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lianna [129]
3 years ago
15

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 104 miles in the same time that Dana travels 96 miles. If

Chuck's rate of travel is 4 mph more than Dana's, at what speed does Chuck travel?
Mathematics
1 answer:
Yanka [14]3 years ago
3 0

Answer: Chuck's travel at a rate of 52mph

Step-by-step explanation:

For Chuck's trip:

D=RT

104= (R+4)T

T= 104 / (R+4)

For Dana's trip:

96 = RT

T= 96/R

Set both equation for Chuck's and Dana together

104/(R+4) =96/R

Then we cross multiply

96(R+4) = 104R

96R + 384 = 104R

104R - 96R = 384

8R = 384

To get R, divide both side by 8

8R/8 = 384/8

R= 48mph

This means Dana's speed is 48mph

Chuck's speed will be: 48mph+4mph = 52mph

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Answer:

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Step-by-step explanation:

Given that at her salon, last week Tammy did 25 manicures and collected $ 1000, to calculate the slope to represent the manicures, write an equation to represent this relation and determine how much would Tammy make if she did 78 manicures in a month the following calculations should be performed:

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2 years ago
For what value of c is the function defined below continuous on (-\infty,\infty)?
kozerog [31]
f(x)= \left \{ {{x^2-c^2,x \ \textless \  4} \atop {cx+20},x \geq 4} \right


It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if 
</span><span>\lim_{x \rightarrow 4} \  f(x) = f(4)

</span><span>In notation we write respectively
</span>\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence 
\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2

Thus these two limits, the one from above and below are equal if and only if
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c^2+4c+4=0&#10;\\(c+2)^2=0&#10;\\c=-2

That is to say, if c = -2, f(x) is continuous at x = 4. 

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers (-\infty, +\infty)

4 0
2 years ago
What are the intercepts of the line 2x + 4y = 12?
Darina [25.2K]
<span>if you're finding the x intercept, y is ALWAYS 0, so in this, you can just get rid of the -4y because you know that it's 0, so you're left with 2x=12 divide by 2 on both sides so you find x intercept is (6,0) on the graph 
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x int.= (6,0) 
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by the way, when it's written like that, it's called standard form, so to find the intercepts on 2x=12+4y, you'd have to convert it into standard form (Ax=By=C) so you subtract 4y on both sides to make it 2x-4y=12, and then once you have it like that you can do the math to find the y and x intercepts.
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blagie [28]

Answer:

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Step-by-step explanation:

Randy's original position lets him make:

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The new position will let him make:

$27,500

Therefore,

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