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pogonyaev
3 years ago
15

How many solutions does this linear system have?

Mathematics
1 answer:
ziro4ka [17]3 years ago
4 0

Answer: C is correct, No solution

Step-by-step explanation:

Let’s simplify the second equation,

8x-4y=-20

We can divide the whole equation by 4...

8x/4-4y/4=-20/4

Which becomes....

2x-y=-5

Now let’s move things around to see if it’s the same equation as the one on top...

-y=-2x-5

y=2x+5

Now we need to solve the systems...

y=2x-5

y=2x+5

Since their slopes are both 2 and their y-intercepts are not identical, the answer is no solution. The two lines will continue on without ever crossing because they have the same slope.

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Equilateral triangle ABC has an area of \sqrt{3}√ ​3 ​ ​​ . If the shaded region has an area of \piπK − \sqrt{3}√ ​3 ​ ​​ , what
Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

  and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

   arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

  of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ (2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)

∴ 4=r^{2}+r^{2}-2(r)(r)(-0.5)

∴ 4=r^{2}+r^{2}-(-r^{2})

∴ 4=r^{2}+r^{2}+r^{2}

∴ 4=3r^{2}

- Divide both sides by 3

∴ r^{2}=\frac{4}{3}

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0
3 years ago
a lady left from Nakuru to Mombasa she drove for 1 hour 45 min she toke a 15 min break then she drives for another 1 hour 20 min
BabaBlast [244]

drove 1h 45 min

break 15 min

drives 1h 20 min

1h 45min+1h 20 min+15min=3h 20min

3h 20 min=3 1/3h

3 1/3h*75 km/hr=<u>250 km</u>

7 0
3 years ago
Write five ordered pairs in a table to represent a relation that is not a function.
QveST [7]

Answer:

Therefore, the relation of the given ordered pairs does NOT represent a function as that x-coordinate values are repeated.

Step-by-step explanation:

We know that a relation is basically a set of input and output values, which are expressed in ordered pairs.

A relation may have any set of ordered pairs.

We also know that a function is a set of ordered pairs in which each x-element has only one y-element associated with it.

Consider the five ordered pairs

x                       y

-2                      1

3                       -4

-2                      -7

4                        6

5                         7

The relation is: {(–2, 1), (3, –4), (–2, –6), (4, 6), (5, 7)}

From the table, it is clear that x-coordinate values are repeated.

In other words, x = -2 twice.

Therefore, the relation of the given ordered pairs does NOT represent a function.

8 0
3 years ago
What is the domain and range for this graph?
11Alexandr11 [23.1K]
Informally, the domain is the set of all possible elements in a set for which there is one and only one output. In interval notation, the domain is (-4, ∞). I am assuming it continues on infinitely to the right because of the arrow. The range is [1, <span>∞). Here, you choose the lowest value on the graph, up to the highest one.</span>
8 0
3 years ago
Help me solve this i need serious help for test ​
olga_2 [115]
Answer for B would be box 8
4 0
2 years ago
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