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Aleksandr [31]
3 years ago
6

Which graph represents the parent function of y=x^2 −5?

Mathematics
1 answer:
hjlf3 years ago
3 0
From the function given:
y=x^2-5
this can be written as:
y=x^2+0x-5
writing in vertex form we get:
y=(x-h)^2+k
where: (h,k) is the vertex
y=(x-0)^2-5
thus the vertex is at (0,-5)
the parent function is y=x^2, thus the graph of the parent function is First graph
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Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?
Lubov Fominskaja [6]

Answer:

  yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

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For the first parabola, the point of intersection is ...

  y^2 = 4(-y-1)

  y^2 +4y +4 = 0

  (y+2)^2 = 0

  y = -2 . . . . . . . . one solution only

  x = -(-2)-1 = 1

The point of intersection is (1, -2).

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For the second parabola, the equation is the same, but with x and y interchanged:

  x^2 = 4(-x-1)

  (x +2)^2 = 0

  x = -2, y = 1 . . . . . one point of intersection only

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If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

7 0
3 years ago
"the quotient of a number and 4"
ladessa [460]

Answer:

a number divided by 4

Step-by-step explanation:

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so n over 4, or n divided by 4

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3 years ago
A jar contains six blue marbles and five red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you ch
TEA [102]

The jar has 6+5=11 marbles.

We have to find the probability of the following event:

1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red

2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)

The probability of the first event is:

P_1=\frac{5}{11}

The probability of the second event is:

P_2=\frac{4}{10}=\frac{2}{5}

The probability of the both events to happen is:

P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818

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3 years ago
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Irina18 [472]
The perimeter would be 84
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3 years ago
Solve for x: 4 = (-8) +3x. Will you please help?
Zanzabum
8 + 4 = 3x
12 = 3x
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x= 4
8 0
3 years ago
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