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goldenfox [79]
3 years ago
9

-

Mathematics
1 answer:
Valentin [98]3 years ago
7 0

Answer:

  • Todd: 25
  • Andrew: 45

Step-by-step explanation:

We can let "a" stand for the number of goldfish Andrew has. Then the number Todd has is (70-a). We are told the difference is ...

  a - (70-a) = 20

  2a = 90 . . . . . . .  .collect terms, add 70

  a = 45

  70-a = 25

Andrew has 45 goldfish; Todd has 25.

_____

<em>Comment on the problem</em>

I call this a "sum and difference" problem. You are given the total of two counts, and also their difference. If you were paying attention to the above solution, you see that <em>the larger of the counts</em> is (70+20)/2, <em>half the sum of the given numbers</em>. This is generically true of all <em>sum and difference</em> problems.

Knowing this, you can work most of these problems in your head.

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How do you find the equation of a triangles altitude using point slope formula?
forsale [732]
<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047)   (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle: 

 

Let point 
A=(xA,yA)
B=(xB,yB)
C=(xC,yC) 



------------------------------- 
Let's find the equation of the segment AB 


Start with the general formula 

 


Plug in the given points 

 


Simplify and combine like terms 

 


So the equation of the line through AB is  


------------------------------- 
Let's find the equation of the segment BC 


Start with the general formula 

 


Plug in the given points 

 


Simplify and combine like terms 

 


So the equation of the line through BC is  




------------------------------- 
Let's find the equation of the segment CA 


Start with the general formula 

 


Plug in the given points 

 


Simplify and combine like terms 

 


So the equation of the line through CA is  




So we have these equations of the lines that make up the triangle 


 



So to find the equation of the line that is perpendicular to  that goes through the point C(2,-5), simply negate and invert the slope  to get 

Now plug the slope and the point (2,-5) into  


 

 Solve for y and simplify 

So the altitude for vertex C is  



Now to find the equation of the line that is perpendicular to  that goes through the point A(4,5), simply negate and invert the slope to get  

Now plug the slope and the point (2,-5) into  


 

 Solve for y and simplify 

So the altitude for vertex A is  




Now to find the equation of the line that is perpendicular to  that goes through the point B(-4,1), simply negate and invert the slope to get  

Now plug the slope and the point (-4,1) into  


 

 Solve for y and simplify 

So the altitude for vertex B is  



------------------------------------------------------------ 
Now let's solve the system 


 

 Plug in  into the first equation 

 Add 2x to both sides and subtract 2 from both sides 

 Divide both sides by 3 to isolate x 


Now plug this into  

 

 



So the orthocenter is (-2/3,1/3) 

So if we plug in  into the third equation , we get 


 


 


 

 

So the orthocenter lies on the third altitude 





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3 0
3 years ago
Help plsss Show me the work plsss
velikii [3]

Answer:

a) y = 6x - 3

b) 1/3y = 2x -1

The first thing you need to do is isolate (y) in the second equation

3 x (1/3y) = 3 x (2x - 1)

y =6x - 3

After isolating (y) in equation b they end up being the same.

Graphing:

In order to graph this, you have to make the first point at (0, -3) since this is the Y-intercept of the equation.

In order to graph the other points, you must move 6 units up and 1 unit to the right. Or vise versa If you need a visual I'll gladly link one.

5 0
3 years ago
X=y+1400<br> 0.08x+0.05=840
mezya [45]

Answer:

x = 7000

y = 5600

(7000, 5600)

Step-by-step explanation:

To solve the system of equations means to find the point of intersection (graphically). You are finding what value of 'x' and what value of 'y' fits both equations.

x = y + 1400

0.08x + 0.05y = 840

We can solve using the method <u>substitution</u>, where you replace a variable in one equation with an equivalent expression.

<u>Since "x" is y + 1400, we can replace "x" in the second equation.</u>

0.08x + 0.05y = 840

0.08(y + 1400) + 0.05y = 840    

Distribute over brackets by multiplying 0.08 with y, then 0.08 with 1400.

0.08y + 112 + 0.05y = 840         Collect like terms (with "y" variable)

112 + 0.13y = 840

Now isolate "y" in the simplified equation.

112 - 112 + 0.13y = 840 - 112         Subtract 112 from both sides

0.13y = 728

0.13y/0.13 = 728/0.13         Divide both sides by 0.13

y = 5600         Solved for y

We can substitute "y" with 5600 in any other equation that has "x".

x = y + 1400

x = 5600 + 1400          Add

x = 7000         Solved for x

You may express the answer as a coordinate, or an ordered pair (x, y).

The solution is (7000, 5600).

3 0
3 years ago
Read 2 more answers
Determine which of the following numbers could not represent the probability of an event. Explain your reasoning. (a). 33.3% (b)
statuscvo [17]

Answer:

B and F

Step-by-step explanation:

The simple golden rule that we need to know here is

<em><u>"The probability of any event is always between 0 and 1 inclusive"</u></em>

<em><u /></em>

If an event has a probability of p(x), we can say:

0 \leq p(x) \leq 1

Also, probability is ALWAYS POSITIVE.

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A) OK because 33.3% is 0.333, which is between 0 and 1

B) NOT OK, because probability isn't negative

C) 0.0002 is in between 0 and 1, so possible

D) 0 probability means it can't happen, so that's okay as well

E) this is a fraction with numerator less than denominator, which means its between 0 and 1, so OK

F) this fraction's numerator is greater than denominator, so it's greater than 1. Probability can't be greater than 1, so NOT OK

Out of these B and F cannot represent the probability of an event

6 0
3 years ago
HELP ME PLeaSEEEEEEEEEE<br><br><br><br> thank you &lt;3
Tcecarenko [31]

Answer:

2nd option

Step-by-step explanation:

Graph both equations and find the point where they both intersect. In this case, it's (4,2).

3 0
1 year ago
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