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3 years ago

The data in this table represents a linear function.

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

8 0

Answer:

Step-by-step explanation:

$Slope (m) = \frac{y}{x} = \frac{3}{1} = 3$

X = 5 – 2 = 3

Y = 16 – 7 = 9

$0 = arctan(\frac{y}{x}) = 71.565051177078°$

$Distance (d) = \sqrt{X2} + Y2 = \sqrt{90} = 9.4868329805051$

Equation of the line:

y = 3x + 1

When x=0, y = 1

When y=0, x = -0.33333333333333

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Albert jumped 100 times in 97.5 seconds. Round off the time taken to the nearest second.

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3 years ago

Segment AB has point A located at (6, 6). If the distance from A to B is 5 units, which of the following is the coordinate for p

Ierofanga [76]

The choices are (3, 2) (2, 5) (6, 7) and (7, 5). The distance formula given two points is d = square root of [(y2−y1)^2+(x2−x1)^2]. In this case, we try every point in the choices and substitute y1 equal to 6 and x1 equal to 6 as well. The answer is A from the choices.
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4 years ago

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Step-by-step explanation:

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3 years ago

PLEASE HELP: write a possible function, f(x), in factored form that could model the graph below

tatiyna

Hi there! Your answer is f(x) = x(x+3)²(x-4)

Please see an explanation for a clear and better understanding to your problem.

Any questions about my answer or explanation can be asked through comments! :)

Step-by-step explanation:

This type of graph is called Graph of Polynomial Function. They have a degree of n where n is the positive integer. The polynomial functions can be broken into these two categorizes:

Odd-Degree
Even-Degree

Note that they are for graph purpose only, may not appear in curriculum.

Odd-Degree functions will have graphs that start from negative infinity to positive infinity for f(x) term. Please see first and two attachments for a clear understanding.

Even-Degree functions will have graphs that start from positive infinity to positive infinity for f(x) term. Please see third and fourth attachment.

Therefore, the graph is even-degree polynomial because it starts from positive infinity where f(x) is decreasing to positive infinity where f(x) is increasing.

Next is to find a factored from of function. Factored forms are basically x-intercepts form of function. Please see the formula.

$\large\boxed{f(x)=(x-a)(x-b)(x-c)}$

This is an example of factored form. The x-intercepts are at a, b and c. Just like how you solve an equation.

So what we need to do is to find x-intercepts.

The graph has x-intercepts at these following:

x = -3 (Double)
x = 0
x = 4

Then we convert them into factored form including swapping from positive to negative and negative to positive. We should get:

$\large{f(x)=(x+3)^2(x+0)(x-4)}\\\large{f(x)=x(x+3)^2(x-4)}$

Notice if we multiply these, we'd get 4-degree polynomial.

[ Reference to double of x = -3 ]

The graph suddenly shifts up when f(x) = 0 on x = -3. Hence, implying that x = -3 are doubled also known as (x+3)(x+3) = (x+3)²

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3 years ago