Andrea is at the grocery store buying fruit for a smoothie stand. She needs 7 boxes of raspberries for every 5 bunches of banana
1 answer:
Answer:
The greatest number of bunches of bananas that Andrea can buy is 15 and the greatest number of boxes of raspberries that Andrea can buy is 21 to maintain the ratio 7:5
Step-by-step explanation:
Let
x ---->the greatest number of boxes of raspberries that Andrea can buy
y ---->the greatest number of bunches of bananas that Andrea can buy
we know that
---> sales tax
----> equation A
----> inequality B
substitute equation A in the inequality B
solve for y
Multiply by 5 both sides to remove the fraction
so
The maximum value of y is 19
Find the value of x
replace the value of y in equation A until you get an integer value that satisfies the ratio 7:5
For y=19
For y=18
For y=17
For y=16
For y=15
therefore
The greatest number of of bunches of bananas that Andrea can buy is 15 and the greatest number of boxes of raspberries that Andrea can buy is 21 to maintain the ratio 7:5
<u><em>Verify the inequality B</em></u>
----> is true
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Answer:
The diagonal of kite intersect at the point p is C. 68°
Answer:
Step-by-step explanation:
The first part of A is easy. Look at the quadratic function, and the constant, the very last number with no t stuck to it represents the height from which the object in question was originally launched. Our constant is 40, so the height of the roof from which the baseball was thrown is 40 feet. Part 2 of A is not quite as simple because it requires factoring using the quadratic formula.Before we do that, let's make our numbers a bit more manageable, shall we? Let's factor out a -8 to get
and a = 1, b = -6, c = -5.
Filling in the quadratic formula now looks like this:
and
and
so the 2 solutions are
and
and since we know time can NEVER be negative, the time it takes for the baseball to hit the ground from a height of 40 feet is 6.74 seconds. Onto part B.
In order to determine exactly how high the baseball did go, we have to find the vertex of the function. We do this by completing the square and getting the function into vertex, or work, form. Begin by setting the quadratic equal to 0, moving over the constant, and then factoring out the leading coefficient. The rule for completing the square are kinda picky in that you have to have a 1 as the leading coefficient, and righ now ours is a -8. So following the rules I stated above:
Next is the take half the linear term, square it, and then add it to both sides. Our linear term is a -6. Half of -6 is -3, and -3 squared is 9, so we add 9 into the parenthesis first:
Because this is an equation, we can't add 9 to one side without adding the equivalent to the other side. But, we cannot forget about that -8 sitting out front there, refusing to be ignored. We didn't just add in a 9, we actually added in a -8 times 9 which is -72. That's what goes on the right side in place of the ??.
The reason we complete the square is found on the left side of the equals sign. We have, in the process of completing the square, formed a perfect square binomial that will serve as the h in our vertex (h, k) where h is the number of seconds it takes for the baseball to reach its max height of k, whatever k is. That's what we have to find out. Putting the left side into its simplified perfect square binomial and adding the numbers on the right gives us:
For the last step, add over the -112 and set it back equal to f(t):
From that we determine that the vertex is (3, 112). The max height of this baseball was 112 feet...so no, it did not make it up to the height of 120 feet that Jimmy wanted for the baseball.