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jekas [21]
3 years ago
9

How many solutions does the system have?

Mathematics
1 answer:
umka21 [38]3 years ago
3 0

One solution

<h2>Explanation:</h2>

For a system of linear equations in two variables, we could have three possible cases:

<h3>Case 1. No solution.</h3>

This happens when the lines are parallel and have different y-intercepts.

<h3>Case 2. One solution.</h3>

This happens when the lines intersect at a single point.

<h3>Case 1. Infinitely many solutions</h3>

This happens when the lines are basically the same having the same slope and y-intercept.

So, let's rewrite our lines in Slope-intercept form y=mx+b:

Line \ 1: \\ \\  4x-2y = 8 \\ \\ 2y=4x-8 \\ \\ y=\frac{4}{2}x-\frac{8}{2} \\ \\ y=2x-4 \\ \\ \\ Line \ 2: \\ \\ 2x + y = 2 \\ \\ y=-2x+2

As you can see, they have different slopes and y-intercepts. So they will intersect at a single point which is the solution of the system. By using graphing tool we get that this point is (1.5, -1) as indicated in the figure below.

<h2>Learn more:</h2>

Parametric equations: brainly.com/question/10022596

#LearnWithBrainly

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6 0
3 years ago
You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4,
Kitty [74]

Answer:

D(4,-3)

Step-by-step explanation:

Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)

Let the coordinate of the fourth vertex be D(x,y).

We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.

The diagonals are BD and AC

Midpoint of BD = Midpoint of AC

\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3

The coordinates of the fourth vertex is D(4,-3)

3 0
3 years ago
Question 1
Vikki [24]

Answer:

(B)15,36,39

Step-by-step explanation:

To determine which of the line segments could create a Right Triangle, we check if it satisfies the Pythagoras Theorem, taking the longest part to be the Hypotenuse in all cases.

By Pythagoras Theorem: Hypotenuse^2=Opposite^2+Adjacent^2

In  15,30,35

35^2\neq 15^2+30^2\\1225\neq 1125

In 15,36,39

39^2=36^2+15^2\\1521=1521

In 15, 20, 29

29^2\neq 15^2+20^2\\841\neq 625

In 5,15,30

30^2\neq 15^2+5^2\\900\neq 250

We can see that only 15,36,39 satisfies the required condition and thus it could be used to create a right triangle.

4 0
3 years ago
Estimate the product of 67 x 23<br> by rounding to the nearest ten.
elena-14-01-66 [18.8K]

Answer:

1400

Step-by-step explanation:

67 rounds to 70 because 7 is bigger than 5 so it rounds up. 23 rounds down since 3 is smaller than 5.

So, 70x20=1400

5 0
2 years ago
ali sorced 66 and 72 marks respectively. for his two tests what is the lowest marks he must have sorced for his third test if an
dimaraw [331]

Answer:

87

Step-by-step explanation:

66 + 72 + 87 = 225

225 / 3 = 75

6 0
2 years ago
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