MATHEMATICS COLLEGE

What is a root function of the polynomial function F(x)= x^3 + 3x^2 - 5x - 4

Answers

Answer 1

Answer: This is your answer
Xxxx

Answer 2

Answer:

Step-by-step explanation:

Factor by grouping.

f(x) = x³ + 3x² − 5x − 4

f(x) = x³ + 3x² − 4x − x − 4

f(x) = x (x² + 3x − 4) − (x + 4)

f(x) = x (x − 1) (x + 4) − (x + 4)

f(x) = (x² − x) (x + 4) − (x + 4)

f(x) = (x² − x − 1) (x + 4)

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Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is divisible by 4.

Answers

We want an integer $x$ such that

$x\equiv\begin{cases}2&\pmod3\n0&\pmod4\n2&\pmod5\end{cases}$

Note that the moduli are all relatively prime, so we can use the Chinese remainder theorem right away. As a first step, let's suppose

$x=4\cdot5\cdot2+3\cdot5\cdot0+3\cdot4\cdot2$

Taken modulo 3, the last two terms immediately vanish, and $4\cdot5\cdot2=40\equiv1\pmod3$ . We want a remainder of 2, so we just multiply this term by 2.

$x=4\cdot5\cdot2^2+3\cdot5\cdot0+3\cdot4\cdot2$

Next, taken modulo 4, all terms vanish, so we're good here.
Then, taken modulo 5, the first two terms vanish and we're left with $3\cdot4\cdot2\equiv24\equiv4\pmod5$ . We want a remainder of 2. To rectify this, we can first multiply this term by the inverse of 4 modulo 5, then multiply again by 2. This guarantees that

$3\cdot(4\cdot4^(-1))\cdot2^2\equiv2\pmod5$

The inverse of 4 modulo 5 is 4, since $4^2\equiv16\equiv1\pmod5$ , so we end up with

$x=4\cdot5\cdot2^2+3\cdot5\cdot0+3\cdot4^2\cdot2^2=272$

You can confirm for yourself that 272 satisfies the desired conditions. The CRT says that any integer of the form

$272\pmod{3\cdot4\cdot5}\equiv32\pmod60$

will work, i.e. $32+60n$ where $n\in\mathbb Z$ , and in particular 32 is the smallest positive solution.

On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5). The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –1 k = 1 k = 2.5

Answers

9514 1404 393

Answer:

(a) k = –2.5

Step-by-step explanation:

When the function f(x) is transformed to f(x -h) +k, the graph is translated h units right and k units up.

If the absolute value function has its original vertex of (0, 0) moved to (1, -2.5), then (h, k) = (1, -2.5).

The value of k is -2.5.

_____

Additional comment

The above answer applies to the given problem statement. The question asked in the comment has a vertex of (0, 2.5), so (h, k) = (0, 2.5) for that question.

If you're going to copy the answer, make sure it is the answer to the question you're looking at.

In an absolute value function expressed as f(x) = |x – h| + k, the value of k corresponds to the y-coordinate of the function's vertex. In this case, as the vertex is at the point (1, -2.5), the value of k is -2.5.

The student's question relates to the concepts of Two-Dimensional (x-y). Graphing and the graphing of the absolute value function. It is vital to remember that the vertex of an absolute value graph in the form f(x) = |x – h| + k corresponds to the point (h, k) on the Cartesian coordinate plane. The student states that the vertex is at the point (1, -2.5), so based on our function analysis, the value of k, which represents the y-coordinate of the vertex, is -2.5. Therefore, the correct answer is k = -2.5.

For more about Absolute Value Graph here:

brainly.com/question/19848212

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You want to rent an unfurnishedone-bedroomapartment for next semester. The mean monthlyrent for a random
sample of 10 apartments advertised in the localnewspaper is $580.
Assume that the standard deviation is$90. Find a 95% confidence
interval for the mean monthly rentfor unfurnished one bedroom
apartments available for rent in thiscommunity.

Answers

Answer: $(\$524.22,\ \$635.78)$

Step-by-step explanation:

Confidence interval for population mean is given by :-

$\overline{x}\pm z^* (\sigma)/(√(n))$

, where $\overline{x}$ = Sample mean

z* = critical z-value.

$\sigma$ = Population standard deviation.

n= Sample size.

Let x be the denotes the monthly rent for unfurnished one bedroom apartments available for rent in this community.

As per given , we have

n= 10

$\overline{x}=\$580$

$\sigma=\$90$

Critical value for 95% confidence : z* = 1.96

So the 95% confidence interval becomes,

$580\pm (1.96) (90)/(√(10))$

$=580\pm (1.96) (90)/(3.162278)$

$=580\pm (1.96)(28.46)$

$=580\pm 55.78$

$=(580-55.78,\ 580+55.78)=(524.22,\ 635.78)$

Hence, a 95% confidence interval for the mean monthly rent for unfurnished one bedroom apartments available for rent in this community= $(\$524.22,\ \$635.78)$

Find reason and statements

Answers

Answer:

Missing reason/statements:

R1, R2, R3 - Given
S4. ∠1 ≅ ∠3
R4. Transitive property
R5. Definition of congruence
S6. m∠1 = 120°
R6. Substitution

Please help me thank you so much. Just not sure of my answers

Answers

Answer:

An interesting experiment is given. We need to address various questions based on our knowledge of calculus.

Step 2

Part (a)

Time taken for the radius to grow to 2 cm = t1 = r/0.5 = 2/0.5 = 4 hours

Time taken for the radius to become 0 = t2 and the same can be obtained by solving:

r = 2 - √t2 = 0

Hence, t2 = 22 = 4 hours

Hence, the time duration of the entire experiment (from the introduction of the bacteria until its disappearance) = t1 + t2 = 4 + 4 = 8 hours

Step 3

Part (b)

r(t) = 0.5t for 0 ≤ t ≤ 4

and

r(t) = 2 - √(t - 4) for t > 2

Step-by-step explanation:

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.8 years, and standard deviation of 2.2 years.If 5 items are picked at random, 5% of the time their mean life will be less than how many years?

Answers

First of all we need o use the standard normal table to see what value if z will have 10% of the area (probability) to the left of it. We see that z value is approximately z = -1.282

Now all we have to do is calculate the value of x that corresponds to this value of z. We have

( x - µ ) / σ = -1.282 Substituting in the known values, we have

( x - 4.4 ) / 1.3 = -1.282 and x = 2.73 years

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