All categories

3 years ago

PLEASE HELP ME!!!!! Factor completely b^4 − b^3 + b − 1

Mathematics

1 answer:

Afina-wow [57]3 years ago

7 0

b^4 − b^3 + b − 1
=(b^4 − b^3) + (b − 1)
= b^3(b - 1) + (b - 1)
=(b - 1)(b^3 + 1)

You might be interested in

Emma is standing 10 feet away from the base of a tree and tries to measure the angle of elevation to the top. She is unable to g

Vaselesa [24]

The complete question in the attached figure

step 1
find the tree height for an angle of elevation of 55°
tan 55°=opposite side angle 55°/adjacent side angle 55°
opposite side angle 55°=the tree height h1
adjacent side angle 55°=10 ft
so
tan 55°=h/10-------> h=10*tan 55°-----> h=14.28 ft

step 2
find the tree height for an angle of elevation of 75°
tan 75°=opposite side angle 75°/adjacent side angle 75°
opposite side angle 75°=the tree height h2
adjacent side angle 75°=10 ft
so
tan 75°=h2/10-------> h2=10*tan 75°-----> h2=37.32 ft

therefore

the height of the tree is within the range [14.26,37.32]

Part 1) 4.2 ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

Part 2) 14.7 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 3) 24.4 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 4) 33.9 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 5) 39.1ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

Part 6) 58.7 ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

4 0

3 years ago

Use substitution to solve the system of equations.

polet [3.4K]

The answer is (3,-6)

8 0

3 years ago

Read 2 more answers

Olivia has taken an initial dose of a prescription

mrs_skeptik [129]

Answer:

0.56 milligrams

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

M(6) = 50·e^(-0.75·6) = 50·e^-4.5 ≈ 0.56 . . . . milligrams

8 0

3 years ago

Merrill is playing a simple game of dice. For every 6 rolled, Merrill will win $5. For any other number, he must pay $2. How muc

Schach [20]

Solution -

The probability of getting 6 from a single roll of a fair dice = $\frac{1}{6}$

The probability of getting any other number rather than 6 would be $1-\frac{1}{6} = \frac{5}{6}$

So when the outcome is 6, then he wins $5 ,otherwise he has to pay $2

E(X) = Expectation value = $(\frac{1}{6} )(5) - (\frac{5}{6} )(2)$ ( ∵ $5 gain so +ve and $2 loss so -ve)

= $\frac{-5}{6}$

∴ So Merrill will lose $\frac{5}{6}$ dollar

7 0

3 years ago

Read 2 more answers

Determine the roots of f(x) = -12-2.1x+18x^2-2.75x^3 graphically. in addition, determine the first root of the function with

vesna_86 [32]

The given function is that is a cubic polynomial

$f(x)=-12-2.1x+18x^2-2.75x^3$

when arranged in descending order that is from highest degree to lowest degree

$f(x)=-2.75x^3+18x^2-2.1x-12$

Since it is a three degree polynomial it has three roots.

According to rational root theorem , the possible roots of the above expression that is factors of $\frac{12}{2.75}$ = $\frac{48}{11}$ are $\pm1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24, \pm 48, \pm\frac{1}{11}, \pm\frac{2}{11}, \pm\frac{3}{11}\pm\frac{4}{11}\pm\frac{6}{11},\pm\frac{8}{11},\pm\frac{12}{11}, \pm\frac{24}{11},\pm\frac{48}{11}$

As you can see from the graph all roots of this polynomial are real.

The smallest positive root is 0.954 and smallest negative root are -0.724.

4 0

2 years ago