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3 years ago

If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.

Mathematics

1 answer:

klio [65]3 years ago

4 0

<h3>Answer:</h3>

±12 (two answers)

<h3>Explanation:</h3>

Suppose one root is a. Then the other root will be -3a. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:

(a)(-3a) = -27/4

a² = -27/(4·(-3)) = 9/4

a = ±√(9/4) = ±3/2

Then the other root is

-3a = -3(±3/2) = ±9/2 . . . . . . the roots will have opposite signs

We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...

-(a + (-3a)) = b/4

2a = b/4

b = 8a = 8·(±3/2)

b = ±12

_____

Check

For b = 12, the equation factors as ...

4x² +12x -27 = (2x -3)(2x +9) = 0

It has roots -9/2 and +3/2, the ratio of which is -3.

For b = -12, the equation factors as ...

4x² -12x -27 = (2x +3)(2x -9) = 0

It has roots 9/2 and -3/2, the ratio of which is -3.

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BC has endpoints B(-3,-5) and C(12,12). FInd the coordinates of the midpoint of BC

forsale [732]

Answer:

(9/2, 7/2)

Step-by-step explanation:

The easiest way to remember how to do this problem is to average the x-coordinates and average the y-coordinates.

So, in your problem (-3 + 12)/2 = 9/2 and (-5 + 12)/2 = 7/2

The midpoint is (9/2, 7/2)

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3 years ago

Find the amount after 2 years for 25000 at 10% pa compounded annually and halfyearly

Molodets [167]

Answer:

8358.7

Step-by-step explanation:

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3 years ago

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kkurt [141]

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5 0

3 years ago

Determine whether a figure with the given vertices is a rectangle using the Distance Formula.

Alex Ar [27]

Answer:

Yes; Opposite sides are congruent, and diagonals are congruent.

Step-by-step explanation:

we have

$A(4, -7), B(4, -2), C(0, -2), D(0, -7)$

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the length of the sides

Find the distance AB

substitute the values

$d=\sqrt{(-2+7)^{2}+(4-4)^{2}}$

$d=\sqrt{(5)^{2}+(0)^{2}}$

$AB=5\ units$

Find the distance BC

substitute the values

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

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

$BC=4\ units$

Find the distance CD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-0)^{2}}$

$d=\sqrt{(-5)^{2}+(0)^{2}}$

$CD=5\ units$

Find the distance AD

substitute the values

$d=\sqrt{(-7+7)^{2}+(0-4)^{2}}$

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

$AD=4\ units$

Compare the length sides

AB=CD

BC=AD

therefore

Opposite sides are congruent

step 2

Find the length of the diagonals

Find the distance AC

substitute the values

$d=\sqrt{(-2+7)^{2}+(0-4)^{2}}$

$d=\sqrt{(5)^{2}+(-4)^{2}}$

$AC=\sqrt{41}\ units$

Find the distance BD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-4)^{2}}$

$d=\sqrt{(-5)^{2}+(-4)^{2}}$

$BD=\sqrt{41}\ units$

Compare the length of the diagonals

AC=BD

therefore

Diagonals are congruent

The figure is a rectangle, because Opposite sides are congruent, and diagonals are congruent

8 0

4 years ago

Read 2 more answers

In a basketball skills competition, Corson successfully made 5 of 7 shots and Charleigh made 3 of 5

xxTIMURxx [149]

Answer:

Corson had a better performance at the skills competition.

Step-by-step explanation:

In order to determine which player had a better performance at the skills competition, we need to find the percentage performance of both the players.

Therefore,

Corson's percentage performance

$=\frac{5}{7}\times 100= 71.43%$

Charleigh's percentage performance

$=\frac{3}{5}\times 100= 60%$

$\because$ Corson's percentage performance > Charleigh's percentage performance

So, Corson had a better performance at the skills competition.

6 0

3 years ago