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tresset_1 [31]
3 years ago
15

Last year, Garcia rented 127 videos from the movie store while his brother Raul rented 46. Together they rented 83 more videos t

han their friend Rosa. If video rentals cost $3.75 each, how much did Rosa spend last year on video rentals?
A. $960.00 B. $337.50
C. $90.00 D. $311.25
Mathematics
1 answer:
KIM [24]3 years ago
8 0
The answer is B: $337.50
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Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution
Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\

for y=e^{6x}:

y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\

Now we replace in the differential equation  y'' − y' − 30y = 0

for y=e^{-5x}:

25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0

for y=e^{6x}:

36e^{6x}-6e^{6x}-30=0\\36-6+30=0

Now, to know if both function are linearly independent we calculate the Wronskian

W(f,g)=fg'-f'g

W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0

I hope this is useful for you

Best regard

7 0
3 years ago
The miller’s drove 160 miles in four hours to Texas at that rate how far will the millers travel in six hours?
irina1246 [14]
The millers will travel 240 miles in six hours.
5 0
3 years ago
Read 2 more answers
Kyle’s total sales for the month of January were $10,000, and his total earnings for that month were $1,350.
omeli [17]

Answer:

$900

Step-by-step explanation:

<u>Let the fixed salary be x and the commission be y, then as per given, the earnings:</u>

  • 10000y + x = 1350
  • 15000y + x = 1575

<u>Subtract the first equation from the second:</u>

  • 15000y - 10000y = 1575 -1350
  • 5000y = 225

then

  • 10000y =2*5000y = 2*225 = 450

<u>Using the first equation:</u>

  • x = 1350 - 450 = 900

<u>So the fixed salary is</u> $900

7 0
3 years ago
A​ salesperson's ratio of successful signups to the number of people called is 0.625. This​ month, the salesperson had 125 signu
stellarik [79]

Answer:

The salesperson called 200 people this month.

Step-by-step explanation:

Let us denote the total people that the salesperson called by a variable "x".

Then,

The ratio of successful signups(success ratio) is given as=0.625

Then total no. of successful signups is the product of the success rate and the total no. of signups ,

i.e. Total successful signups = 0.625*x

According to the data given in the question,

The total no. of successful signups this month =125

or , 0.625*x= 125

or,  x=\frac{125}{0.625}

   ∴x= 200

So, the salesperson called 200 people, out of which only 125 signed up.

4 0
3 years ago
How do I solve for the variable? 3(x-14) + 1= -4x + 5
bearhunter [10]

Answer:

3·(x - 14) + 1 = - 4·x + 5

3·x - 42 + 1 = - 4·x + 5

3·x - 41 = - 4·x + 5

7·x - 41 = 5

7·x = 46

x = 46/7

6 0
3 years ago
Read 2 more answers
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