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2 years ago

What is the domain of the rational expression x-4/2x-6

Mathematics

1 answer:

Natasha2012 [34]2 years ago

4 0

Answer:

Interval Notation: ( − ∞ , 3 ) ∪ ( 3 , ∞ )

Set-Builder Notation: { x | x ≠ 3 }

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How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?

Svet_ta [14]

There are $\dbinom{10}2$ ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are $\dbinom83$ ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's $\dbinom55=1$ way of doing that.

So we have

$\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520$

The last expression has a more compact form in terms of the so-called multinomial coefficient,

$\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520$

5 0

2 years ago

How many terms dose the polynomial have 2x^9 + 3x^6 - x - 20?

riadik2000 [5.3K]

Answer:

Step-by-step explanation:

2x^9 = 1

3x^6 = 2

- x - 20 = 3

6 0

3 years ago

The length of a rectangle is 5 times larger than x. The width is 4 cm less than the length. The perimeter is at least 96 cm. Wha

Ede4ka [16]

We know that the perimeter of a rectangle = 2(l + w)

l = length

w = width

In our problem,

l = 5x

w = 5x - 4

Let's create an inequality to help us solve this problem.

2(5x + (5x - 4)) ≥ 96

Let's start off by simplifying the terms inside the parentheses.

2(10x - 4) ≥ 96

Distribute the 2

20x - 8 ≥ 96

Add 8 to both sides.

20x ≥ 104

Divide both sides by 20

x ≥ 5.2

Let's plug 5.2 into x for our length and width.

Length = 5x = 5(5.2) = 26 cm

Width = 5x - 4 = 5(5.2) - 4 = 26 - 4 = 22 cm

The smallest possible dimensions for the rectangle are, length = 26 cm and width = 22 cm

6 0

3 years ago

Read 2 more answers

Triangle A B C is shown. The length of B C is 6 and the length of A B is 2 StartRoot 2 EndRoot. Angle A B C is 80 degrees. Trigo

lawyer [7]

Answer:

8.4 square units

Step-by-step explanation:

See attachment for the figure.

Trigonometric area formula is Area = $\frac{1}{2}\times absin(C)$

Where a and b are two sides of the triangle and C is the angle between these two sides.

Given:

side a = 6 units, c = 2√2 units and ∠B = 80°

Then area of the triangle :

Area = $\frac{1}{2}\times acsin(B)$

= $\frac{1}{2}\times acsin(B)$

= $\frac{1}{2}\times 6\times 2\sqrt{2}\times sin(80)$

= 6√2×sin80°

= 6×(1.414)×0.9848

= 8.36 square units

≈ 8.4 square units

6 0

3 years ago

Students at a middle school signed up for a community service options. One half of the students signed up to paint houses, 1/5 s

dem82 [27]

Answer: Please include rest of question

Step-by-step explanation:

Then I’ll be able to answer

6 0

3 years ago