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2 years ago

Which ordered pair (a, b) is a solution to the given system? 2a-5b=1 3a+5b=14

Mathematics

1 answer:

irakobra [83]2 years ago

8 0

2a - 5b = 1
3a + 5b = 14

Let's solve this system using elimination. Add the equations together to cancel the b-terms, then solve for a.

2a - 5b = 1
3a + 5b = 14
+___________
5a - 0 = 15
5a = 15
a = 3

Next, plug 3 for a into either of the equations and solve for b.

2a - 5b = 1
2(3) - 5b = 1
6 - 5b = 1
- 5b = -5
b = 1

Lastly, check all work by plugging both values for their respective variables.

2a - 5b = 1
2(3) - 5(1) = 1
6 - 5 = 1 -- This is true

3a + 5b = 14
3(3) + 5(1) = 14
9 + 5 = 14 -- This is true

The solution to the system of equations is (3, 1).

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a regular heptagon has a radius of approximately 27.87cm and the lengthof each side is 24.18cm. what is the approximate area of

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The Answer is B: 2,125 cm²

n = 7
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x = 128.571 °
y = 51.4286 °

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3 0

2 years ago

Read 2 more answers

At the county fair, the operator of a game guesses a contestant’s weight. For each pound the operator’s guess differs from the c

BartSMP [9]

Answer: $| x - \frac{15}{3} | = 120$ or $\frac{1}{3}| 3 x - 15|= 120$ or $| 3x - 15| = 360$ or $| x - 5 | = 120$

Step-by-step explanation:

Since, According to the question,

For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3.

And, If a contestant weighing x pounds received $15

Then the guessed weight of contestant = $| x - \frac{15}{3} |$

But, Again according to the question,

The guessed weight is 120 pounds,

Thus, $| x - \frac{15}{3}|= 120$

⇒ $\frac{1}{3}| 3 x - 15|= 120$

⇒ $| 3x - 15|= 3\times 120$ (by multiplying 3 on both sides)

⇒ $| 3x - 15|= 360$

⇒ $3| x - 5|= 360$

⇒ $| x - 5|= 120$ ( On dividing both sides by 3 )

4 0

2 years ago

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After a number of complaints about its tech assistance, a computer manufacturer examined samples of calls to determine the frequ

icang [17]

Answer:

a) Upper Control Limit = 0.10

Lower Control Limit = 0.01

b) The tech assistance process is stable and in control.

Step-by-step explanation:

Given - After a number of complaints about its tech assistance, a

computer manufacturer examined samples of calls to determine

the frequency of wrong advice given to callers. Each sample

consisted of 100 calls.

SAMPLE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Number of errors 5 3 5 7 4 6 8 4 5 9 3 4 5 6 6 7

To find - a. Determine 95 percent limits.

b. Is the tech assistance process stable (i.e., in control)

Proof -

z = 95% confidence interval

= 1.96

⇒z = 1.96

Proportion of defects,P = total defectives/total observations

= 0.0544

⇒P = 0.0544

Now,

Q = 1-P

= 0.9456

⇒Q = 0.9456

Now,

Average sample size, N = 100

Standard deviation = $\sqrt{\frac{P.Q}{N} }$

= 0.0227

Now,

Upper Control Limit = P + z(Standard deviation)

= 0.0988

⇒Upper Control Limit = 0.0988 ≈ 0.10

And

Lower Control Limit = P - z(Standard deviation )

= 0.0099

⇒Lower Control Limit = 0.0099 ≈ 0.01

∴ we get

Upper Control Limit = 0.10

Lower Control Limit = 0.01

b.)

Now,

it is clear that the fraction defective values are wit in upper an lower control limits.

So, The tech assistance process is stable and in control.

5 0

2 years ago

X-7y=-21<br> 2x - 14y = -42<br> What’s the solution

maxonik [38]

Answer:

Step-by-step explanation:

i tried but i cant succed.

7 0

2 years ago

At Brighton Middle School, Mr. Yule asked 50 randomly selected students from each grade level about their favorite subject, and

Ugo [173]

Answer:

Yes, he made a reasonable inference by saying about 25 percent of students choose the science.

Step-by-step explanation:

Given that

Number of students for survey = 50

Number of students who choose science = 12

Now

Percentage of student who choose science = $\frac{12}{50} x 100$

Percentage of student who choose science = $\frac{12*100}{50}$

Percentage of student who choose science = 24 %

Now as Mr. Yule said "about 25" percent of students choose the science it can be treated as reasonable approximation.

Now if the number of students in survey become 200, then we can expect 12 out of every 50 students would choose the science. So, in total 48 students would choose the science.

Now lets calculate the percentage of students who choose science.

Percentage of student who choose science = $\frac{48}{200} x 100$

Percentage of student who choose science = $\frac{48*100}{200}$

Percentage of student who choose science = 24 %

7 0

2 years ago

Read 2 more answers