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kotykmax [81]
3 years ago
5

1. Find a solution to the following system of equations. -3x +3y = -9 -3x + y = 7

Mathematics
1 answer:
Softa [21]3 years ago
3 0
X=-5 y=-8
subtract the equation and then substitute it in
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What is the equation of the perpendicular to y=2/3x+1 that passes through the point (12,-6)
postnew [5]
Well, first off let's check what is the slope of y = 2/3x+1.... .hmmmmm, notice    \bf y=\stackrel{slope}{\cfrac{2}{3}}x+1  , since the equation is already in slope-intercept form, we can see it has a slope of 2/3.

well then, a line perpendicular to that one, will have a negative reciprocal to it.

\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
slope=\cfrac{2}{{{ 3}}}\qquad negative\implies  -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}

so, we're really looking for the equation of a line whose slope is -3/2 and goes through 12, -6.

 \bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ 12}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-6)=-\cfrac{3}{2}(x-12)
\\\\\\
y+6=-\cfrac{3}{2}x+18\implies y=-\cfrac{3}{2}x+12
7 0
3 years ago
A freight train from city A to city B and a passenger train from city B to city A left the cities at the same time, at 10:00 AM,
djyliett [7]

Answer: Both trains would meet at 1 pm

Step-by-step explanation:

Let t represent the time at which both trains will pass each other.

The distance between the cities is 360 miles. This means that by the time both trains meet, the total distance covered would be 360 miles.

Distance = speed × time

The freight train is travelling at 50 mph. Distance covered by the freight train in t hours is 50t.

The passenger train is travelling at 70 mph. Distance covered by the passenger train in t hours is 70t.

Since the total distance covered is 360 miles, it means that

50t + 70t = 360

120t = 360

t = 360/120

t = 3 hours

Both trains would meet at 1 pm

8 0
3 years ago
a ticket office sold 553 tickets one day. the receipts totaled $3936. how many $9 adult tickets and how many $6 child tickets we
Vsevolod [243]

This is the assumption method ;)

Take all tickets to be adult tickets

$9 x 553 = $4977

Then..... $4977 - $3936 = $1041

The difference between the child and adult ticket is $3, so divide $1041 by $3

$1041 divided by $3 = 347

347 is the number of <em>child </em>tickets sold

347 x $6 = $2082

So 553 - 347 = 206 ( no. of adult tickets )

206 x $9 = $1854

Child tickets sold : 347

Adult tickets sold : 206

:0 ITS MAGIC IM SO SMART

6 0
3 years ago
Read 2 more answers
How do you round 600 to the nearest hundred?
Svetllana [295]

Answer:

600

Step-by-step explanation:

600 hundred is already rounded.

Say if the number was 650, it would round to 700. But if it was 610 it would round to 600.

7 0
3 years ago
After the closing of the mill, the town of Sawyerville experienced a decline in its population.
vfiekz [6]

Step-by-step explanation:

P(t) = 12,000 (2)^(-t/15)

9,000 = 12,000 (2)^(-t/15)

0.75 = 2^(-t/15)

ln(0.75) = ln(2^(-t/15))

ln(0.75) = (-t/15) ln(2)

-15 ln(0.75) / ln(2) = t

t = 6.23

4 0
3 years ago
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