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KonstantinChe [14]

3 years ago

9

Matilda needs at least $112 to buy a new dress. She already has saved $40. She earns $9 an hour by babysitting. Write an inequal

ity that can be used todetermine how many hours, X, Matilda will need to buy the dress?

1 answer:

Ymorist [56]3 years ago

6 0

Answer:

8

Step-by-step explanation:

9*8 = 72 + 40 = 112

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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.

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

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

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

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

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

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6 0

2 years ago

What is 32.043 in expanded form

natima [27]

<span>30 + 2 + 0.04 + 0.003</span>

7 0

3 years ago

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This is an ADDMATHS QUESTION so I'm not sure if anyone can help me but please try to ㅠ ㅠ: Find the equation of the normal to the

zepelin [54]

You can go through the effort of determining the zero of the function analytically and evaluating an analytic expression for the derivative at that point, or you can let a graphing calculator do that heavy lifting. Since the numbers have to be "nice" for your equation to have the desired form, it is easy to know what to round to in the event that is necessary (it isn't).

We find the positive zero-crossing at x=2, and the slope of the curve at that point to be 8. Thus the line will have slope -1/8 and can be written as
.. x +8y -2 = 0

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3 years ago

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Questions is: the sum of 28+29+42=99. what addition property was used commutative, associative, identity, and distributive ?

Arturiano [62]

Since, it is given that $28+29+42= 99$

Now, we have to identify the addition property for the given equation.

Associative property of addition states that for any real numbers say 'a' , 'b' and 'c', a+(b+c) = (a+b)+c

So, in the given question 28+29+42

We can use associative property as

(28+29)+42 = 28+(29+42)

57+42 = 28+71

99 = 99

Hence, among the given properties, associative addition property is used.

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3 years ago

An inelastic collision occurs between a large truck and smaller sedan. Calculate the final velocity of the objects and explain t

k0ka [10]

The final velocity is 15.8 m/s in the forward direction

Step-by-step explanation:

An inelastic collision occurs when the two object after the collision stick together.

In any case, the total momentum of the system is conserved before and after the collision, in absence of external forces. Therefore, we can write:

$p_i = p_f\\m u + MU = (m+M)v$

where in this problem:

m = 1300 kg is the mass of the small sedan

u = 20 m/s is the initial velocity of the small sedan

M = 7100 kg is the mass of the truck

U = 15 m/s is the initial velocity of the truck

v is the final combined velocity of the small sedan + truck

Here we have taken both the velocity of the sedan and the truck in the positive (forward) direction

Solving the equation for v, we find the final velocity:

$v=\frac{mu+MU}{m+M}=\frac{(1300)(20)+(7100)(15)}{1300+7100}=15.8 m/s$

And since the sign is positive, this means that is direction is the same as the initial direction of the sedan and the truck, so forward.

Learn more about collisions:

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7 0

4 years ago