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NeTakaya
3 years ago
15

Eugene wrote a riddle: A positive number is 5 less than another positive number. Six times the lesser number minus 3 times the g

reater number is 3. Find the two positive numbers.
Mathematics
1 answer:
a_sh-v [17]3 years ago
8 0
N-5=m
6m-3n=3
6(n-5)-3n=3
6n-30-3n=3
3n=33
n=11
m=6
just use substitution to plug in m in terms of n and solve
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Kitty [74]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: x < 3

Interval Notation: (-∞, 3)

6 0
3 years ago
PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwi
il63 [147K]
To solve our questions, we are going to use the kinematic equation for distance: d=vt
where
d is distance 
v is speed  
t is time 

1. Let v_{w} be the speed of the wind, t_{w} be time of the westward trip, and t_{e} the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so d=2400. We also know that the speed of the plane is 450 mi/hr, so v=450. Now we can use our equation the relate the unknown quantities with the quantities that we know:

<span>Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
</span>d=vt
2400=(450-v_{w})t_{w}

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
d=vt
2400=(450+v_{w})t_{e}

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:450-v_w Time:t_w
Going eastward -Distance: 2400 Rate:450+v_w Time:t_e

2. Notice that we already have to equations:
Going westward: 2400=(450-v_{w})t_{w} equation(1)
Going eastward: 2400=(450+v_{w})t_{e} equation (2)

Let t_{t} be the time of the round trip. We know from our problem that the round trip takes 11 hours, so t_{t}=11, but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so t_{t}=t_w+t_e. Using this equation we can express t_w in terms of t_e:
t_{t}=t_w+t_e
11=t_w+t_e equation
t_w=11-t_e equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns: 
2400=(450-v_{w})t_{w}
2400=(450-v_{w})(11-t_e) 

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

3. Lets solve our system of equations to find the speed of the wind: 
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

Step 1. Solve for t_{e} in equation (2)
2400=(450+v_{w})t_{e}
t_{e}= \frac{2400}{450+v_{w}} equation (3)

Step 2. Replace equation (3) in equation (1) and solve for v_w:
2400=(450-v_{w})(11-t_e)
2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} )
2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}}
2400(450+v_{w})=1147500+2400v_w-11(v_w)^2
1080000+2400v_w=1147500+2400v_w-11(v_w)^2
(11v_w)^2-67500=0
11(v_w)^2=67500
(v_w)^2= \frac{67500}{11}
v_w= \sqrt{\frac{67500}{11}}
v_w=78

We can conclude that the speed of the wind is 78 mi/hr.
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3 years ago
The following table represents a proportional relation. Find the missing values:
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Answer:16288.xy

Step-by-step explanation:

7 0
3 years ago
Breaking information down into manageable pieces can help you:
scZoUnD [109]

Answer no answers

Step-by-step explanation:

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What do you call to the set of ordered pairs
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Answer:

A relation is a set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation and the set of all second components of the ordered pairs is called the range of the relation.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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