Answer:
Chocolate Chips cost $2.25 and Walnuts cost $3.25 per pound each
Step-by-step explanatChocion:
Let x = cost of pounds of chocolate chip cookies and y = cost of pounds of walnuts.
From the question, we get 5x+3y = 21 and 2x+6y = 24. To solve the equation, we use substitution. From the first equation, we get y = (21-5x)/3. We substitute the y into the second equation to get 2x + 6(21-5x)/3 = 24. This turns out to be 2x+(42-10x) = 24. Adding like terms you should get 42-8x = 24. Solving for x, x = $2.25 per pound. Plugging this into the first equation, we get 5(2.25)+3y = 21. Solving for y, we get $3.25 per pound of walnuts. If we plug in the numbers into the 2 equations, we will get the right total.
Suppose that equation of parabola is
y =ax² + bx + c
Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c
Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c
Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c
Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5
Solving it we get that
a = −2, b = −4, c = 1
Thus, equation of parabola is
y = −2x²− 4x + 1
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Rewriting in the form of
(x - h)² = 4p(y - k)
i) -2x² - 4x + 1 = y
ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)
iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)
iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)
v) -3(x + 7/6)² = y - 445/36
vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)
vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)
So, after rewriting the equation would be -
(x + 7/6)² = 4(-⅛)(y - 445/36)
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I hope this is what you wanted.
Regards,
Divyanka♪
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5. million 6. Ten thousand
Answer: 0.714286
turn 7/10 into .7 and divide normally
Given:
Circular racetrack with a diameter of 1/2 mile
Find: how far does a car travel in one lap around the track?
We need to find the circumference of the racetrack.
Circumference is multiplying pi to the diameter of the racetrack.
Circumference = 3.14 * 1/2 mile
Circumference = 3.14/2 mile
Circumference = 1.57 miles rounded to the nearest tenth is 1.60 miles.
