If gas prices are now $3.75 and they were up 10% from 6 months ago, how much were gas prices 6 months ago?
1 answer:
Given
gas prices are now $3.75 and it up 10% from 6 months ago.
Find out how much were gas prices 6 months ago.
To proof
gas prices now = $3.75
let the gas price 6 month ago = x
gas price now is rise up 10% from 6 months ago
First write 10% in simpler form
= 0.1
Now the equation becomes
0.1x + x = 3.75
1.1x = 3.75
x = 3.41 (approx)
Thus gas prices 6 months ago be $ 3.41 (approx )
Hence proved
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Answer:
Part A:
( 1.8333, -0.08333)
Part B:
x = 2 or x = 5/3
Step-by-step explanation:
The quadratic equation
has been given.
Part A:
We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.
Setting the derivative to 0;
6x - 11 = 0
6x = 11
x = 11/6
The corresponding y value is determined by substituting x = 11/6 into the original equation;
y = 3(11/6)^2 - 11(11/6) + 10
y = -0.08333
The vertex is thus located at the point;
( 1.8333, -0.08333)
Find the attached
Part B:
We can use the quadratic formula to solve for x as follows;
The quadratic formula is given as,
From the quadratic equation given;
a = 3, b = -11, c = 10
We substitute these values into the above formula and simplify to determine the value of x;
Amy has $30 to spend on snacks and beverages for herself and her friends at the movie theater. The cost for nachos was $5. The cost for each beverage was half the cost of the nachos
Let x be the number of nachos and y be the number of beverages
The cost for nachos was $5. So the cost of 'x' nachos = 5x
The cost for each beverage was half the cost of the nachos.
The cost of each beverage =
so the cost of y beverage = 2.5 y
Cost of x nachos + cost of y beverage = total amount spend
5x + 2.5y = 30
Now we find x and y intercept
When Amy does not buy any beverages we put y=0
5x + 2.5(0) = 30
5x = 30
x= 6. The x intercept is (6,0)
When Amy does not buy any nachos we put x=0
5(0) + 2.5y = 30
2.5y = 30
y=12. The y intercept is (0,12)
The graph is attached below
(b) The graph is a straight line. From the graph we can see that when Amy does not buy any nachos then she can spend #30 to buy 12 beverages .
when Amy does not buy any beverages then she can spend #30 to buy 6 nachos.
