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tiny-mole [99]
4 years ago
8

Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes

at three-quarters the rate she biked to the market. At any given time, t, the distance biked can be calculated using the formula d = rt, where d represents distance and r represents rate. If the trip home takes 12 minutes longer than the trip to the market, how many minutes does it take Carmen to bike home?
Mathematics
1 answer:
prisoha [69]4 years ago
7 0
We will use the equation:
r t = 3/4 r ( t+12 )    /:r
t = 3/4 t + 9
t - 3/4 t = 9
1/4 t = 9
t = 9 * 4 = 36 minutes ( takes a trip to the market )
36 + 12 = 48 minutes
The ride home takes 48 minutes.
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The focal length F of a lens made by combining two lenses of focal length U and V is given I/F=I/U+I/V
jolli1 [7]

Answer:

a). V=\frac{U.F}{U-F}

b). V = 15 units

Step-by-step explanation:

Focal length F of a lens made by combining two lenses of different focal lengths U and V will be,

\frac{1}{F}=\frac{1}{U}+\frac{1}{V}

A). By solving the given formula,

    \frac{1}{V}=\frac{1}{F}-\frac{1}{U}

    \frac{1}{V}=\frac{U-F}{U.F}

    V=\frac{U.F}{U-F}

B). If F = 6 and U = 10 then we have to find the value of V.

    By substituting the given values in the formula,

    V=\frac{6\times 10}{10-6}

    V=\frac{60}{4}

    V = 15 units

    Therefore, focal length (V) of the lens = 15 units

4 0
3 years ago
what is the solution to the system of equations: x- - y-z = 2, - x - 3 y - 2 z + 4, -x - 2 z = 10
ladessa [460]

Given equations are x- - y-z = 2, - x - 3 y - 2 z + 4, -x - 2 z = 10 .

It seems you have missed to write = in the 2nd equation so i have fixed the sign and going to solve the following system of equations:

x-y-z=2 ...(i)

-x-3y-2z=4 ...(ii)

-x-2z=10 ...(iii)


solve (i) for x

x=2+y+z ...(iv)

plug (iv) into (ii)

-x-3y-2z=4

-(2+y+z)-3y-2z=4

-2-y-z-3y-2z=4

-2-4y-3z=4

-4y-3z=6...(v)


plug (iv) into (iii)

-x-2z=10

-(2+y+z)-2z=10

-2-y-z-2z=10

-2-y-3z=10

-y=12+3z

y=-12-3z...(vi)


plug (vi) into (v)

-4y-3z=6

-4(-12-3z)-3z=6

48+12z-3z=6

48+9z=6

9z=-42

z=-14/3


Now plug value of z into (vi)

y=-12-3z=-12-3(-14/3)=-12+14=2

y=2


plug value of y and z into (iv)

x=2+y+z=2+2-14/3=-2/3


Hence final answer is x=-2/3, y=2, z=-14/3

3 0
3 years ago
Simplify by combining like terms. Type the terms<br> in alphabetical order.<br> -59-2+29-8=
Gnom [1K]

Answer:

Step-by-step explanation:

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Here -59 & -2 have same sign, so add both

                          = -61 - 8 + 29

                         = - 69 + 29

-69 & 29 have different sign. so subtract and the answer will have the sign of the bigger number

                         = - 40

7 0
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anyanavicka [17]

Answer:

c= -5

Step-by-step explanation:

6 0
3 years ago
Timed please help added picture​
DaniilM [7]

Answer:

\sqrt[4]{2}^{3}

Step-by-step explanation:

7 0
3 years ago
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