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Archy [21]
2 years ago
5

Simplify.

Mathematics
1 answer:
sveta [45]2 years ago
6 0
C I think I hope this is correct
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Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does
Reil [10]
The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)

4x+3y=12

3y=-4x+12

y=-4x/3+12/3

So a line perpendicular to the bank will be:

y=3x/4+b, and we need it to pass through (7,5) so

5=3(7)/4+b

5=21/4+b

20/4-21/4=b

-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank.  When it does y=y so we can say:

(3x-1)/4=(-4x+12)/3  cross multiply

3(3x-1)=4(-4x+12)

9x-3=-16x+48

25x=51

x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

d^2=38.44

d=√38.44

d=6.2 units

Since he can run at 10 uph...

t=d/v

t=6.2/10

t=0.62 hours  (37 min 12 sec)

So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.




8 0
3 years ago
Unit rate of 15 pounds in 6 weeks<br><br> Please help me!!! Will mark as brainiest!
erastova [34]
The unit rate is 2.5 pounds a week.
15/6 = 2.5
I hope this helps.
3 0
3 years ago
Read 2 more answers
A mechanic charges $20.00 an hour, h for labor plus parts. If the parts cost $217.00, write a linear equation that will find the
Dennis_Churaev [7]

Answer:

y=20x+217

Step-by-step explanation:

8 0
2 years ago
What is revenue from property taxes usually used for?
grandymaker [24]
Revenue from property taxes is used to fund all the services the municipal government provides us with, such as building a new park in the neighbourhood.
4 0
3 years ago
Read 2 more answers
F(x)=5(x-2) <br> find x if f(x)=-20
Lapatulllka [165]

Answer:

x = -2

Step-by-step explanation:

f(x)= 5(x-2)

since, f(x)= -20

-20 = 5(x-2)

x-2 = -20/5

x = - 4 + 2

x = -2

3 0
2 years ago
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