Acil çözümünü yazın bana

State the range of the relation shown

Genrish500 [490]

Answer: Choice A. {-3,-1,0,1,2}

Explanation:

The range is the list of y coordinates of each point.

4 0

2 years ago

Please help. Don’t understand this math problem!

oksian1 [2.3K]

Answer:

{ 4 }

Step-by-step explanation:

First you need to solve the equation. Then you need to write the solutions as a set.

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I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...

{ 4 }

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Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.

√(5x +16) -2 = 3x -8 . . . . given

√(5x +16) = 3x -6 . . . . . . add 2

5x +16 = (3x -6)^2 . . . . . square both sides

5x +16 = 9x^2 -36x +36 . . . . expand the square

9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form

Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...

9x^2 -36x -5x +20 = 0

9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs

(9x -5)(x -4) = 0

The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...

√(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9

3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same

x = 5/9 is NOT A SOLUTION

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√(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4

3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...

x = 4 is a solution

The set of solutions is then ...

{ 4 } . . . . . solution set

5 0

3 years ago

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref

hichkok12 [17]

Answer:

P is exactly 3km east from the oil refinery.

Step-by-step explanation:

Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:

$\sqrt{(3 - d)^2 + 2^2} = \sqrt{(3 - d)^2 + 4}$

So the cost of laying pipe under water with this distance is

$800000\sqrt{(3 - d)^2 + 4}$

And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:

$800000\sqrt{(3 - d)^2 + 4} + 400000d$

We can find the minimum value of this by taking the 1st derivative and set it to 0

$800000\frac{2*0.5*(3-d)(-1)}{\sqrt{(3 - d)^2 + 4}} + 400000 = 0$

We can move the first term over to the right hand side and divide both sides by 400000

$1 = 2\frac{3 - d}{\sqrt{(3 - d)^2 + 4}}$

$\sqrt{(3 - d)^2 + 4} = 6 - 2d$

From here we can square up both sides

$(3 - d)^2 + 4 = (6 - 2d)^2$

$9 - 6d + d^2 + 4 = 36 - 24d + 4d^2$

$3d^2-18d+27 = 0$

$d^2 - 6d + 9 = 0$

$(d - 3)^2 = 0$

$d -3 = 0$

d = 3

So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.

3 0

3 years ago

Please I need this now<br>Whoever can answer this I will make a brainliest

qwelly [4]

Answer:

djchdjcycuchrivivurtiytvivytivi8fr cgdyhcd8w

3 0

3 years ago

Read 2 more answers

Please Help!

AleksAgata [21]

<span>Answer:
1. AC = AC [Reflexive property]
2. <A = <C [Corresponding angles are congruent]
3. AD = BC [Parallelogram has two congruent opposite legs]
4. Both triangles are congruent by SAS</span>

5 0

3 years ago

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