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mihalych1998 [28]
3 years ago
13

Use the quadratic formula to solve for x.

Mathematics
1 answer:
ivann1987 [24]3 years ago
5 0

Answer:

x = 1/3 + sqrt(5/2)/3 or x = 1/3 - sqrt(5/2)/3

Step-by-step explanation:

Solve for x:

6 x^2 - 4 x = 1

Divide both sides by 6:

x^2 - (2 x)/3 = 1/6

Add 1/9 to both sides:

x^2 - (2 x)/3 + 1/9 = 5/18

Write the left hand side as a square:

(x - 1/3)^2 = 5/18

Take the square root of both sides:

x - 1/3 = sqrt(5/2)/3 or x - 1/3 = -sqrt(5/2)/3

Add 1/3 to both sides:

x = 1/3 + sqrt(5/2)/3 or x - 1/3 = -sqrt(5/2)/3

Add 1/3 to both sides:

Answer: x = 1/3 + sqrt(5/2)/3 or x = 1/3 - sqrt(5/2)/3

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An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the
julsineya [31]

Answer:

  • The maximum height is 136 ft
  • The time it takes to achieve this height is 1.5 s.

Explanation:

<u>1. Function for the height (given):</u>

    h(t)=-16t^2+48t+100

<u />

<u>2. Type of function</u>

That is a quadatic function, whose graph is a parabola that opens downward.

The maximum of the function, i.e. the maximum height, is the vertex of the parabola.

The vertex of a parabola with the genral equation   y=ax^2+bx+c  is at the x-coordinate

                       x=-b/(2a)

<u>3. Time to achieve the maximum height</u>

Substitute b with 48 and a with - 16:

        t=-48/(2(-16))=48/32=3/2=1.5

Then, time when the object achieves the maximum height it 1.5s

<u />

<u>4. Maximum height:</u>

Replace t with 1.5 in the equation, to find the maximum height, h(1.5)

     h(1.5)=-16(1.5)^2+48(1.5)+100=136

Then, the maximum height is 136 ft

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3 years ago
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Josie used 1/2 of the milk for pancakes this morning. If her brother and sister divided what was left to eat cookies with their
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Answer:

1/4 cup of milk

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1. {26, 69, 30, 27, 19, 54, 27}<br><br> Mean: <br> , Median: <br> , Mode: <br> , Range:
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Answer:

Mean:36

Median:27

Mode:27

Range:50

Step-by-step explanation:

Mean: 19+26+27+27+30+53+69/7=36

Median: The middle number in the sequence when arranged in ascending order which is 27

Mode: The number that appeared more than others which is 27

Range: This is the difference between the largest number and the lowest number in the sequence which is 50.

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