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3 years ago

Given that x=1.5 is the only solution to the equation 4x^2 - ax + b = 0, find the values of a and b. Show all workings.

1 answer:

5 0

If x = 1.5 is the only solution to the equation 4x² - ax + b =0 then

4x² - ax + b = 4(x - 1.5)² |use p² - 2pq + q² = (p - q)²

4x² - ax + b = 4(x² - 2x · 1.5 + 1.5²)

4x² - ax + b = 4(x² - 3x + 2.25)

4x² - ax + b = 4x² - 12x + 9 |subtract 4x² from both sides

-ax + b = -12x + 9

therefore

-a = -12 ⇒ a = 12 and b = 9

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3 years ago

determine an equation and the radius for the circle that has its centre at the origin (0,0) passes through the point A 4-3

g100num [7]

Given:

The center of the circle is at (0,0).

The circle passes through the point A(4,-3).

To find:

The radius and the equation of the circle.

Solution:

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The radius of the circle is the distance between the points (0,0) and (4,-3).

$r=\sqrt{(4-0)^2+(-3-0)^2}$

$r=\sqrt{(4)^2+(-3)^2}$

$r=\sqrt{16+9}$

$r=\sqrt{25}$

$r=5$

So, the radius of the circle is 5 units.

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is center of circle and r is the radius.

Putting h=0, k=0, r=5, we get

$(x-0)^2+(y-0)^2=5^2$

$x^2+y^2=25$

Therefore, the radius of the circle is 5 units and the equation of the circle is $x^2+y^2=25$ .

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3 years ago

What’s 4+5+6+7+8. Plzzzzzzzz

irina1246 [14]

It's 30

Hope that helped!

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Leya [2.2K]

Answer:

So first, there is an acronym for the strategy, KFC.

°π°

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Flip the second fraction. Ex, 4/5 ÷ 5/1

Change symbol. Ex, 4/5 ÷ 5/1 turns into 4/5x5/1

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3 years ago

2. The temperature during the night dropped 2 degrees every hour. How many degrees did the temperature drop altogether after 3 1

Alenkasestr [34]

If it dropped 2° every hour then after 3 hours it would drop (2*3=6) 6°

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6 + 0.5 = 6.5°

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3 years ago

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