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4 years ago

Match each system of linear equations with the correct number of solutions

Mathematics

2 answers:

nadezda [96]4 years ago

4 0

Answer:

1 - No solution

2 - Infinitely many solutions

3 - One solution

Step-by-step explanation:

Hey there!

Well to find if there is no solution, one solution, or infinitely many we need to look at the slope and y intercept.

1) - No solution

This is no solution because both slopes are the same meaning they are parallel meaning they have no solution.

2) - Infinitely many solutions

We need to convert into slope-intercept.

y = -x + 4

Since both slopes and y-intercepts are the same they overlap meaning they have infinite solutions.

3) - One solution

Slope-intercept,

y = -3x + 11

y = -1/3x + 1/3

Because both slopes are y-intercepts are different they have only one solution.

Hope this helps :)

kondaur [170]4 years ago

3 0

Answer:

Hey there!

The first equation has no solutions, as it is parallel lines.

The second equation has infinitely many solutions, as it is basically the same line, and the two lines intersect at infinite points.

The third equation is just one solution.

Let me know if this helps :)

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Nat2105 [25]

Answer:

x² - x + c

Step-by-step explanation:

Using the power rule for integration

∫ a $x^{n}$ dx = $\frac{a}{n+1}$ $x^{n+1}$

∫ $\frac{8x-4}{4}$ dx ( divide terms on numerator by 4 )

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Morgarella [4.7K]

Answer:

440

Step-by-step explanation:

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220, 440

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3 years ago

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Gnesinka [82]

The correct answer is B. (3x - 4)(3x + 4)

In order to find this we first can note that the term in the front and the term in the back are both perfect squares. Since the middle term is cancelled out, we can use the difference of two squares to factor.

a^2 - b^2 = (a - b)(a + b)

Since the square root of 9x^2 is 3x, we can use that for a. Since the square root of 16 is 4, we can use that b.

(3x - 4)(3x + 4)

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3 years ago

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Step-by-step explanation:

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2 years ago

Read 2 more answers

A parabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5. The equation that represents the parabola is

Xelga [282]

Answer:

In vertex form the equation is $y=-\frac{1}{2}(x-2)^2+2$

In standard form the equation is $y=-\frac{1}{2}x^2+2x$

Step-by-step explanation:

The equation of the directrix tells us that this is an x-squared parabola. Because the directrix is above the vertex, the parabola will open downward. The vertex form of this equation is:

$4p(y-k)=-(x-h)^2$

where p is the number of units between the directrix and the vertex. The number of units here is .5 or 1/2. Filling in the coordinates of the vertex and the p value of 1/2:

$4(.5)(y-2)=-(x-2)^2$