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valentina_108 [34]
3 years ago
12

Monique is factoring the expression 4x + 16xy. Her work is shown below.

Mathematics
2 answers:
agasfer [191]3 years ago
6 0

Answer:

D. Monique made and error when writing the factored expression.

Step-by-step explanation:

Edge 2020

PtichkaEL [24]3 years ago
4 0

Answer:

D

Step-by-step explanation:

She made an error writing the expression

it should be 4(x + 4y)

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The solutions are x = -9 , x = -5

Step-by-step explanation:

* Lets find the vertex of the parabola

- In the quadratic equation y = ax² + bx + c, the vertex of the parabola

 is (h , k), where h = -b/2a and k = f(h)

∵ The equation is y = x² + 14x + 45

∴ a = 1 , b = 14 , c = 45

∵ h = -b/2a

∴ h = -14/2(1) = -14/2 = -7

∴ The x-coordinate of the vertex of the parabola is -7

- Lets find k

∵ k = f(h)

∵ h = -7

- Substitute x by -7 in the equation

∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4

∴ The y-coordinate of the vertex point is -4

∴ The vertex of the parabola is (-7 , -4)

- Plot the point on the graph and then find two points before it and

 another two points after it

- Let x = -9 , -8 and -6 , -5

∵ x = -9

∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0

- Plot the point (-9 , 0)

∵ x = -8

∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3

- Plot the point (-8 , -3)

∵ x = -6

∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3

- Plot the point (-6 , -3)

∵ x = -5

∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0

- Plot the point (-5 , 0)

* To solve the equation x² + 14x + 45 = 0 means find the value of

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- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates

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∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)

∴ The solutions of the equation are x = -9 and x = -5

* The solutions are x = -9 , x = -5

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3 years ago
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