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2 years ago

Josh bought 3 bottles of grape juice and 5 bottles of water for a total of $14.50. Mary bought 2 bottles

Mathematics

1 answer:

sesenic [268]2 years ago

3 0

Answer:

Bottle of water = $2
Bottle of grape juice = $1.50

Step-by-step explanation:

Grape juice = g
Water = w

Equations:

3g + 5w = 14.50
2g + 3w = 9.00

Subtract the 3 times the second equation from the twice the first:

2*(3g + 5w) - 3(2g + 3w) = 2*14.50 - 3*9.00
6g + 10w - 6g - 9w = 29 - 27
w = 2

Then, finding g:

3g + 2*5= 14.50
3g = 14.50 - 10
3g = 4.5
g = 1.50

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Answer: 3a = (0, 1) 3b = (2, 1) 3c = (2.5, 1) 3d = (1.6, 1)

4a = (2, 3.5) 4b = (2, 3) 4c = (2, 5.375)

Step-by-step explanation:

The length of AB is 6 and is horizontal (affects the x-coordinate)

$3a)\quad 6\bigg(\dfrac{1}{2}\bigg)\quad =3\qquad \qquad A(-2, 1) +(3, 0)= C(1,1)\\\\\\3b)\quad 6\bigg(\dfrac{2}{3}\bigg)\quad =4\qquad \qquad A(-2, 1) +(4,0)= C(2,1)\\\\\\3c)\quad 6\bigg(\dfrac{3}{4}\bigg)\quad =\dfrac{9}{2}\qquad \qquad A(-2, 1) +(4.5,0)= C(2.5,1)$

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3 years ago

Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

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