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joja [24]
3 years ago
13

Which statements about the system are true?

Mathematics
1 answer:
Kruka [31]3 years ago
5 0

2 Answers:

  • B)  The lines are parallel
  • C)  The lines have the same slope.

Parallel lines always have equal slope, but different y intercepts.

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

Explanation:

Let's solve the second equation for y

3y - x = -7

3y = -7+x

3y = x-7

y = (x-7)/3

y = x/3 - 7/3

y = (1/3)x - 7/3

The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.

However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.

Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.

Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.

I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.

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Archy [21]
Question (1):
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Question (2):
The given expression is:
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a = 2
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Question (3):
Quadratic formula (the one used in the previous question, also shown in attached images) is the best method to get the solution of any quadratic equation. This is because, putting the equation in standard form, we can simply get the values of a, b and c, substitute in the formula and get the precise solutions of the equation.

Hope this helps :)

8 0
3 years ago
Read 2 more answers
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likoan [24]

Answer:

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Step-by-step explanation:

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Answer:

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One way to solve this problem is to convert the equation to the vertex form.

We do that by completing the square.

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(-1/16)h = t² - ⁷/₂t

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Add and subtract it on the right-hand side

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Write the first three terms as the square of a binomial

(-1/16)h = (t - ⁷/₄)² - 49/16

Multiply both sides by -16

h = -16(t - ⁷/₄)² + 49

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y = a(t - h)² + k = 0,

where (h, k) is the vertex.

h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).

The time to reach maximum height is ⁷/₄ s = 1.75 s.

The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.

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