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Vilka [71]
3 years ago
6

Select the correct text in the table. Use the fundamental theorem of algebra to determine whether each statement is sometimes tr

ue, always true, or never true.
1. A quadratic function has 2 distinct roots. always sometimes never
2. A cubic function has at least 1 real root. always sometimes never
3. A function with a degree of 5 has 5 roots. always sometimes never

4. A quadratic function can have only 1 complex solution. always sometimes never
Mathematics
2 answers:
Mariana [72]3 years ago
6 0

Answer:

MY ANSWER IS CORRECT IN PLATO!!!

1. Sometimes

2. Always

3. Always

4. Never

Step-by-step explanation:

1. A quadratic function has 2 distinct roots SOMETIMES

2. A cubic Function has at least 1 root ALWAYS

3. A function with a degree of 5 has 5 roots ALWAYS

4. A quadratic function can have only 1 complex solution NEVER

I JUST GOT 100% on the quiz in PLATO

yan [13]3 years ago
5 0

Answer:

1. Sometimes

2. Sometimes

3. Always

4. Sometimes

Step-by-step explanation:

1. Quadratic function : in which maximum power of x is two.

The roots of quadratic function can be either equal or different.

For example:

  • x^{2} -2x+1 will have two equal roots i.e. 1 and 1.
  • x^{2} -3x+2 will have two different roots i.e. 1 and 2.

So, <em>sometimes </em>is the correct answer.

2. Cubic function has atleast 1 real root.

Cubic function has maximum power of x as 3.

If the coefficients are real numbers then atleast 1 real root.

If the coefficients are imaginary in nature, then this is not true.

For example:

Cubic equation x^3 +i = 0 does not have any real root.

Cubic equation x^3 +1 = 0 has a real root x = -1.

So, it is sometimes true.

3. A function with degree 5 i.e. maximum power of x as 5 will have 5 roots.

It is always true that a function will have number of roots equal to its degree.

4. Quadratic function can have only 1 complex solution.

Two complex solutions are also possible for a quadratic function.

For example:

x^{2} +1=0 will have two imaginary roots: x=i, -i

It is also possible to have 1 complex solution,

For example:

(x-1)(x-i) = 0 will have one complex root and one real root.

So, the statement is <em>sometimes </em>true.

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What is the minimum number of degrees that an equilateral triangle can be rotated before it carries onto itself?
mash [69]
Since the triangle has equal sides it will carry onto it self at 120, since it can rotate 360 grades only and it has 3 sides so it will rotate in one third of 360 so 120

i hope i helped you
7 0
3 years ago
Read 2 more answers
Here is a tunnel for a toy train.
jonny [76]

The <em>total</em> area of all six faces of the tunnel is 614.197\pi square centimeters.

<h2>Procedure - Surface area of a tunnel for a toy train</h2>

The surface area of the solid (A) used to represent the tunnel for a toy train is the sum of its six faces (two <em>semicircular</em> sections, inner <em>semicircular</em> arc section, outer <em>semicircular</em> arc section, two rectangles).

<h3>Determination of the surface area of the tunnel based on information of the diagram</h3>

We calculate the surface area as following:

A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)

A = 614.197\pi\,cm^{2}

The <em>total</em> area of all six faces of the tunnel is 614.197\pi square centimeters. \blacksquare

To learn more on surface areas, we kindly invite to check this verified question: brainly.com/question/2835293

5 0
2 years ago
Suppose Austin, Texas, is hit by a tornado that destroys 25 percent of the housing in the area. Would you expect the total expen
notsponge [240]

Answer:

<u>greater than what it was before</u>

Step-by-step explanation:

<em>Remember</em>, a tornado usually causes significant structural damages to houses within its area of impact., and this requires running expenses to repair the damage.

Hence,<u> since the term </u><u>expenditure, </u><u>also implies expenses; we can expect the total expenditure on housing after the tornado to be </u><u>greater than</u><u> what it was before the tornado since families would be paying for repairs.</u>

4 0
2 years ago
2/3 is less than 4/5 true or false
mojhsa [17]

Answer: False

Step-by-step explanation:

When comparing fractions such as 2/3 and 4/5, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

6 0
3 years ago
Read 2 more answers
What is a solutions of x^2-2x+10=0?​
Debora [2.8K]

Answer:

x = 1± 3i

Step-by-step explanation:

x^2-2x+10=0

We can complete the square to solve by subtracting 10 from each side

x^2-2x+10-10=-10

x^2 -2x = -10

We need to add (2/2) ^2  to each side or 1

x^2 -2x+1 = -10 +1

x^2 -2x+1 = -9

The left side factors into (x- (2/2) ) ^2

(x-1) ^2 = -9

Take the square root of each side

sqrt((x-1) ^2 =± sqrt(-9)

x-1 = ±sqrt(-1) sqrt(3)

Remember the sqrt(-1) = i

x-1 = ± 3i

Add 1 to each side

x-1+1 = 1± 3i

x = 1± 3i

8 0
2 years ago
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