Factor the expression 5x^3 - x^2 + 5x - 1

Answers

Answer 1

Answer: Hello,

5x^3-x^3+5x-1=x²(5x-1)+(5x-1)=(5x-1)(x²+1)=(5x-1)(x-i)(x+i)

Answer 2

Answer: $5 x^(3) - x^(2) + 5x - 1$

Group like terms
$( 5x^(2) - x^(2) ) + (5x - 1)$

Find the common factor of each term and simplify
$x^(2) (5x - 1) + 1 (5x - 1)$
$( x^(2) + 1) (5x - 1)$

Additional :-
Find the roots of each of the terms:
(i) $( x^(2) + 1)$
- using the quadratic equation ( $x = \frac{-b (+ or -) \sqrt{ b^(2) - 4ac } }{2a}$ )
- $\frac{-0 + \sqrt{0^(2 - 4(1)(1)) } }{2}$ OR $\frac{-0 - \sqrt{0^(2 - 4(1)(1)) } }{2}$
- Since the discriminant is negative ( $√(-4)$ ) [a negative number cannot be rooted] then this equation has no real roots (imaginary roots)

(ii) $5x - 1$
- Simply Solve for x
5x - 1 = 0
5x = 1
x = $(1)/(5)$

Thus the only solution this has or the only root this expression has is $(1)/(5)$ OR 0.2

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randy's garden 3 rows of carrots with 3 plants in each row. Next year he plans to plant 4 times the number of rows. How many plants will he have next year

Answers

Answer:

Currently, Randy has 3 rows of carrots with 3 plants in each row, which gives a total of 3 * 3 = 9 plants.

Next year, Randy plans to plant 4 times the number of rows. Therefore, he will have 4 * 3 = 12 rows of carrots.

If each row still has 3 plants, then next year Randy will have a total of 12 * 3 = 36 plants.

Answer: 36 plants

Step-by-step explanation: 4 times the amount of rows is 12 (4x3) and 12 x 3 (amount of plants in each row) is equal to 36 plants

A rectangle has a length of 7 and a width of w. What is an expression for the perimeter?

Answers

(7x2)+(2x w). Times 2 because you need each side and the opposite sides are the same size.

Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?

Answers

If there is a 22.4% chance that a soccer player will make 4 shots in a row, then the probability that he/she WON'T make 4 shots in a row is...

100 -22.4 = 77.6%

So the number of simulations that he/she will miss at least one shot in 2500 simulations would be...

2500 x 77.6% =
2500 x .776 = 1940

What's the verbal expression for the algebraic expression 1/8y .?

Answers

your answer is going to be one over eight times y

Jenny wants a total of 12 barbie dolls by the time she is 9 years old.She has 4 barbie dolls. how many more does she need?

Answers

Answer:

she needs 8

Step-by-step explanation:

12-4=8

Please help with the whole page

Thank you :)

Answers

First Part:
A cube has all equal sides and therefore the formula of:
-Volume of Cube=side³
=3³=27 cm³
-Volume of Cuboid=Area of base×Height of prism
1st prism =4×3×1=12 cm³
2nd prism =7×4×9=252 cm³
3rd prism   =3.5×5×6=105 cm³
Second part:
Volumes are given with one side missing
  V=Area of base×Height of Prism
1st prism
360=6×12×x
360=72x
$(360)/(72)$ = $(72x)/(72)$
5 cm=x
Check: V=6×12×5=360 cm³
2nd question:
break it into 2 parts:
1st: find the volume of the first cuboid:
V=3×3×4=36 cm³
So now we know the volume of the second cuboid since both of them have the same volume.
2nd: 36=6×4×x
36=24x
$(36)/(24) = (24x)/(24)$
1.5 cm=x
Check: 1.5×6×4=36 cm³

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