1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gulaghasi [49]
3 years ago
10

Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state thi

s.
15x + 9y = 240
6x + 3y = 90 ...?
Mathematics
1 answer:
vladimir2022 [97]3 years ago
6 0
The answer is x = 10, y = 10.

Step 1: rearrange the second equation for y.
Step 2: substitute y from the second equation into the first equation.
Step 3. Calculate y.

Step 1.
<span>The second equation is: 6x + 3y = 90
Divide both sides of the equation by 3:
(6x + 3y)/3 = 90/3
6x/3 + 3y/3 = 30
2x + y = 30
Rearrange the equation:
y = 30 - 2x

Step 2.
</span>Substitute y from the second equation (y = 30 - 2x) into the first equation:
<span>15x + 9y = 240
15x + 9(30 - 2x) = 240
15x + 270 - 18x = 240
15x - 18x = 240 - 270
-3x = -30
x = -30/-3
x = 10

Step 3.
Since </span>y = 30 - 2x and x = 10, then:
y = 30 - 2 * 10
y = 30 - 20
y = 10
You might be interested in
A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen
noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 5, p = 0.93

Calculate P(at least one valve opens).

This is P(X \geq 1)

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807

Finally

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193

There is a 99.99998% probability that at least one valve opens.

5 0
3 years ago
Read 2 more answers
A triangle with side lengths of 32, 60 and 68 is a right triangle?<br> true or false
Troyanec [42]
I believe that it would come out to become true
5 0
3 years ago
Read 2 more answers
Only need to answer question 1 but if you can pls answer both
algol [13]
Use the app photo map
5 0
3 years ago
What are the properties of the incenter of a triangle
Anit [1.1K]
<span>Located at intersection of the angle bisectors. See Triangle incenter definition</span>
5 0
3 years ago
Solve for the formula C=2pir solve for r
Ulleksa [173]
C = 2pi r
C/2 Pi = r.

I believe this would be the solution.
7 0
3 years ago
Read 2 more answers
Other questions:
  • (a)It takes 51
    12·1 answer
  • Write an expression for the calculation the sum of the product of 4 and 3 and 1 and 1
    10·1 answer
  • Solve the quadratic equation below by completing the square. What are the solutions?
    12·1 answer
  • Age of car = 5 years. Original cost = $16,995. The current market value is $______. 3,399.00 5,098.50 11,896.50 13,596.00
    5·1 answer
  • Temperature rose 9°f in 3 hours if the starting wad -5°f what was the final temperature
    10·1 answer
  • During the first week of school Andrew purchased two pounds of Jellies and two pounds of Bonbons for $38. The second week of sch
    8·1 answer
  • Gle<br> 22+22<br> Whoever answers first gets Brainlyiest
    10·2 answers
  • Please pls pls pls ANSWER ASAP!!! :P<br> :)
    15·2 answers
  • Andrew measured a line to be 12.2 inches long. If the actual length of the line is 12.7 inches, then what was the percent error
    11·1 answer
  • On a ΔABC, mΔA=80, mΔB=60<br> Find mΔC
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!