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4 years ago

(-4x^4+5x^3-x^2+1)+(2x^4-7x^3+6x^2+2x) Answer in standard form

Mathematics

1 answer:

Tema [17]4 years ago

5 0

Answer by Distributing Like Terms: $-4x^4+5x^3-x^2+1+2x^4-7x^3+6x^2+2x$

$=-4x^4+5x^3+-x^2+1+2x^4+-7x^3+6x^2+2x$

Combine Like Terms:

$=-4x^4+5x^3+-x^2+1+2x^4+-7x^3+6x^2+2x\\=(-4x^4+2x^4)+(5x^3+-7x^3)+(-x^2+6x^2)+(2x)+(1)\\\=-2x^4+-2x^3+5x^2+2x+1$

Answer: =−2x^4−2x^3+5x^2+2x+1

Formula rewritten in standard form: $-2x^{2} -2x^{3}+5x^{2} +2x+1$

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3 years ago

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The arithmetic sequence a_ia i a, start subscript, i, end subscript is defined by the formula: a_1 = 15a 1 =15a, start subsc

daser333 [38]

Answer:

-1,512,390

Step-by-step explanation:

Given

a1 = 15

$a_i = a_{i-1} -7$

Let us generate the first three terms of the sequence

$a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8$

For $a_3$

$a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1$

Hence the first three terms ae 15, 8, 1...

This sequence forms an arithmetic progression with;

first term a = 15

common difference d = 8 - 15 = - -8 = -7

n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)

Using the formula;

$S_n = \frac{n}{2}[2a + (n-1)d]\\$

Substitute the given values;

$S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390$

Hence the sum of the first 660 terms of the sequence is -1,512,390

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3 years ago

When the figure below is rotated 90 degrees counterclockwise about the origin what would be the new coordinates of point c?

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Rotating a figure 90° counterclockwise about the origin results in an ordered pair (x, y) mapping to its image (-y, x). Thus point C, which is at (3, 5), will map to (-5, 3).

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4 years ago

The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of

noname [10]

Answer:

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

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.

Mean of 10 minutes and a standard deviation of 3 minutes

This means that $\mu = 10, \sigma = 3$