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2 years ago

Which equation represents the graphed function?

Mathematics

2 answers:

makvit [3.9K]2 years ago

8 0

The equation y = –2 x + 3 represents the graphed function.

Answer: Option A

<u>Step-by-step explanation:</u>

As per the mapping points in the attached figure, A (0, 3) and B (1, 1)

Step 1: Find the slope of the line.

We know that the formula to calculate the slope between two points is equal to

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

$\left(x_{1}, y_{1}\right)=(0,3) \text { and }\left(x_{2}, y_{2}\right)=(1,1)$ . So, the slope ‘m’ would be

$m=\frac{1-3}{1-0}=-2$

Step 2: Find the y-intercept

We know that the y-intercept is the value of y when the value of x is equal to zero. In this problem the y-intercept is the point A (0, 3)

Step 3: Find the equation of the line into slope-intercept form

We know that the equation of the line into slope-intercept form is equal to

y = m x + b

We have m = - 2 and b = 3 as b is equal to the y-coordinate of the y-intercept. Substitute these, we get

y = - 2 x + 3

klasskru [66]2 years ago

4 0

Answer:A

Step-by-step explanation:

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Simplify the following rational expression and state for what values they are undefined.

QveST [7]

Answer:

d-2 and d cannot = 8

Step-by-step explanation:

d^2 -10d+16

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d-8

Factor the numerator

( d-8)(d-2)

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The undefined values occur when the denominator is equal to zero

d-8 = 0

d= 8

This means d cannot equal 8

Now cancel like terms in the equation ( d-8)

This yields d-2

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2 years ago

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Aleksandr-060686 [28]

Answer:

Step-by-step explanation:

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1 year ago

If n is even, which represents the first consecutive even integer after n?

kow [346]

Answer: $n+2$

Step-by-step explanation:

1. By definition, an even number is that number that can be divided by two.

2. Therefore, keeping this definition on mind, if you have an even number $n$ , the next consecutive even integer after it can be obtained by adding 2.

3. Then, you can conclude the expression that represents the first consecutive even integer after $n$ is:

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2 years ago

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What is the answer to 5+x=-9

aleksandr82 [10.1K]

5+x=-9

Use the subtractive property of equality to isolate x.

5+x=-9

-5 -5

x=-14

The value that satisfies x is -14. You can check your work by substituting x as -14 and checking if the equation is satisfied.

5+x=-9

x=-14

5+(-14)=-9

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the answer is correct. Succinctly, x=-14.

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2 years ago

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EXPLAIN why we placed the value of x= 4/3( the minimum value) into the equ of gradient(dy/dx) [in the answer, marking scheme att

aliina [53]

$y=x(x-2)^2$
$\implies y'=(x-2)^2+2x(x-2)=3x^2-8x+4=(3x-2)(x-2)=0$
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are the critical points, and judging by the picture alone, you must have $b=\dfrac23$ and $a=2$ . (You might want to verify with the derivative test in case that's expected.)

Then the shaded region has area

$\displaystyle\int_0^2x(x-2)^2\,\mathrm dx=\dfrac43$

I'll leave the details to you.

Now, for part (iv), you're asked to find the minimum of $\dfrac{\mathrm dy}{\mathrm dx}=y'$ , which entails first finding the second derivative:

$y'=3x^2-8x+4$
$\implies y''=6x-8$

setting equal to 0 and finding the critical point:

$6x-8=0\implies x=\dfrac86=\dfrac43$

This is to say the minimum value of $\dfrac{\mathrm dy}{\mathrm dx}$ *occurs when $x=\dfrac43$ *, but this is not necessarily the same as saying that $\dfrac43$ is the actual minimum value.

The minimum value of $\dfrac{\mathrm dy}{\mathrm dx}$ is obtained by evaluating the derivative at this critical point:

$m=\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=4/3}=3\left(\dfrac43\right)^2-8\left(\dfrac43\right)+4=-\dfrac43$

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3 years ago