Answer the question for brainilest and 30 points

ITS TIMED PLEASE HELP

Lubov Fominskaja [6]

Answer:

The graph of the function $f(x)=\frac{1}{2}x^{2}-4x+5$ has a minimum located at (4,-3)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

a is a coefficient

(h,k) is the vertex of the parabola

If a > 0 the parabola open upward and the vertex is a minimum

If a < 0 the parabola open downward and the vertex is a maximum

In this problem

The coefficient a must be positive, because we need to find a minimum

therefore

Check the option C and the option D

Option C

we have

$f(x)=\frac{1}{2}x^{2}-4x+5$

Convert to vertex form

$f(x)-5=\frac{1}{2}x^{2}-4x$

Factor the leading coefficient

$f(x)-5=\frac{1}{2}(x^{2}-8x)$

$f(x)-5+8=\frac{1}{2}(x^{2}-8x+16)$

$f(x)+3=\frac{1}{2}(x^{2}-8x+16)$

$f(x)+3=\frac{1}{2}(x-4)^{2}$

$f(x)=\frac{1}{2}(x-4)^{2}-3$

The vertex is the point (4,-3) ( is a minimum)

therefore

The graph of the function $f(x)=\frac{1}{2}x^{2}-4x+5$ has a minimum located at (4,-3)

5 0

4 years ago

Can someone please help me solve this? thank you!:)

Nataliya [291]

First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.

P = L + 2W

A = L * W

Now that we have our equations, we need to plug in what we know, which is the 40m of rope.

40 = L + 2W

A = L * W

Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.

L = 40 - 2W

Now, we can substitute the value for L into L in the area equation and get a quadratic equation.

A = W(40 - 2W)

A = -2W^2 - 40W

The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.

V = -b/2a

V = 40/2(2) = 40/4 = 10

Derivative:

-4w - 40 = 0

-4w = 40

w = |-10| = 10

To find the other dimension, use the perimeter equation.

40 = L + 2(10)

40 = L + 20

L = 20m

Therefore, the dimensions of the area are 10m by 20m.

Hope this helps!

4 0

3 years ago

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The cosine of 55 1/2 degrees is approximately 0.566. What angle, in degrees, has a sine of approximately 0.566?

astra-53 [7]

Given:

$\cos (55\dfrac{1}{2})^\circ\approx 0.566$

To find:

The angle, in degrees, that has a sine of approximately 0.566.

Solution:

We know that,

$\sin(90^\circ-x)=\cos x$

We have,

$\cos (55\dfrac{1}{2})^\circ\approx 0.566$

Using the above trigonometric identity, it can be written as:

$\sin (90-55\dfrac{1}{2})^\circ\approx 0.566$

$\sin (90-\dfrac{110+1}{2})^\circ\approx 0.566$

$\sin (90-\dfrac{111}{2})^\circ\approx 0.566$

Taking LCM, we get

$\sin (\dfrac{180-111}{2})^\circ\approx 0.566$

$\sin (\dfrac{69}{2})^\circ\approx 0.566$

$\sin (34\dfrac{1}{2})^\circ\approx 0.566$

Therefore, the angle $34\dfrac{1}{2}$ degrees has a sine of approximately 0.566.

4 0

3 years ago

Which angles are verticle angles?

Yuri [45]

Answer:

c

Step-by-step explanation:

4 0

4 years ago

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Plz help fast! worth 100 points

zloy xaker [14]

An equilateral triangle sides are all equal to each other. This means that is one side of an equilateral triangle is x + 3 then the sides of the other two triangles as also each x + 3

The formula for perimeter of a triangle is:

Perimeter = side 1 + side 2 + side 3

Or in the case of an equilateral triangle it would be:

Perimeter = 3(side)

This means that for the formula of this equilateral triangle you have:

Perimeter = 3(x + 3)

If asked the three out side of the parentheses can be distributed, meaning that you multiply the outside number (in this case that is 3) to all the number inside the parentheses (in this case that is x and 3)

Perimeter = (3 * x) + (3*3)

Perimeter = 3x + 9

Both of these are correct:

P = 3(x + 3)

P = 3x + 9

Hope this helped!

~Just a girl in love with Shawn Mendes

6 0

4 years ago

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