1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
malfutka [58]
3 years ago
15

Use the Rational Root Theorem to determine all possible rational roots of 5x^3 + 4x^2 + 4x + 10 = 0. Do NOT find the actual root

s.
The roots of a certain polynomial are -2/5, -6, and 4/3. What might the linear factors of the polynomial be?

A) (5x + 2)(x + 6)(3x + 4)

B) (5x + 2)(x – 6)(3x – 4)

C) (5x – 2)(x + 6)(3x – 4)

D) (5x + 2)(x + 6)(3x – 4)

ANSWER BOTH AND SHOW OF EXPLAIN ANSWERS :)
Mathematics
1 answer:
geniusboy [140]3 years ago
5 0
Problem 1

Answers: 
The possible rational roots are: 
-10, -5, -2, -1, -2/5, -1/5, 
10, 5, 2, 1, 2/5, 1/5

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

Explanation:

The first term is 5x^3 with the coefficient 5
The last term is 10

Factors of 10 (last term): 1, 2, 5, 10
Factors of 5 (first coefficient): 1, 5

Divide the factors of 10 over the factors of 5
10/1 = 10
10/5 = 2
5/1 = 5
5/5 = 1
2/1 = 2
2/5 = 2/5
1/1 = 1
1/5 = 1/5

And throw in the minus versions of those results as well: -10, -2, -5, -1, -2, -2/5, -1, -1/5

Combine the two sets and toss out the duplicates
-10, -5, -2, -1, -2/5, -1/5, 
10, 5, 2, 1, 2/5, 1/5

So those are the possible rational roots

=======================================================================

Problem 2

Answer: Choice D) (5x+2)(x+6)(3x-4)

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

Explanation:

I'm going to use the rule
if x = a/b is a root, then (bx-a) is a factor
If we set the factor bx-a equal to zero and solve, then we get
bx-a = 0
bx = a
x = a/b
where b is nonzero

So if x = -2/5 is a root, then
x = -2/5
5x = -2
5x+2 = 0
making (5x+2) a factor

If x = -6 is a root then
x = -6
x+6 = 0
making (x+6) a factor

And if x = 4/3 is a root, then
x = 4/3
3x = 4
3x-4 = 0
making (3x-4) a factor

The three factors found were: (5x+2) and (x+6) and (3x-4)

So one factorization could be (5x+2)(x+6)(3x-4)
which is what choice D is showing


You might be interested in
List the laws of solid friction​
FinnZ [79.3K]
* The force of friction acts in opposite direction in which the surface is having tendency to move .
* the force of friction is equal to force applied to surfaces , so long as surface is at rest .
5 0
3 years ago
Read 2 more answers
Any help would be great!
seropon [69]

Answer:

143 calories

Step-by-step explanation:

We can use a ratio to solve

110 calories      x calories

----------------- = ---------------

28.4 grams         36.92 grams

Using cross products

110* 36.92 = 28.4 * x

Divide each side by 28.4

110*36.92 / 28.4 = x

143 calories = x

8 0
4 years ago
1. y=900(1.27)^x
Sophie [7]

Answer:

The initial value is 900

It is experiencing exponential growth by 27%

Step-by-step explanation:

Exponential functions are in the form y=a(b)^x, where a is the initial value, b is the multiplier, and x is the input, such as how many years past a certain date.

Exponential growth is when the multiplier is above 1.00, or above 100%, because b is determined by 1 + r if you have exponential growth, or 1 - r if you have exponential decay. You will never use negatives with exponential decay.

7 0
2 years ago
I am lazy answer these 3 questios for meh
eimsori [14]

Answer:

#

Tiffany ate ¼ of a pizza. If there were 16 slices of pizza to begin with, how many slices did Tiffany eat?

Solution given;

Since total=16 slices

Tiffany ate =¼ part of pizza

now

Tiffany ate=¼ part of 16 slices=¼*16=4slices

Tiffany ate 4 slices.

#

Katelyn ate ⅓ of an apple pie, and Chad ate 3/8 of the same pie. What fraction of the pie was eaten?

Solution given:

Katelyn ate ⅓ of an apple pie

Chad ate ⅜ of the same pie

now

eaten fraction of the pie =⅓+⅜=\frac{1*8+3*3}{3*8}

<h3>=\frac{17}{24} fraction of the pie was eaten.</h3>

#

Vince has ½ ton of gravel to spread equally in 8 square yards for his driveway. How many tons of gravel will be spread in each square yard?

Solution given:

8square yards=½ ton of gravel

each square yards=½*⅛=\frac{1}{16}ton of gravel

Candice spent 345 hours, and Shane spend 2 10 hours at track practice over the weekend. How many more hours did Candice spend than Shane at track practice?

3 0
3 years ago
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m
olga_2 [115]

The average speed is obtained by finding the slope of the function in the given interval:

v =\frac{y2-y1}{x2-x1}

Substituting values we have:

v =\frac{6-3}{8-4}

Rewriting:

v =\frac{3}{4}

v = 0.75

Then, the generic equation of the line is:

 n-n0 = v (t-t0)

Where,

v: average speed (slope of the line)

(t0, n0): ordered pair that belongs to the line.

Substituting values we have:

 n-6 = 0.75 (t-8)

Answer:

the average speed of the car is:

b. 0.75

an equation of the line is:

b. n-6= 0.75(t-8)

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is 2 accomplishments Katherine Johnson made
    14·1 answer
  • I need to find the value of Y
    5·2 answers
  • HELP MEEE WITH THESE MATH PROBLEMS!!!
    15·1 answer
  • Which of the following results in the expression 0.22 x 86? SVE ME PLZ
    11·1 answer
  • All the events in the sample space that are not part of the specified event are called
    13·1 answer
  • The double number line shows that to make 4 apple pies takes 14 pounds of apples.Select the double number line that correctly la
    6·1 answer
  • 40 pints of juice in 2 containers​
    15·1 answer
  • At what coordinate would you place point B so that it is 1/4 of the distance from A to C?
    13·1 answer
  • (3x - 70)<br> The m TIMED QUIZ PLEASE HURRY
    9·2 answers
  • PLEASE HELP! <br><br> i’ll mark brainliest if you’re correct!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!