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3 years ago

Let the universal set be the set of integers and let A = {x | x^2 ≤ 5}. Write A using the roster method.

Mathematics

1 answer:

Zarrin [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Given that Z the set of integers is the universal set and

A is given in set builder form.

$A = {x | x^2 ≤ 5}$

To convert this into roster form, we can find solutions for x

When $x^2\leq 5\\|x|\leq \sqrt{5} =2.236$

i.e. all integers lying between -2.236 and 2.236

The only integers satisfying this conditions are

-2,-1,0,1,2

Hence A in roster form is

A= ${-2,-1,0,1,2}$

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A car that travels along the highway to Denver at a steady speed. When it begins, it is 300 miles from Denver. After 3 hours, it

umka21 [38]

Answer: $y=-40x+300$

Step-by-step explanation:

This car follows a line, hence its motion can be modeled by the Line equation.

In fact, we already have two points of the line, if we call $x$ the time in hours and $y$ the traveled distance in miles:

Point 1: $(x_{1},y_{1})=(0,300)$

Since we are told the car's initial position is 300 miles in the time 0 h

Point 2: $(x_{2},y_{2})=(3,180)$

Since we are told the car's final position is 180 miles after 3h

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<u>Let's find the Slope $m$ : </u>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=-40$ This is the slope of the line

Now, the equation of the line is:

$y=mx+b$

We already know the slope, now we have to find the intersection point with the y-axis ( $b$ ) with any of the given points. Let's choose Point 1: $(x_{1},y_{1})=(0,300)$

$300=-40(0)+b$

Isolating $b$ :

$b=-300$

Then, the equation of the line is:

$y=-40 x+300$

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3 years ago

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Pleaseeee help me solve this

Ulleksa [173]

Answer:

3/5 is the answer!

Step-by-step explanation:

y = 3x/5 also means y = 3/5 * x

Which means in y = mx form, the 3/5 = m

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2 years ago

In 3 hours, a car travels 120 miles. What is the speed of the car

-Dominant- [34]

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3 years ago

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S_A_V [24]

Answer: The first one. 2 to the 20th power over 3 to the 8th power

Step-by-step explanation:

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2 years ago

If 588 digits were used to number the pages of a book how many pages are in this book.

iVinArrow [24]

Answer: 232 pages

Step-by-step explanation:

Total digits = 588

1 digit page number:

1 to 9 = 1 × 9 = 9

Number of pages = 9/1 = 9

2 - digit page number :

10 - 99 = 2 × 90 = 180

Number of pages = 180/2 = 90

3 - digit page number :

588 - (9 + 180) = 588 - 189 = 399

Number of pages with 3 - digits = 399/3 = 133

Therefore, the total number of pages the book has is :

(9 + 90 + 133) = 232 pages

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3 years ago