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3 years ago

Form a polynomial whose zeros and degree are given.

Mathematics

1 answer:

andriy [413]3 years ago

5 0

Answer:

$f(x)=x^{3}-7x^{2}+16x-12$

Step-by-step explanation:

we know that

Is a polynomial of degree 3

The roots are

x=3, multiplicity 1 -----> (x-3)=0

x=2, multiplicity 2 -----> (x-2)(x-2)=0

The equation of the polynomial is

$f(x)=a(x-3)(x-2)(x-2)\\\\f(x)=a(x-3)(x-2)^{2}$

The leading coefficient is 1

a=1

substitute

$f(x)=(1)(x-3)(x-2)^{2}$

$f(x)=(x-3)(x-2)^{2}$

Convert to expanded form

$f(x)=(x-3)(x^{2}-4x+4)\\\\f(x)=x^{3}-4x^{2}+4x-3x^{2}+12x-12\\\\f(x)=x^{3}-7x^{2}+16x-12$

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Use The Alternate Interior Angles Theorem diagram to answer the question. Give the missing reason in this proof for the letter g

Serjik [45]

The missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

Two angles lying opposite each other along a transversal, and are within the two lines crossed by the transversal are referred to as alternate interior angles.

According to the Alternate Interior Angles Theorem, the two alternate interior angles are congruent to each other.

Let's state out our proof using the image given:

Statement 1: line l is parallel to line m

Reason: Given

Statement 2: $\angle 2 \cong \angle 6$

Reason: Corresponding Angles (both angles occupy the same corner, hence they correspond to each other. Corresponding angles have the same measure).

Statement 3: $\angle 4 \cong \angle 2$

Reason: Vertical angles (both angles are directly opposite each other as they share the same point, which makes them vertical angles. Vertical angles have equal measure).

Statement 4: $\angle 6\cong \angle 4$

Reason: Alternate Interior Angles (applying the transitive property which says if a = b, and b = c, then a = c, therefore, since $\angle 2 \cong \angle 6, $ and $ \angle 4 \cong \angle 2, $ then $ \angle 6 \cong \angle 4$ )

In conclusion, the missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

Learn more here:

brainly.com/question/18898800

4 0

2 years ago

The following table shows the final scores for a group of mini golf reset adventure Land find the median number of strokes

solong [7]

The median would be the middle data point. Let’s list the points

25, 26, 31, 39, 32, 57

Put them in order from least to greatest

25, 26, 31, 32, 39, 57

There is an even amount of data so take the two center points and divide by 2

31 + 32 = 63

Divide by 2

31.5

There would be an average of 31.5 strokes

7 0

3 years ago

Read 2 more answers

What is the 2nd equvilent fraction to 1/2

zhuklara [117]

Answer:

The 2nd equivalent fraction to 1/2 is 2/4

Step-by-step explanation:

The 2nd equivalent fraction of 1/2 is obtained by multiplying 1/2 by 2/2.

2nd equivalent fraction = 1/2 × 2/2 = 2/4

5 0

3 years ago

Plz help its due tonight!!!!

Natalka [10]

Answer:

Domain is (infinity, infinity) so it would hit every single number of x. The range which is y would be greater than or equal to -3. Range starts at -3 and hits every number above that.

8 0

3 years ago

PLSSSSSS HELP PLS

andreev551 [17]

Answer:

Given ,

student's age = x years.

Also ,

Teacher's age = 2x + 6

And ,

Principal's age = 3x + 10

------------------------------------------

Difference between ages ,

$\bold{(3x + 10) - (2x + 6)} \\\bold{ = > 3x + 10 - 2x - 6} \\ \bold{= > x + 4}$

therefore ,

second option is the correct answer.

hope helpful ~

5 0

2 years ago