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yan [13]
3 years ago
14

A mechanic charges $75 per hour for her services and $60 for the initial call. What is the dependent variable in the situation?

Mathematics
1 answer:
tresset_1 [31]3 years ago
8 0

Answer:

The amount of hours it takes for the service to be completed

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A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
Kitty [74]

Answer: ab =6

have:

\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\\frac{a+b+1}{ab}=1

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

4 0
2 years ago
What's 4x + 3 = 2x + 17
Svet_ta [14]

Answer:

x=7

Step-by-step explanation:

Move all terms containing x to the left side of the equation.

2x+3=17

Move all terms not containing x to the right side of the equation.

2x=14

Divide each term by 2 and simplify.

x=7

7 0
3 years ago
The function G(x)=f(x+3)+2 which of the following is true of the graph of g(x)?
zepelin [54]
G(x)=(x+3)+2

G(x) = (x-h) + k
h translates the graph left/right and k translates the graph up/down.
Because the equation is x- the parenthesis is (x - - 3) which makes h a negative 3 and will translate left. The k positive so it will move up.
Letter B
7 0
3 years ago
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar
jeyben [28]

Hi,

Let assume a the west side,

b the length of the north wall (i suppose the answer is smaller then the barn.

Cost of the fence= a*6+a*12+b*12=3000 $.

So 3a+2b=500==>b=(500-3a)/2

Area =a*b=a(500-3a)/2= 250a-3/2a²

Derivate the area ==> 250-3a=0

==> a=250/3 and b=(500-3*250/3)/2=125

Width=125 (feet)

Length=250/3=83.333 (feet)

3 0
3 years ago
Which is the prime factorization of 40?
Lana71 [14]

Hey there!

Which is the prime factorization of 40?


Option A.

2 * 5

= 2 + 2 + 2 + 2 + 2

= 4 + 4 + 2

= 8 + 2

= 10


Option B.

2^3 * 5

= 2 * 2 * 2 * 5

= 4 * 2 * 5

= 8 * 5

= 40


Option C.

2 * 53

= 53 * 2

= 53 + 53

= 106


2 * 3 * 5

= 6 * 5

= 6 + 6 + 6 + 6 + 6

= 12 + 12 + 6

= 24 + 6

= 30


Therefore, your answer is:

Option B. 2^3 * 5


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

4 0
2 years ago
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