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3 years ago

Mr Smith has six ties it to the ties are red what fraction are red

Mathematics

1 answer:

expeople1 [14]3 years ago

4 0

The fraction is 2/6, because he has six ties which gives you the denominator of six and 2 are red. to simplify 1/3

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

3 years ago

Help with these plz thanks

asambeis [7]

10x = 5 Answer: x = 1/2

−5 = x + 6 Answer: x = -11

22 = 22x Answer: x = 1

0 = −7x Answer: x = 0

−x = 7 Answer: x = -7

x/4 = 1/2 Answer: x = 2

x/5 = 20 Answer: x = 100

x/-2 = -5 Answer: x = 10

5x = 55 Answer: x = 11

−3x = 18 Answer: x = -6

12 = x -6 Answer: x = 18

7 0

3 years ago

elixir [45]

The area of the track will be 78501 m². The area of the track is equal to the area of the circle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square meters and other similar units are used to measure area.

The area of the track is found as;

$\rm A=\frac{\pi}{4} d^2 \\\\ \rm A=\frac{3.14}{4} (100)^2 \\\\ A=7850 \ m^2$

Hence, the area of the track will be 78501 m².

To learn more about the area, refer to the link;

brainly.com/question/11952845

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8 0

2 years ago

Simplify the expression <br><br> -2b - 6 + 3b - 2

Scilla [17]

Hello!

To do this we need to combine like terms, meaning combine the terms that have the same variables.

b is one variable that can be combined:

-2b - 6 + 3b - 2
b - 6 - 2

Now, combine the digits:

b - 8

Hope this helped!

8 0

3 years ago

Nitella [24]

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

<h3>How to find the production level that'll maximize profit?</h3>

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

Read more on maximized profit here: brainly.com/question/13800671

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6 0

2 years ago