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3 years ago

according to the fundamental theorem of algebra , how many zeros does the polynomial below have x^4 +5x^3+10x^2+20x+24

Mathematics

2 answers:

Vinil7 [7]3 years ago

8 0

Answer:

Step-by-step explanation:

the Fundamental Theorem of Algebra states that for any polynomial of degree n, there are n roots, some of which may be complex

The polynomial shown is of degree 4 ( highest exponent of x )

Hence the polynomial has 4 roots/ zeros

laiz [17]3 years ago

5 0

Answer:

Step-by-step explanation:

Cause the highest power is 4

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If f(x)=x-1/x g(x)=x-1 and h(x)=x+1 what is (g•h•f)(x)

eimsori [14]

Answer:

( f o f )(x) = f ( f (x))

= f (2x + 3)

= 2( ) + 3 ... setting up to insert the input

= 2(2x + 3) + 3

= 4x + 6 + 3

= 4x + 9Step-by-step

explanation:

8 0

3 years ago

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Thomas drove 230 miles in 4 hours. What is the ratio of miles to hou

Elena L [17]

115:2 should be the correct answer in reduced form.

3 0

3 years ago

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Please prove this........

Crazy boy [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π → C = π - (A + B)

→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))

→ sin C = sin (A + B) cos C = - cos(A + B)

Use the following Sum to Product Identity:

sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]

cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]

Use the following Double Angle Identity:

sin 2A = 2 sin A · cos A

<u>Proof LHS → RHS</u>

LHS: (sin 2A + sin 2B) + sin 2C

$\text{Sum to Product:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-\sin 2C$

$\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C$

$\text{Simplify:}\qquad \qquad 2\sin (A + B)\cdot \cos (A - B)-2\sin C\cdot \cos C$

$\text{Given:}\qquad \qquad \quad 2\sin C\cdot \cos (A - B)+2\sin C\cdot \cos (A+B)$

$\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]$

$\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B$

$\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C$

LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C $\checkmark$

7 0

3 years ago

Find the value of r so the line that passes through the pair of points has the given slope.

SOVA2 [1]

Answer:

The missing value in the ordered pair is 66

Step-by-step explanation:

Given that:

(12,10) and (-2,r)

Slope = m = -4

We have to find the value of r so that the line has a slope of -4.

Slope is the steepness of line which is denoted by m.

Here,

$x_1=12, y_1=10\\x_2=-2, y_2=r$

Putting the values in slope of line formula,

$-4=\frac{r-10}{-2-12}\\ -4=\frac{10-r}{-14}\\$

Multiplying both sides by -14

$-4*-14=\frac{r-10}{-14}*-14\\56=r-10\\56+10=r\\66=r\\ r=66$

The value of r is 66

Hence,

The missing value in the ordered pair is 66

4 0

3 years ago

Hunter had seven gallons of water in the refrigerator. Of those, two and one-fourth gallons were spring water and one and one-fi

Crank

Answer:

3 11/20

Step-by-step explanation:

Total gallons of water=7

Spring water=two and one-fourth gallon=2 1/4

Filtered water=one and one-fifth

=1 1/5

Spring water+filtered water=2 1/4 + 1 1/5

=9/4+6/5

= 45+24/20

=69/20

=3 9/20

How many gallons of water were not spring or filtered

=Total gallons- (spring+ filtered water)

=7-69/20

=140-69/20

=71/20

=3 11/20

5 0

3 years ago