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3 years ago

The table below shows selected points from a function.

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

6 0

The rate change of interval for the given table is Constant , so the function a linear function.

Step-by-step explanation:

A linear function is defined as a function which yields a line in a graph and the rate of change(constant) is called as slope.

Since the rate is constant, then function will result in a straight line.

From the given table the slope m=1 and it changes constantly.

The linear equation formula is y=mx+c.

where m is the slope and c is the y-intercept.

The linear equation for the given table is y=x+1.

∴ The rate change of interval for the given table is Constant , so the function a linear function.

If the graph for a function has any shapes other than a straight line then it doesn't have a constant slope and it will be a non-linear function.

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Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

One root of f(x) = 2x3 9x2 7x – 6 is –3. explain how to find the factors of the polynomial.

m_a_m_a [10]

We have the following polynomial:

$f(x)=2x^{3}+9x^{2}+7x-6$

The problem states that one root is -3. Thus, it is true that $(x+3)$ is a factor of the polynomial. Given that this is fulfilled, it is also true that:

 $f(x)=(x+3)Q(x) \therefore Q(x)=\frac{f(x)}{x+3} \\ \\ where \ Q(x) \ has \ a \ degree \ of \ 2$ 

We can find Q(x) by applying Ruffini's rule, thus:

 $\ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ 7 \ \ \ \ \ \ -6 \\ -3 \\ \rule{50mm}{0.1mm} \\ \ {} \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 3 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ 0$ 

Therefore:

$Q(x)=2x^{2}+3x-2$

The roots of this polynomial can be get as follows:

$x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \rightarrow x_{12}=\frac{-3\pm\sqrt{3^2-4(2)(-2)}}{2(2)}\\x_{1}=\frac{1}{2};\ x_{2}=-2$

These are the roots along with $-3$ . Finally, the factored polynomial can be written as follows:

$f(x)=(x+3)(x+2)(2x-1)$

4 0

4 years ago

Read 2 more answers

If the room has a square area of 16 square meters and the rug is placed in the middle of the room, how much space would there be

alukav5142 [94]

Answer

the space would unknow between each side of the rug and the wall

Step-by-step explanation:

because we don't know how big the room is and what the shape of the room is we have no idea what the answer will be it could be a little less than the distance around the world or it could be no distance cause it is the same size as the room

(also the rug is in the middle of the the room)

5 0

3 years ago

Suppose a store has an item on sale for 25% off the original amount. By what percent does the store have to increase the price o

natita [175]

Answer:

25%

Step-by-step explanation:

6 0

3 years ago

Tonya prepared 4 different letters to be sent to 4 different addresses. for each letter, she prepared an envelop with its correc

nikitadnepr [17]

There are 4! = 24 poosible permutations of the four letters. Let the letters be A, B, C and D. Two permutations will have only letter A in the correct envelope, two more permutations will have only letter B in the correct envelope, two more will have only letter C in the correct envelope and two more will have only letter D in the correct envelope. Therefore 8 out of the 24 possible permutations will have only one letter with the correct address. The required probability is 8/24 = 1/3.

3 0

3 years ago