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3 years ago

(4). Simplifying polynomials, help pls:) brainliest involved

Mathematics

1 answer:

Roman55 [17]3 years ago

5 0

Answer:

Explanation:

To simplify a polynomial, we have to do two things: 1) combine like terms, and 2) rearrange the terms so that they're written in descending order of exponent.

First, we combine like terms, which requires us to identify the terms that can be added or subtracted from each other. Like terms always have the same variable (with the same exponent) attached to them. For example, you can add 1 "x-squared" to 2 "x-squareds" and get 3 "x-squareds", but 1 "x-squared" plus an "x" can't be combined because they're not like terms.

Let's identify some like terms below.

f(x)=−4x+3x2−7+9x−12x2−5x4

Here you can see that -4x and 9x are like terms. When we combine (add) -4x and 9x, we get 5x. So let's write 5x instead:

f(x)=5x+3x2−7−12x2−5x4

Let's do the same thing with the x-squared terms:

f(x)=5x+3x2−7−12x2−5x4

f(x)=5x−9x2−7−5x4

Now there are no like terms left. Our last step is to organize the terms so that x is written in descending power:

f(x)=−5x4−9x2+5x−7

Step-by-step explanation:

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Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (in miles per gallon

Leviafan [203]

Answer: 0.82 miles per gallon

Step-by-step explanation:

Given : Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (x) (in miles per gallon) of her car.

The results are :45 44 43 44 45 44 43

The formula to find the standard deviation is given by :-

$\sigma=\sqrt{\dfrac{\sum_{i=1}^n(x_i-\overline{x})^2}{n-1}}$

First we find mean of the given data ,

$\overline{x}=\dfrac{\sum^n_{i=1}x_i}{n}\\\\=\dfrac{45+44+43+44+45+44+43}{7}=\dfrac{308}{7}=44$

Now,

${\sum_{i=1}^n(x_i-\overline{x})^2=(1)^2+(0)^2+(-1)^2+(0)^2+(1)^2+(0)^2+(-1)^2$

$=1+1+1+1=4$

Now, standard deviation of the above results will be :-

$\sigma=\sqrt{\dfrac{4}{7-1}}\\\\=\sqrt{\dfrac{4}{6}}\\\\=\dfrac{2}{\sqrt{3}}=0.816496580928\approx0.82$

Hence, the standard deviation of these results = 0.82 miles per gallon

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4 years ago

Devise the exponential growth function that fits the given data, then answer the accompanying question. Be sure to identify the

NemiM [27]

Answer:

The cost in 2015 will be $283.45.

What is the reference point (t=0)?

d. The year 2005.

Step-by-step explanation:

The exponential growth model for the cost is the following:

$C(t) = C_{0}e^{rt}$

In which C(t) is the cost after t years, $C_{0}$ is the initial cost and r is the decimal inflation rate

In this problem, we have that:

$C_{0} = 190, r = 0.04$

What will it cost in 2015 assuming the rate of inflation remains constant?

2015 is 10 years after 2005, so this is C(10).

$C(t) = C_{0}e^{rt}$

$C(10) = 190*e^{0.04*10} = 283.45$

The cost in 2015 will be $283.45.

The reference point is the year in which t = 0, so the year 2005.

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4 years ago

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(50 PTS Trick Question)

s344n2d4d5 [400]

(xy(2zx18+2zx yz^2))^3=
(xy(36z+2yz^3))^3=
(36xyz+2z^3y^2x)^3=
(36xyz)^3+3(36xyz)^2(2z^3y^2x)+3(36xyz)(2z^3y^2x)^2+ (2z^3y^2x)^3
=46656x^3y^3z^3+3888(2z^5y^4x^3)+108 (4z^73y^5x^3)+8z^9y^6x^3

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3 years ago

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(K3+2k2-82k-28)/(k+10)

Ne4ueva [31]

So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:

(Note that synthetic division can only be used when the divisor is a 1st degree binomial)

-10 | 1 + 2 - 82 - 28
---------------------------

Now firstly, drop the 1:

-10 | 1 + 2 - 82 - 28
↓
-------------------------
1

Next, you are going to multiply -10 and 1, and then combine the product with 2.

-10 | 1 + 2 - 82 - 28
↓ - 10
-------------------------
1 - 8

Next, multiply -10 and -8, then combine the product with -82:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80
-------------------------
1 - 8 - 2

Next, multiply -10 and -2, then combine the product with -28:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80 + 20
-------------------------
1 - 8 - 2 - 8

Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).

Putting it together, the quotient is $k^2-8k-2-\frac{8}{k+10}$ 

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3 years ago

1)The table below represents a linear function f(x) and the equation represents a function g(x):

irga5000 [103]

1)The table below represents a linear function f(x) and the equation represents a function g(x):

x y
-1 -11
0 -1
1 9

g(x) = 5x + 1

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

slope of the data of the table:

slope = rise / run = Δy / Δx = [ 9 - ( - 1) ] / [1 - 0] = 10/1 = 10

Also Δy / Δx = [-1 - (-11) ] / [ 0 - (-1) ] = 10 / 1 = 10

the slope of the function given in the form f(x) = mx + b is m, so the slope of g(x) = 5x - 1 is 5.

Comparisson: the slope of the function g(x) = 5x - 1 is half the slope of the function f(x) represented by the table.

Part B: Which function has a greater y-intercept? Justify your answer.

The y-intercept is the value of y when x = 0, so it is - 1 for the function represented by the table.

The y-intercept of a function given in the form f(x) = mx + b is b, so the y-intercept of g(x) = 5x - 1 is - 1.

So, both functions have equal y-intercept.

2)The table below shows the values of y for each value of x:

x y
1 0
1 -1
2 1
2 -2

Part A: Does the table represent a relation that is a function? Justify your answer by using the values shown in the table. (4 points)

No, it is not a function, because the relation is ambiguous: the x-coordinate 1 may have two differente values, and the x-coordinate 2 may have two different. So you cannot determine the images of x = 1 and x = 2.

Part B: The function f(x) shown below represents the number of baskets Jess made at different distances, x, in meters, from the hoop:

f(x) = -x + 6

Calculate and interpret the meaning of f(4). (4 points)

f(4) = - 4 + 6 = 2

It means that Jess made 2 baskets at the distant of 4 meters.

Part C: Write an ordered pair to represent the input and output of the function in Part B when Jess is at a distance of p meters from the hoop. (2 points)

input, p output, f(p)

6 -6 + 6 = 0

So the ordered pair is (6,0)

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3 years ago

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