Simplify: (4x2 − 8xy + 2y2) − (9x2 − 4xy − 7y2)

Find the maximum and minimum values of f(x,y) = 8x+y for the polygonal convex set having vertices at (0, 0), (4, 0), (3, 5), (0,

Helen [10]

F(x,y)=8x+y

This means, f is a function where we plug in pairs of numbers.
then, f calculates the first number times 8, to which it then adds the second number we plugged.

let's calculate f for the vertices:

f(0,0)=8*0+0=0+0=0

f(4, 0)=8*4+0=32+0=32

f(3, 5)=8*3+5=24+5=29

f(0, 5)=8*0+5=0+5=5

the maximum value of f is 32
the minimum value of f is 0

4 0

3 years ago

What is the distance between points (3,2) and (6,4) to the nearest tenth?

vekshin1

Distance formula: √((y2-y1)^2+(x2-x1)^2)

Plug in the values √((4-2)^2+(6-3)^2)
√((2)^2+(3)^2) = √(4+9) = √13 = 3.6

3.6 is your answer.

4 0

3 years ago

Ashley is choosing a popsicle from the freezer at random the probability of her picking a grape popsicle is 3/8 the probability

netineya [11]

If an experiment has $N$ possible outputs, each with probability

$P_1,\ P_2,\ldots,\ P_N$

then the sum of all probabilities is always one:

$P_1 + P_2 + \ldots + P_N=1$

So, in your case, you have

$P(\text{grape}) + P(\text{cherry}) + P(\text{orange}) = 1$

plugging in the given values:

$\dfrac{3}{8} + \dfrac{1}{3} + P(\text{orange}) = 1 \iff \dfrac{17}{24} + P(\text{orange}) = 1$

we can deduce that

$P(\text{orange}) = 1-\dfrac{17}{24} = \dfrac{7}{24}$

8 0

3 years ago

You can answer either question but just know you will get brainliest!

Elden [556K]

Answer:

1. x= -4

2. x= 7

Step-by-step explanation:

hope this helps :)

7 0

2 years ago

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seropon [69]

The shape of the graph of quadratic functions is the shape of a parabola.

The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;

(a) Plot the vertex (-4, -3)

(b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)

(c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)

(d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)

(e) Draw the axis of symmetry x = -4

(f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)

(g) Draw a U shaped parabola.

Reasons:

The given function is; f(x) = 2·(x + 4)² - 3

The function is given in the vertex form; f(x) = a·(x - h)² + k

Therefore, the vertex, (h, k) = (-4, -3)

Step (a);

The vertex can be plotted on the graph

Plot the vertex (-4, -3)

Step (b);

Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²

From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)

Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)

Step (c);

To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)

Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)

Step (d);

A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;

(-4 + 3, -3 + (2 × 3²)) = (-1, 15)

Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)

Step (e);

The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4

The line x = -4 can be drawn on the graph next

Draw the axis of symmetry x = -4

Step (f);

The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;

(-3, -1) $\underrightarrow {R_{(x = -4)}}$ (-5, -1)

(-2, 5) $\underrightarrow {R_{(x = -4)}}$ (-7, 5)

(-1, 15) $\underrightarrow {R_{(x = -4)}}$ (-7, 15)

Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)

Step (g);

The parabola that is U shaped can be drawn from the points plotted in the steps above.

Draw a U shaped parabola

Learn more about drawing the graph of a quadratic function here:

brainly.com/question/6353430

5 0

1 year ago