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2 years ago

10

A person standing on a moving walkway travels 60 feet in 20 seconds. What equation represents this relationship? How many feet w

ill person travel 10 seconds?

2 answers:

Sphinxa [80]2 years ago

7 0

30 feet in 10 seconds

Inga [223]2 years ago

6 0

Answer:

The person will travel 30 feet in 10 seconds

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To play a game, you spin a spinner like the one shown. You win if the arrow lands in one of the areas marked "WIN". Lee played t

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The data collected from the actual game experiment is:

Win: 8 times
Lose: 40 times
Total trials: 48 times

Therefore, the probability that you will win when you play this game is:

WIN = 8/48
= 1/6 or 0.1667 = 16.67% chance of winning

LOSE = 40/48
= 5/6 or 0.8333 = 83.33% chance of losing.
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The metric system originated in France in 1799 following the French Revolution although decimal units had been used in many other countries and cultures previously. Although there have been many different measurements and the definitions of the units have been revised, the official system of measurements of most countries is the modern form of the metric system which is known as the "International System of Units".

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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:

2

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.

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7. Fred had 85 marbles. After a few games, he had 120% of his original number. How many

Gnoma [55]

Answer:

102 marbles

Step-by-step explanation:

100% of 85 is 85.

20% of 85 = 17

85 + 17 = 102

Hope that helps!

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