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NeX [460]
2 years ago
7

(a) Use the fundamental theorem of algebra to determine the number of roots for 2x^2 + 4x + 7

Mathematics
1 answer:
zysi [14]2 years ago
4 0

Answer:

Step-by-step explanation:

A 2nd order polynomial such as this one will have 2 roots; a 3rd order polynomial 3 roots, and so on.

The quadratic formula is one of the faster ways (in this situation, at least) in which to find the roots.  From 2x^2 + 4x + 7 we get a = 2, b = 4 and c = 7.

Then the discriminant is b^2 - 4ac, or, here, 4^2 - 4(2)(7), or -40.  Because the discriminant is negative, we know that the roots will be complex and unequal.

Using the quadratic formula:

       -4 ±√[-40]         -4 ± 2i√10

x  = ------------------ = ------------------

                4                       4

                                       -2 ± i√10

Thus, the roots are x = ------------------

                                               2

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Find the slope given the following information <br> (3,7) and (-4,10)
hram777 [196]

Answer:

m=-3/7

Step-by-step explanation:

m=rise/run=Δy/Δx

m=y2−y1/x2−x1

m=10−7/−4−3

m=3/−7

m=−3/7

6 0
1 year ago
How do you represent the five in 6.75
Mila [183]
It is in the hundreths place if that answers your question.
3 0
3 years ago
Can anyone help me?
goldfiish [28.3K]

Given:

A right angle triangle ABC, right angled at C.

To find:

The measure of θ.

Solution:

In a right angle triangle,

\tan \theta=\dfrac{Opposite}{Adjacent}

In triangle ABC,

\tan \theta=\dfrac{AC}{BC}

\tan \theta=\dfrac{2.7}{5}

\tan \theta=0.54

It can be written as

\theta=\tan^{-1}0.54

\theta\approx 28.369

Therefore, the measure of θ is 28.369.

5 0
3 years ago
Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa
12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

  • Samuel traveled 3 km/h faster than Heather
  • After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
  • Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

   distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

   and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

3 0
3 years ago
Which gives the prices in order, from least to greatest unit rate? Price B, Price A, Price C Price C, Price B, Price A Price C,
MArishka [77]

Answer:

Price B, Price A, Price C

Step-by-step explanation:

Look at the table showing different prices for oranges.

Prices for Oranges

Price A

$2.25 for 6

Price B

$1.30 for 4

Price C

$0.97 for 2

Which gives the prices in order, from least to greatest unit rate?

Price B, Price A, Price C

Price C, Price B, Price A

Price C, Price A, Price B

Price B, Price C, Price A

Price A

$2.25 for 6

Price per orange = $2.25 / 6

= $0.375

Price B

$1.30 for 4

Price per orange = $1.30 / 4

= $0.325

Price C

$0.97 for 2

Price per orange = $0.97 / 2

= $0.485

From least to greatest unit rate

Price B , price A, price C

7 0
2 years ago
Read 2 more answers
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