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2 years ago

The discriminant of a quadratic equation is equal to -8, which statement describes the roots?

Mathematics

1 answer:

Maslowich2 years ago

6 0

Answer:

(a) There are two complex roots

Step-by-step explanation:

The discriminant of a quadratic function describes the nature of its roots:

negative: two complex roots
zero: one real root (multiplicity 2)
positive: two distinct real roots.

Your discriminant of -8 is negative, so it indicates ...

There are two complex roots

_____

Additional comment

We generally study polynomials with real coefficients. These will never have an odd number of complex roots. Their complex roots always come in conjugate pairs.

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If the coefficient of determination for a data set is 0.25 and the SSE for the data set is 6, what is the SST for the data set ?

Cerrena [4.2K]

Answer: The SST for the data set is 8.

Step-by-step explanation:

Since we have given that

Coefficient of determination (R²) = 0.25

SSE for the data = 6

SST = ?

As we know the formula for coefficient of determination:

$R^2=1-\dfrac{SSE}{SST}\\\\0.25=1-\dfrac{6}{SST}\\\\0.25-1=-\dfrac{6}{SST}\\\\-0.75=-\dfrac{6}{SST}\\\\SST=\dfrac{6}{0.75}\\\\SST=8$

Hence, the SST for the data set is 8.

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3 years ago

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If both the numerator and denominator of 48/64 are divided by 8, the fraction will be in lowest terms. True False

Licemer1 [7]

If 48/64 are both divided by 8 you would get 6/8! these can still be reduced to 3/4, So FALSE!

4 0

3 years ago

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In the figure above, PQRS is a circle. If PQT and SRT are straight lines, find the value of x.

Elena L [17]

Given:

PQRS is a circle, PQT and SRT are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

$m\angle SPQ+m\angle QRS=180^\circ$

$81^\circ+m\angle QRS=180^\circ$

$m\angle QRS=180^\circ-81^\circ$

$m\angle QRS=99^\circ$

Now, SRT is a straight line.

$m\angle QRT+m\angle QRS=180^\circ$ (Linear pair)

$m\angle QRT+99^\circ=180^\circ$

$m\angle QRT=180^\circ-99^\circ$

$m\angle QRT=81^\circ$ ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

$m\angle PQR=m\angle QRT+m\angle QTR$

$x=81^\circ+22^\circ$

$x=103^\circ$

Therefore, the value of x is 103 degrees.

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3 years ago

A cube-shaped box has a volume of 1/8 of a cubic meter. What is the perimeter of each of its

belka [17]

Given:

The volume of a cube-shaped box is $\dfrac{1}{8}$ cubic meter.

To find:

The perimeter of each of its faces.

Solution:

Let "a" be the side length of the cube shaped box. Then the volume of the box is:

$V=(side)^3$

$V=a^3$

It is given that the volume of a cube-shaped box is $\dfrac{1}{8}$ cubic meter.

$a^3=\dfrac{1}{8}$

Taking cube root on both sides, we get

$a=\dfrac{1}{2}$

Now, the perimeter of each face of a cube is:

$P=4a$

Where, a is the side length of the cube.

Putting $a=\dfrac{1}{2}$ , we get

$P=4\times \dfrac{1}{2}$

$P=2$

Therefore, the perimeter of each face of a cube-shaped box is 2 meters.

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3 years ago

How do you get the domain and range of a bar graph

Murljashka [212]

X is the domain and y is the range

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2 years ago