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3 years ago

How many solutions does this system have? y=5x-1 y=-3x+7

Mathematics

1 answer:

Vesnalui [34]3 years ago

8 0

Answer:

One solution

Step-by-step explanation:

We have the system

$y=5x-1\\y=-3x+7$

To solve the system, equate both equations and solve for the variable x.

$5x-1= -3x+7\\\\5x + 3x = 7 +1\\\\8x = 8\\\\x=1$

Now substitute the value of x in any of the two equations and solve for the variable y.

$y=5(1)-1$

$y=4$

Finally the system of equations has one solution

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Heather invested $8000 in a 4- year certificate of deposit (CD) that pays 4.1 interest compound annually. What is the value of t

aliya0001 [1]

8000(1.041) $x^{4}$ =9394.91

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3 years ago

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must p

rusak2 [61]

The answer is incomplete. Here is the complete question:

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each. Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella does because Stella only has enough supplies to make 40 pies. let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes.

Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.

Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.

Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.

Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.

Answer:

Part 1: $25x\geq 600$

Part 2: $15y\geq 600$

Part 3: $y\leq 40$

Part 4: Yes, she makes exactly 600 dollars by making 40 pies.

Step-by-step explanation:

Given:

Total money needed for the trip is 600 dollars.

Money earnt by Jamie for washing one car is $25.

Money earnt by Stella for making one pie is $15.

Let $x$ represent the number of cars Jamie washes. Let $y$ represent the number of pies Stella makes.

Part 1:

Since the cost for washing one car is $25

Therefore, the cost of washing $x$ cars is $25x$ .

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600.

Therefore, $25x\geq 600$

Part 2:

Since the cost for making one pie is $15

Therefore, the cost of making $y$ pies is $15y$ .

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600.

Therefore, $15y\geq 600$

Part 3:

As per the question, the maximum number of pies that Stella can make is 40. So, the value of $y$ can't exceed 40 and must be less than or equal to 40. Therefore,

$y\leq 40$

Part 4:

Now, in order to sign up for the trip, Stella's total earning must be at least $600. So, $15y=600$ is the minimum condition for signing up for the trip. Now, let us solve the above equation for $y$ . This gives,

$15y=600\\y=\frac{600}{15}=40$

Therefore, minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

8 0

3 years ago

What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of pro

seropon [69]

Let us compute first the probability of ending up an odd number when rolling a dice. A dice has faces with numbers 1 up to 6. The odd numbers within that is 3 (1, 3 and 5). Therefore, each dice has a probability of 3/6 or 1/2. Then, you use the repeated trials formula:

Probability = n!/r!(n-r)! * p^r * q^(n-r), where n is the number of tries (n=6), r is the number tries where you get an even number (r=0), p is the probability of having an even face and q is the probability of having an odd face.

Probability = 6!/0!(6!) * (1/2)^0 * (1/2)^6
Probability = 1/64

Therefore, the probability is 1/64 or 1.56%.

6 0

3 years ago

Write 65% as a fraction in simplest form.

rusak2 [61]

Answer:

13/20

Step-by-step explanation:

This is actually pretty simple. I had trouble with this for the longest time but it makes sense to me now. A number that is a percent is equal to that number over 100.

65%=65/100

Then all you have to do is simplify! (yaaay)

65/100=<u>13/20</u>

<u></u>

If you need anymore help with this or anything else just let me know!

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3 years ago

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katrin [286]

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3 years ago