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2 years ago

Complete the square for 5x^2-30x=5

Mathematics

2 answers:

xxMikexx [17]2 years ago

8 0

Answer: (x-3)^2=10

Step-by-step explanation:

Nikitich [7]2 years ago

3 0

Solve for x over the real numbers: by completing the square:

5 x^2 - 30 x = 5

Divide both sides by 5:

x^2 - 6 x = 1

Add 9 to both sides:

x^2 - 6 x + 9 = 10

Write the left hand side as a square:

(x - 3)^2 = 10

Take the square root of both sides:

x - 3 = sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

x = 3 + sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

Answer: | x = 3 + sqrt(10) or x = 3 - sqrt(10)

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Find positive numbers x and y satisfying the equation xyequals12 such that the sum 4xplusy is as small as possible. Let S be the

WITCHER [35]

Answer:

The objective function in terms of one number, x is

S(x) = 4x + (12/x)

The values of x and y that minimum the sum are √3 and 4√3 respectively.

Step-by-step explanation:

Two positive numbers, x and y

x × y = 12

xy = 12

S(x,y) = 4x + y

We plan to minimize the sum subject to the constraint (xy = 12)

We can make y the subject of formula in the constraint equation

y = (12/x)

Substituting into the objective function,

S(x,y) = 4x + y

S(x) = 4x + (12/x)

We can then find the minimum.

At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0

(dS/dx) = 4 - (12/x²) = 0

4 - (12/x²) = 0

(12/x²) = 4

4x² = 12

x = √3

y = 12/√3 = 4√3

To just check if this point is truly a minimum

(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)

4 0

2 years ago

Write an equation for the following and then solve. Twice a number is 8. Find the number.

Yakvenalex [24]

Answer:

The number u are looking for is 4

Step-by-step explanation:

Let X be the unknown number that we want to find.

So it becomes,

2X = 8

move 2 to the other side, so it becomes a divide

X = 8/2

X = 4

6 0

2 years ago

ABCD is a parallelogram. E is the point where the diagonals AC and BD meet. Prove that triangle ABE is congruent to triangle CDE

Darina [25.2K]

ABCD is a parallelogram Given
AE=CE, BE=DE The diagonals of a parallelogram are bisect each other
∠AEB=∠CED Vertical angles are congruent
ΔABE is congruent to ΔCDE SAS theorem

5 0

2 years ago

Read 2 more answers

A rectangular lot that measures 150 ft by 200 ft is completely fenced. What is the approximate length, in feet, of the fence?

Ivenika [448]

300,000 because you have to just multiply 150 by 200

3 0

3 years ago

The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3

Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is $258.75\ in^3$ .

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

$Volume = Length\times height\times width$

Substitute all given value in above formula.

$258.75 = (h-4)\times h\times 3$

Rewrite the equation as:

$258.75 = 3h(h-4)$

$258.75 = 3h^2-12h$

$3h^2-12h-258.75=0$

whole equation divided by 3.

$h^2-4h-86.25=0$

Use quadratic formula with $a = 1, b = -4,c=-86.25$

$h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}$

Put these a, b and c value in above equation.

$h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}$

$h=\frac{4\pm \sqrt{16+345}}{2}$

$h=\frac{4\pm \sqrt{361}}{2}$

$h=\frac{4\pm 19}{2}$

For positive sign

$h=\frac{23}{2}$

h = 11.5 in

For negative sign

$h=\frac{-15}{2}$

h = -7.5

We take positive value of h.

Therefore, the height of the box h = 11.5 in

4 0

2 years ago