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il63 [147K]
3 years ago
11

Raychel drove to the mountains last week there was heavy traffic on the way there and on the trip took 12 hours when Raychel dro

ve home there was no traffic and the trip only took eight hours if her average rate was 20 mph faster on the trip home how far away does Rachel live from the mountains
Mathematics
1 answer:
nevsk [136]3 years ago
4 0
Suppose that this person drives at r mph going to the mountains, and gets there in 12 hours.  Returning, this person drives at (r+20) mph and gets home in 8 hours.  We don't know the distance yet, but can solve for the initial speed, r, by setting

d = 12r = (r+20)(8).  Solving for r, r=40 mph (going) and (40+20)mph = 60 mph (returning.  Since d=12 r, d = (12 hrs)(40 mph) = 480 miles (answer).
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Y = -5x + 1 graph the equation by making a table of values. Use 3 values of x.
Naily [24]

Answer:

Table -

x=-1 y= 6

x=0 y= 1

x=1 y= -4

Step-by-step explanation:

Answers are found by plugging in any 3 values of x

3 0
3 years ago
Pemdas, thank you! <br>(-8 × -6) -4² ​
Aleksandr-060686 [28]

Answer:

32

Step-by-step explanation:

(-8 × -6) - 4² ​

48 - 4²

48 - 16 = 32

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

8 0
2 years ago
Read 2 more answers
The circumference of a circle is 32π. What is the diameter of this circle?
lawyer [7]
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32 (pi)= 2 (pi) r 

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hope that helps
4 0
3 years ago
Noah applies two transformations to WXYZ so that the final vertices of the transformed
krok68 [10]

Answer:

ok

Step-by-step explanation:

4 0
3 years ago
If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(
timama [110]

Use the change-of-basis identity,

\log_x(y) = \dfrac{\ln(y)}{\ln(x)}

to write

xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}

Use the product-to-sum identity,

\log_x(yz) = \log_x(y) + \log_x(z)

to write

xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}

Redistribute the factors on the left side as

xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}

and simplify to

xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)

Now expand the right side:

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}

Simplify and rewrite using the logarithm properties mentioned earlier.

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1

xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}

xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}

xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)

\implies \boxed{xyz = x + y + z + 2}

(C)

6 0
2 years ago
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