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Maslowich
3 years ago
6

What is the slope of the line shown below?

Mathematics
1 answer:
alexandr402 [8]3 years ago
5 0

Answer:

m=-2

Step-by-step explanation:

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240 pennies out of 600 pennies = 40% 
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What is the value of x in the equation x – y = 30, when y = 15?
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Answer the questions below about the quadratic function.f(x) = -2x² - 4x
Juli2301 [7.4K]

We are given the function below;

f(x)=-2x^2-4x

PART A

We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.

ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum

PART B and C

To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.

From the graph, the black point helps answer part A and part B.

ANSWER: The function's maximum value is f(x)=2.

This is the point where the slope of the graph is equal to zero

ANSWER: The maximum value then occurs at x= -1

We can also solve this by differentiating the function.

\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}

5 0
1 year ago
Equation for a parabola with a focus of (2, -2) and a directrix of y=-8
Fantom [35]

Answer:

y=1/8(-x^2+4x+44

Step-by-step explanation:

In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.

Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.

Distance between (x,y) and (2,4)

= √(x-2)²+(y-4)²

And the distance between (x,y) and directrix y=8

= (y-8)

Now √(x-2)²+(y-4)² = (y-8)

(x-2)²+(y-4)² = (y-8)²

x²+4-4x+y²+16-8y = y²+64-16y

x²+20+y²-4x-8y = y²-16y+64

x²+20-4x-8y+16y-64=0

x²+8y-4x-44 = 0

8y = -x²+4x+44

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What are all the possible rational roots of f(0) = 2x^4+ x^3+ 4?
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Answer: the answer is 4, just 4

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