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Damm [24]
3 years ago
10

At a garage sale, Darnell buys 5 dozen golf balls for $45.00 and 2 dozen cans of tennis balls for $30.00. What is the unit price

per golf ball and per can of tennis balls?
Mathematics
1 answer:
gregori [183]3 years ago
8 0

Answer:

The answer to your question is:

1 golf ball = $0.75

1 can of tennis balls = $1.25

Step-by-step explanation:

Data

5 dozen golf balls for $45.00

2 dozen cans of tennis balls = $30.00

Golf

              # of golf balls = 5 x 12 = 60

                            60 balls ---------------  $45

                               1 ball -----------------   x

                   x = 1x 45/60 = $0.75

Tennis

             # of cans of tennis balls = 2 dozens = 24 cans

                          24 cans --------------------- $30

                             1 can ----------------------   x

                  x = 1 x 30 / 24 = $1.25

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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b
madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding (ax+by)^7 using Binomial expansion, we have that:

(ax+by)^7 =

(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7

= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> a^7 = 128

=> a = \sqrt[7]{128}\\ \\\\a = 2

For the second term:

a^6b = -224

b = \frac{-224}{a^6}

b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5

Therefore, a = 2, b = 3.5

5 0
2 years ago
The graph of the equation -5x + By=18 is a line that passes through (-6,-2)
g100num [7]

Answer:

6

Step-by-step explanation:

B(Y)=5x+18

input the values

-2B=5(-6)+18

-2B=-30+18

-2B=-12

B=-12/-2

B=6

7 0
2 years ago
Solve the following question algebraically, show your work<br><br> 13 + w/7 &lt;-(fraction) = -18
evablogger [386]

Solve for w: by simplifying both sides of the equation, then isolating the variable.

w=-217

Work: 1.  Subtract 13 from both sides (w/7 = -18 - 13), 2.Simplify -18-13 to -31 (w/​7=-31), 3.Multiply both sides by 7 (w = -31 * 7), 4. Simplify 31*7 to 217 (w=-217)

8 0
3 years ago
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Answer:

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Step-by-step explanation:

4 0
2 years ago
Maria and jane bought a whole pizza pie. marie ate 1/5 of the pie and jane ate 1/4 of the pie. write a number sentence to find o
Papessa [141]
Eleven Twentieths of the pie are left, so that's 11/20

Method to solve; 
Since its given a 1/4 and a 1/5 it's easiest to convert these to twentieths (the lowest common multiple of 4 and 5)
So 1/4= 5/20
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How much is eaten = 5/20 + 4/20 = 9/20
How much remains = Total (20/20) - How much eaten (9/20) = 11/20
8 0
3 years ago
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