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Irina18 [472]
2 years ago
5

Use the Substitution method to solve the system of equations 3x+4y=10 y=x-1

Mathematics
1 answer:
kifflom [539]2 years ago
5 0

Answer: 2

Step-by-step explanation:

3x+4y=10

3x+4(x-1)=10

3x+4x-4=10

7x-4=10

Add 4 to both sides

7x=14

x=2

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Suppose 4 mg of a drug is injected into a person's bloodstream. As the drug is metabolized, the quantity diminishes at the conti
Brut [27]
Let Q(t) = the mass (mg) remaining after t hours.
We are told that Q diminishes by 3% every hour.

When t = 0, Q = 4 mg
When t = 1,  Q = 4*0.97 mg
When t = 2, Q = 4*(0.97)² mg

By induction,
Q(t) = 4 (0.97)^{t} \, mg

Q'(t) = 0.97Q
Therefore the rate of decrease is 3% per hour.

The person receives an additional dosage when Q falls to 0.50 mg. This happens when
4(0.97)^{t}=0.5 \\0.97^{t} = 0.125 \\ t \,ln(0.97) = ln(0.125) \\ t =  \frac{ln(0.125)}{ln(0.97)} =68.27 \, hrs

After the second injection, the mass is now 4.5 mg. Therefore
Q(t)=4.5(0.97)^{t}

When the mass again reaches 0.50 mg, then
4.5(0.97)^{t}=0.5 \\ 0.97^{t}=0.1111 \\ t \, ln(0.97) = ln(0.1111) \\ t = 72.14 \, hrs

Answers: 
(a) Q(t) = 4(0.97)^{t}
(b) 3% per hour
(c) 68.3 hours
(d) 72.1 hours

3 0
3 years ago
(I have a deadline in 3 hours :c ) Ann's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs
max2010maxim [7]
A=3B
4.35A+5.40B=780.95
Substitute 3B into A for the second equation:
4.35(3B)+5.40B=780.90
13.05B+5.40B=780.90
18.45B=780.90
B=42.33
Plug into equation 1:
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A=3(42.33)
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7 0
3 years ago
Read 2 more answers
Find the length of each side of the polygon for the given perimeter
butalik [34]

Answer:

choice number 2) 10 in, 18.5 in 31.5 in

Step-by-step explanation:

we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y  with 5 because they are not like terms.

2y +1 + 7y + 3y + 5 = 60

(2y+7y+3y)+(1+5) = 60

12y + 6 = 60

The 6 crosses the equal sign to the other side because of like terms.And becomes a minus

12y = 60 - 6

12y = 54

y = 4.5

so,

2y +1= 2 x 4.5 + 1 =10

7y = 7 x 4.5 = 31.5

3y + 5= 3 x 4.5 + 5 =18.5

Answer is 10 in, 18.5 in, 31.5 in

If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx

Hope this helps and if it does pls mark as branliest answer thx

8 0
2 years ago
Map Readinghwhich is the nearest Planet of Earth ​
Alika [10]

Answer: do you mean which is the closest? If so that would be mars

Step-by-step explanation:

7 0
2 years ago
What are the solutions to this system of equations?
saveliy_v [14]

Answer:

A

Step-by-step explanation:

The solution is at the points of intersections of the graphs

The graphs intersect at (- 3, 0 ) and (2, 5 )  , then

solutions are (- 3, 0 ) and (2, 5 )

4 0
2 years ago
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