What is the domain of the function y=

Diagram below shows the curve of a quadratic function

uranmaximum [27]

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The r is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

= -6.

3 0

4 years ago

Bob makes three different silverware - spoons, forks and knives. Each unit (dozen) of spoon gives him a profit of $9, forks of $

Gala2k [10]

Answer:

Solution is:

z (max) = 687.5

x₁ = 0

x₂ = 16

x₃ = 21

Step-by-step explanation:

From the problem statement we have:

Resources: machine time ( 183 h) labor (250 h) steel 185 (pounds)

Unit

Spoons 4 4 3

forks 4 9 2

knives5 5 5 4

Profit $ 9 20 17.5

Objective function z = 9*x₁ + 20*x₂ + 17.5 *x₃ to maximize

Subject to:

Availability of machine time : 183 h

4*x₁ + 4*x₂ + 5*x₃ ≤ 183

Availability of labor : 250 h

4*x₁ + 9*x₂ + 5*x₃ ≤ 250

Availability of steel : 185 pounds

3*x₁ + 2*x₂ + 4*x₃ ≤ 185

Requirement:

x₂ ≥ 16

General constraints:

x₁ ≥ 0 x₃ ≥ 0 all integers

After 6 iteration the solution using AtomZmath on-line solver

z (max) = 687.5

x₁ = 0

x₂ = 16

x₃ = 21

Resources used:

Machine time: 16* 4 + 21*5 = 64 + 105 = 169

remains 183 - 169 = 14 h

Labor: 16*9 + 21* 5 = 144 + 105 = 249

remains 250 - 249 = 1 h

Steel : 16*2 + 21*4 = 32 + 84 = 116

remains 185 - 116 = 69 pounds.

If it is decided that 20 units of forks are to be made then

we will need 4*4 = 16 h of machine time

9*4 = 36 h of labor

2*4 = 8 pounds of steel

We can get that from abandom to make one unit of x₃ ??

No because as we said we need 36 hours of labor ( we still have 1 we need 35 more hours ) if we make 20 x₃ insted of 21 we get only 5 hours.

z we got is maximum

5 0

3 years ago

ANSWER ASAP PLS <3 20 points ! Which expression matches the graph?

KiRa [710]

Answer: the answer is b?

hope this helps

4 0

3 years ago

Solve for x x-4 — = 5 y+2

yulyashka [42]

I think the question is wrong!

It must be

x-4

___= 5

x+2

Answer: x - 4= 5x + 10

or,-10 -4 = 5x - x

or, -14=4x

or,-14/4= x

Therefore, x = -14/4

5 0

4 years ago

Find the measure of

Andre45 [30]

Answer:

19 degrees.

Step-by-step explanation:

First solve the angles in the top triangle:

FHG = 180 - 135 = 45 (angles on a straight line = 180)

FGH = 180 - 105 = 75 (angles on a straight line = 180)

Using these we get HFG = 180 - 45 - 75 = 60 (angles in a triangle = 180)

Then because HFG is directly opposite DFC on the crossed lines, we know they are equal: DFC = 60

FDC = 180 - 119 = 61 (anges on a straight line = 180)

Now if we label ABC (the target angle) as x then we known ACB = 180 - 40 - x.

With this we know FCD = 180 - ACB = 180 - (180 - 40 - x) = 40 + x (angles on a straight line).

Finally using the FDC triangle we have 40 + x + 60 + 61 = 180 so x = 180 - 40 - 60 - 61 = 19 degrees.

7 0

3 years ago

What is the domain of the function y=_/x+6-7