
Flori's Flower Shop have 48 <em>white</em> flowers, 40 <em>red</em> flowers, 30 <em>yellow</em> flowers and 15 <em>purple</em> flowers, whose sum equals 133 flowers, which is fewer than 150 flowers.
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