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3 years ago

Which number produces a rational number when added to 1/4

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

7 0

Answer:

0.44

Step-by-step explanation:

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Use the discriminant to determine the number of real solutions for the equation below.

Murljashka [212]

Answer:

there is one real solution

Step-by-step explanation:

use the quadratic formula. what is in the square root is called the discriminant.

since it came out to 0 there is one real solution

5 0

3 years ago

5. Find the discriminant of 15x2 = 4x – 1 and describe

diamong [38]

Answer:

a) The discriminant of the equation = - 44

b)The nature of the roots will be imaginary.

c) $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

Step-by-step explanation:

Here, the given expression is $15x^{2} = 4x -1$

or, $15x^{2} - 4x + 1 = 0$

Now the discriminant (D) of a quadratic equation $ax^{2} +b x + c = 0$

D = $b^{2} - 4ac = (-4)^{2} - 4(15) (1) = 16 - (60) = -44$

Hence, the discriminant of the equation = - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula : $x = \frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}$

So, here $x = \frac{-(-4) \pm \sqrt{D} }{2a} = \frac{4 \pm \sqrt{(-44 )} }{30}$

So, either $x = \frac{4 + \sqrt{(-44 )} }{30} or, x = \frac{4 - \sqrt{(-44 )} }{30}$

or, $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

8 0

3 years ago

The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

Goryan [66]

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

$\cos(60 \degree) = \frac{altitude}{hypotenuse}$

$\cos(60 \degree) = \frac{altitude}{8}$

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

$\sin(60 \degree) = \frac{4 - y}{y}$

$y\sin(60 \degree) = 4 - y$

$y\sin(60 \degree) + y= 4$

$(\sin(60 \degree) + 1)y= 4$

$y= \frac{4}{\sin(60 \degree) + 1}$

$y = 16 - 8 \sqrt{3}$

y=1.857

The diameter is 2y

$d = 32 - 16 \sqrt{3}$

=2(1.875)

The length of a Diameter is 3.714

7 0

3 years ago

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If $400 is invested at the rate of 6% for one year, what will be the total value of the investment (the amount)? $42.40 $424.00

ValentinkaMS [17]

The total value would be the amount he put in plus the amount he earns in interest. The answer should be 424

8 0

3 years ago

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PLEASE HELP VERY CONFUESED

Eva8 [605]

V=(4/3)pir^3
r=3
V=(4/3)pi3^3
V=36pi
v=113.04 cubic feet

7 0

3 years ago

Read 2 more answers