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3 years ago

Examine whether x-1 is a factor of the polynomial 4x³+3x²-4x+3

Mathematics

1 answer:

Yuki888 [10]3 years ago

4 0

Answer:

x - 1 is not a factor.

Step-by-step explanation:

By the Factor theorem if x - 1 is a factor then f1) = 0:

f(1) = 4*1^3 + 3*1^2 - 4*1 + 3

= 4 + 3 - 4 + 3

= 6 so it is not a factor.

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Instructions: Solve the following equation for the variable given.

frutty [35]

Answer:

x = -1

Step-by-step explanation:

1/4 (4x - 4) = -2(6x + 7)

1x - 1 = -12x - 14

13x = -13

x = -1

7 0

3 years ago

2/3 b + 5 =20 - b solve for b

Wittaler [7]

Answer:

$b = 9$

Step-by-step explanation:

$\frac{2}{3} b + 5 = 20 - b$

In order to solve for b, we must isolate the variable. We can start by subtracting 5 from both sides.

$\frac{2}{3} b + 5 - 5 = 20 - b - 5$

Simplify.

$\frac{2}{3} b = 15 - b$

Add b to both sides.

$\frac{2}{3} b + b = 15 - b + b$

Simplify.

$\frac{2}{3} b + b = 15$

Multiply everything by 3 to remove the fractions.

$3(\frac{2}{3}b+b) = 3(15)$

Simplify.

2b + 3b = 45

Simplify.

5b = 45

Divide 5 from both sides.

5b ÷ 5 = 45 ÷ 5

Simplify.

b = 9

For more information on solving variables, check out the following answers!

4 0

1 year ago

Read 2 more answers

The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15c

Alexus [3.1K]

Answer:

a) 5.13% probability that all of the offices are filled by members of the debate team

b) 2.56% probability that none of the offices are filled by members of the debate team

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the people are chosen is important, since the first person is the president, the second is the vice president and so on... So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

(a) What is the probability that all of the offices are filled by members of the debate team?

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 8(candidates of the members debate team).

$D = P_{(8,4)} = \frac{8!}{(8-4)!} = 1680$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{1680}{32760} = 0.0513$

5.13% probability that all of the offices are filled by members of the debate team

(b) What is the probability that none of the offices are filled by members of the debate team?

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 7(candidates who are not of the members debate team).

$D = P_{(7,4)} = \frac{7!}{(7-4)!} = 840$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{840}{32760} = 0.0256$

2.56% probability that none of the offices are filled by members of the debate team

7 0

3 years ago

Select 2 strategies that we can use to add 438 + 362.

yarga [219]

Answer:

Add 438 + 2 + 60 + 300

440 + 360

Step-by-step explanation:

The last one does not add up to 800

Good luck <3

8 0

3 years ago

Read 2 more answers

On a coordinate plane, parallelogram K L M N shown. Point K is at (7, 7), point L is at (5, 3), point M is at (1, 1), and point

Anna007 [38]

Answer:

Option D.

Step-by-step explanation:

Given information: KLMN is parallelogram, K(7,7), L(5,3), M(1,1) and N(3,5).

Diagonals of a parallelogram bisect each other.

If diagonals of a parallelogram are perpendicular to each other then the parallelogram is a rhombus.

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the rate of change is

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of KM is

$m_1=\frac{1-7}{1-7}=1$

Slope of LN is

$m_2=\frac{5-3}{3-5}=-1$

The product of slopes of two perpendicular lines is -1.

Find the product of slopes.

$m_1\cdot m_2=1\cdot (-1)=-1$

The product of slopes of KM and NL is -1. It means diagonals are perpendicular and KLMN is a rhombus.

Therefore, the correct option is D.

4 0

3 years ago

Read 2 more answers

Examine whether x-1 is a factor of the polynomial 4x³+3x²-4x+3​

Examine whether x-1 is a factor of the polynomial 4x³+3x²-4x+3