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Nina [5.8K]
3 years ago
15

Solve:(1/7)x +(1/6)y =3 ; (1/2)x - (1/3)y =5​

Mathematics
1 answer:
Svetach [21]3 years ago
5 0

Answer:

(14, 6 )

Step-by-step explanation:

Given

\frac{1}{7} x + \frac{1}{6} y = 3 ( multiply through by 42 to clear the fractions )

6x + 7y = 126 → (1)

\frac{1}{2} x - \frac{1}{3} y = 5 ( multiply through by 6 to clear the fractions )

3x - 2y = 30 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 6x + 4y = - 60 → (3)

Add (1) and (3)term by term to eliminate x

11y = 66 ( divide both sides by 11 )

y = 6

Substitute y = 6 into either of the 2 equations and evaluate for x

Substituting into (1)

6x + 7(6) = 126

6x + 42 = 126 ( subtract 42 from both sides )

6x = 84 ( divide both sides by 6 )

x = 14

Solution is (14, 6 )

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Answer:

2/3

Step-by-step explanation:

you can set it up as x/y because it varies directly

so when y=6 x=72

72/6 = 12

so x will always be 12 times greater than y

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so if x=8

8=12y

y=8/12

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3 0
2 years ago
Someone help me ASAP
Leni [432]

S = 15.47 units

Step-by-step explanation:

First, convert the degree angle into radians:

68° × (π/180) = 1.19 rad = theta

The arc length S is given by

S = r × theta

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4 0
2 years ago
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Determine the slope of the line passing through the points (0,-3) and (3,-11).
prohojiy [21]

Answer:

-3/8

Step-by-step explanation:

<em>Hey there!</em>

Well to find the slope with 2 points “(0,-3) and (3,-11)”, we’ll use the following formula,

\frac{y^2-y^1}{x^2-x^1}

Plug in the given points.

\frac{-11 - - 3}{3-0}

-11 + 3 = -8

3 - 0 = 3

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<em>Hope this helps :)</em>

4 0
2 years ago
Explain what is meant by "perfect square". Give an example of a number that is a perfect square and an example of a number that
kykrilka [37]

Answer:

Read the explanation

Step-by-step explanation:

Definintion of Perfect square:

In algebra, a term is a perfect square when the numerical coefficient (the number in front of the variable) is a perfect square number, and the exponents of each of the variables are even numbers. The numbers have to be the same just like how 2 x 2 = 4. 3 x 3 = 9, and so on.

<h3>Perfect square examples are numbers like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ..</h3><h3>Non perfect square examples are like 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42 ,43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56 , 57 ,58, 59, 60, ,61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75 ,76, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101,...</h3>
6 0
3 years ago
The dot plots below show the scores for a group of students for two rounds of a quiz: Which of the following inferences can be m
victus00 [196]
<h3>Answer: Choice A) round 2 has larger range</h3>

===================================================

Explanation:

  • Choice A is true. The range is the difference of the max and min. Round 1 has a range of 5-4 = 1, while round 2's range is 5-1 = 4. Round 2 has a larger range of scores. We don't really need to do any kind of math here. We can simply spot that round 2 has its dots more spread out compared to round 1, so round 2 must have the larger range.
  • Choice B is somewhat true. If we compare a score of 4 in round 1 to a score of 5 in round 2, then round 2 has a higher score. But we could easily flip things around. So saying one round has higher scores than the other is not particularly meaningful in this scenario. I would say it all depends on how you phrase the problem carefully. In any event, I would say that choice B is false since we can't definitively say it's true.
  • Choice C is a similar story as choice B, just flip things around. So I'd say this is false too. We would need all of the dots of round 1 to be to the left of all the dots of round 2, in order for choice C to be a true statement. Because there's overlap, we run into a problem.
  • Choice D is false because there is overlap for scores 4 and 5. In other words, both dot plots have dots over "4" and over "5". These are the scores the dot plots share in common.
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