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3 years ago

QUICK !! What is the image point of (2,-7) after a translation right 4 units and up 3 units ?

Mathematics

2 answers:

Paul [167]3 years ago

6 0

Answer:

(6, - 4)

Step-by-step explanation:

A translation of 4 units right is equivalent to adding 4 to the x- coordinate

A translation of 3 units up is equivalent to adding 3 to the y- coordinate

(x, y) → (x + 4, y + 3) ← translation rule

Hence

(2, - 7) → (2 + 4, - 7 + 3) → (6, - 4)

Anon25 [30]3 years ago

5 0

Anwser: (−2,−7)→(−2+4,−7−2)=(2,−9)

Explanation: {right 4 units: add 4 to x-coordinate}

down 2 units: subtract 2 from y-coordinate

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A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3

zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

l represents the length.

w represents the width.

h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

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For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

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1 year ago

Someone please convert this equation to slope intercept form: 2x - 3y = 6?

IgorLugansk [536]

Slope y-intercept form is: y=mx+b

All you have to do is rearrange the equation:

2x-3y=6
2x=6+3y
2x-6=3y

now divide both sides by 3
(2x/3)-(6/3)=(3y/3)

and it becomes
$y= \frac{2}{3}x-2$ x

Bonus: you can plug in any two values for x and y and you can see both equation gives the same answer!

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3 years ago

A line with a slope of 1/3 passes through the point (-8,9). What is its equation in point-slope form?

BARSIC [14]

Answer:

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Step-by-step explanation:

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