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3 years ago

What is the rate of change of the linear relationship modeled in the table (-2,5) (-1,4) (0,3) (1,2)

Mathematics

1 answer:

poizon [28]3 years ago

8 0

The rate of change of the linear relationship is -1.

Explanation:

It is given that there is a linear relationship between all these points, these points lie on a straight line.

The equation to find the slope passing through two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(-2,5)$ and $(-1,4)$ , we get,

$\begin{aligned}m &=\frac{4-5}{-1+2} \\&=\frac{-1}{1} \\&=-1\end{aligned}$

Thus, the slope is -1.

Thus, the rate of change of the linear relationship is -1.

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What is the approximate volume of a basketball with the circumference of 42ft ?

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We know that

[volume of a sphere]=(4/3)*pi*r³

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3 years ago

Increased competition for power among European states and led to imperialism.

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Step-by-step explanation:

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3 years ago

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Given a function <img src="https://tex.z-dn.net/?f=f%28x%29%3D3x%5E4-5x%5E2%2B2x-3" id="TexFormula1" title="f(x)=3x^4-5x^2+2x-3"

Levart [38]

Answer:

$\huge\boxed{f(-1) = -7}$

Step-by-step explanation:

In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

$3(-1)^4 = 3$

WAIT! How is this possible? $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$ , not 3!

It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use $-2^2$ as an example.

What your calculator did was follow BEMDAS since it wasn't explicitly told not to.

BEMDAS:

- Brackets

- Exponents

- Multiplication/Division

- Addition/Subtraction

Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.

So rather than being "-2 squared" - it's "the negative of of 2 squared."

Tying this back into our problem, the squared method would only be true if it looks like $-1^4$ . However, since we're substituting in -1, it looks like $(-1)^4$ , so the expression reads out as "-1 to the fourth."

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$ .

Applying this logic to our original term, $3(-1)^4$ :

$3(-1\cdot-1\cdot-1\cdot-1)$
$3(1)$
$3$

Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

$-5(-1)^2$

Applying the same logic from our first term:

$-5(-1 \cdot -1)$
$-5(1)$
$-5$

Third term: $2x$

$2(-1) = -2$

-3 is just -3, no influence of x.

Combining our terms, we have $3-5-2-3$ .

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is -7.

Hope this helped!

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3 years ago

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Changing this into General Form (Ax + By + C = 0) x = -9 {2 ≤ y ≤ 6}

ahrayia [7]

Answer:

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Step-by-step explanation:

x is negative so i turned it into a negative number b, y is - so 8 and o is slope

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3 years ago

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OverLord2011 [107]

I would feel better if you'd explain how you "know" that a "same-day" ticket is $15.

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Check by substitution to determine whether $15 and $10 are correct. If not, please show your work, so that someone else or I could step back in and help.

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