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shtirl [24]
3 years ago
15

Joe bought 5 apples and 4 bananas for $6. Dawn bought 3 apples and 6 bananas for $6.30. How much foes each apple and each banana

cost?
Mathematics
1 answer:
zepelin [54]3 years ago
4 0

Answer:

Apple = $0.6

Banana = $0.75

Step-by-step explanation:

Let us represent Apple by A and Banana by B

For Joe,

5A + 4B = 6       (1)

For Dawn

3A + 6B = 6.3     (2)

To eliminate A, Multiply equation (1) by 3 and equation (2) by 5

15A + 12B = 18          (3)

15A + 30B = 31.5       (4)

subtracting equation (4) from (3)

15A - 15A +12B - 30B = 18 - 31.5

-18B = -13.5

divide through by -18

-18B/-18 = -13.5/-18

B = 0.75

substitute 0.75 in equation (1)

5A + 4B = 6

5A + 4(0.75) = 6

5A + 3 = 6

subtract 3 from both sides

5A + 3 - 3 = 6 - 3

5A = 3

divide through by 5

5A/5 = 3/5

A = 0.6

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Thepotemich [5.8K]

Answer:The answer is choice B

Step-by-step explanation: (3x-2y)2-(2x-3y)2  

Final result :

 5 • (x + y) • (x - y)

Step by step solution :

Step  1  :

1.1     Evaluate :  (3x-2y)2   =    9x2-12xy+4y2  

1.2     Evaluate :  (2x-3y)2   =    4x2-12xy+9y2  

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  5x2 - 5y2  =   5 • (x2 - y2)  

Trying to factor as a Difference of Squares :

2.2      Factoring:  x2 - y2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

Factorization is :       (x + y)  •  (x - y)  

Final result :

 5 • (x + y) • (x - y)

4 0
3 years ago
HELP PLEASE ASAP! I really need it!
Tomtit [17]

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2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA
professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

A=45e^{-0.0045(t)}

a) To find the initial amount of this substance

At t=0, we get

A=45e^{-0.0045(0)}A=45e^0

We know that e^0=1 ( anything to the power zero is 1)

we get,

A=45

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

\frac{45}{2}=45e^{-0.0045(t)}

\frac{1}{2}=e^{-0.0045(t)}

Taking natural logarithm on both sides we get,

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Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

A=45e^{-0.0045(2500)}A=45e^{-11.25}A=45\times0.000013=0.000585A=0.000585

The amount of substance will be present around in 2500 years is 0.000585 grams

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10 months ago
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Answer:

Step-by-step explanation:

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