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Aleks [24]
3 years ago
9

Factor and find all the roots of x^4 +x=0

Mathematics
1 answer:
Furkat [3]3 years ago
7 0
         x⁴ + x = 0
x(x³) + x(1) = 0
    x(x³ + 1) = 0
x = 0    or    x³ + 1 = 0
                        - 1  - 1
                         x³ = -1
                          x = -1
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The time t required to drive certain distance varies inversely with the speed r. It takes 2 hours to drive the distance at 40 mi
Roman55 [17]

Answer:

\frac{16}{9}  hours

Step-by-step explanation:

Whenever 2 quantities (suppose a and b) are inversely proportional to each other, we can write an proportionality equation (with k as proportional constant) as:

a=\frac{k}{b}

Since, here t is INVERSELY PROPORTIONAL to r, we can say:

t=\frac{k}{r}

Firstly, we have t = 2 hour and r = 40 mph, so we find k:

t=\frac{k}{r}\\2=\frac{k}{40}\\k=2*40\\k=80

Now, secondly, we have r = 45 and k = 80, we need to find t:

t=\frac{80}{45}\\t=\frac{16}{9}

So, it would take  \frac{16}{9}  hours

4 0
3 years ago
An art history professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below
madam [21]

Answer:

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.

This means that \mu = 79.7, \sigma = 8.4

B: Scores below the top 13% and above the bottom 56%

So between the 56th percentile and the 100 - 13 = 87th percentile.

56th percentile:

X when Z has a p-value of 0.56, so X when Z = 0.15. Then

Z = \frac{X - \mu}{\sigma}

0.15 = \frac{X - 79.7}{8.4}

X - 79.7 = 0.15*8.4

X = 81

87th percentile:

X when Z has a p-value of 0.87, so X when Z = 1.13.

Z = \frac{X - \mu}{\sigma}

1.13 = \frac{X - 79.7}{8.4}

X - 79.7 = 1.13*8.4

X = 89

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

4 0
3 years ago
1 5/6 ÷ 3/5 x 2/11 = ?
Allushta [10]

Answer:

75/99

Step-by-step explanation:

8 0
3 years ago
If cosA+sinA=√2, then prove A=45°.
Lyrx [107]

Answer:

1/2 now substitute 45 degrees

Step-by-step explanation:

6 0
2 years ago
a carpenter has a board that is 8 feet long he cuts of 2 pieces one piece is 3 and a half feet long the other is 2 and one feet
kakasveta [241]
3 1/2 I think
8-3 1/2=5 1/2
5 1/2-2=3 1/2
5 0
3 years ago
Read 2 more answers
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