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Mademuasel [1]
3 years ago
8

Solve this equation using the radical equation method

Mathematics
1 answer:
Yuki888 [10]3 years ago
6 0
The domain:
3x+6\geq0\ \ |-6\\3x\geq-6\ \ \ |:3\\x\geq-2\\\\D:x\in\left< -2;\ \infty\right)

2x=\sqrt{3x+6}-1\ \ \ |+1\\\\2x+1=\sqrt{3x+6}\ \ \ \ |^2\\\\(2x+1)^2=\left(\sqrt{3x+6}\right)^2\ \ \ |use:\ (a+b)^2=a^2+2ab+b^2\\\\(2x)^2+2\cdot2x\cdot1+1^2=3x+6\\\\4x^2+4x+1=3x+6\ \ \ \ |-3x-6\\\\4x^2+x-5=0\\\\4x^2-4x+5x-5=0\\\\4x(x-1)+5(x-1)=0\\\\(x-1)(4x+5)=0\iff x-1=0\ \vee\ 4x+5=0\\\\x=1\ \vee\ 4x=-5\\\\x=1\in D\ \vee\ x=-1.25\in D

Answer:\ \boxed{x=-1.25\ \vee\ x=-1}
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Andre45 [30]

Answer:

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c) (-1,-9)

d) x intercepts; (2,0) and (-4,0)

y intercept is (0,-8)

Step-by-step explanation:

a) As we can see, the parabola faces upwards

b) To find the axis of symmetry equation, we look at the plot of the graph and see the point through the vertex of the parabola that exactly divides the parabola into two equal parts

The x-value that the line passes through here is the point x = -1 and that is the equation of the axis of symmetry

c) The vertex represents the lowest point of the circle here,

As we can see, this is the point through which the axis of symmetry passes through to make a symmetrical division of the parabola

We have the coordinates of this point as

(-1,-9)

d) The intercepts

The x-intercept are the two points in which the parabola crosses the x-axis

We have this point as 2 and -4

The x-intercepts are at the points (2,0) and (-4,0)

For the y-intercept; it is the y-coordinate of the point at which the parabola crosses the y-axis and this is the point (0,-8)

5 0
3 years ago
A 5 person sports team has an average 40 yard dash time of 5. 7 seconds. When a 6th player is added to the team, the new mean is
DanielleElmas [232]

The new player's personal time  is 4.5 seconds.

<h3>What is the new player's personal time?</h3>

The first step is to determine the total time the 5 persons complete the dash.

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The second step is to determine the total time for the 6 people to complete the dash.

Total time = 6 x 5.5 = 33 seconds

The third step is to find the difference of the time in the previous two steps: 33 - 28.5 = 4.5 seconds

To learn more about mean, please check: brainly.com/question/25842202

6 0
2 years ago
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tresset_1 [31]
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4 0
2 years ago
Read 2 more answers
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Ipatiy [6.2K]
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3 years ago
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