5. Ryan Just bought 10 gallons of gasoline, the amount of fuel used for the last 355 miles of driving. Being a curious sort , Ry
an wondered how much fuel had been used in freeway driving (which takes on gallon for each 40 miles) Ryan started by guessing 6 gallons for the city driving , then completed the first row of the guess -and-check table below . Notice the failed check . Make your own guess and use it to fill in the next row of the table. city gallons 6 freeway gal 10 - 6 = 4 check city mi. 6(25) = 150 freeway mi. 4(40) = 160 total mi. 150 + 160 = 310 target 355 no Now write c in the city gallon column, fill in the remaining entries in terms of c, and set your expression for the total mileage equal to the target mileage Solve the resulting equation.
1 answer:
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Answer:
A
Step-by-step explanation:
We have the expression:
And we want to find its sign given that a>0 and b<0.
Notice that the expression is already negative since we have -4.
a>0 means that a is positive. Therefore, we can ignore it since it won’t do anything.
b<0 means that b is negative. Therefore, we will have two negatives being multiplied together. Hence, this will make a positive.
Therefore, the sign of our expression will be positive.
We can see this with an example. Let a=1 (1>0) and let b=-1 (-1<0). Then:
So, the sign is positive.
Hence, the answer is A.
Answer:
The statement is now presented as:
In other words, this mathematical statement can be translated as:
<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>
Step-by-step explanation:
Let the coordinates of the center of the circle, which must be transformed into
by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:
Where is the radius of the circle, which remains unchanged in every operation.
Now we proceed to describe the series of operations:
1) <em>Center of the circle is translated 4 units to the right</em> (+x direction):
(Eq. 1)
Where is the translation vector, dimensionless.
If we know that and
, then:
2) <em>Reflection over the x-axis</em>:
(Eq. 2)
Where is the reflection point, dimensionless.
If we know that and
, the new point is:
And thus, and
. The statement is now presented as:
In other words, this mathematical statement can be translated as:
<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>
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