1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dennis_Churaev [7]
3 years ago
9

Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)

Mathematics
1 answer:
Kitty [74]3 years ago
6 0

Answer:

a) Empty set

b)  \{x : x \in N \text{ and } x < 13\}                                        

Step-by-step explanation:

Roster form is a comma separated list form of set.

a) The set of natural numbers x that satisfy x + 4 = 1.  

x + 4 = 1\\x = -3 \notin N

Thus, x is an empty set.

b) set-builder notation for the set  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We use x to represent this set. Now x belongs to natural number and is less than equal to 12.

Thus, it can be written as:

\{x : x \in N \text{ and } x < 13\}

You might be interested in
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

<u />

<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

7 0
3 years ago
Read 2 more answers
If the circumference of a circle is 84.5 ft, find the radius.
Elina [12.6K]

Answer:

13.448, rounded off: 13.5 ft

Step-by-step explanation:

r=\frac{C}{2\pi }

Where r = radius, C = circumference.

r=\frac{84.5}{2\pi } =13.448 = 13.5 ft

6 0
2 years ago
Read 2 more answers
Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0 = 2x2 + 3x – 8? Quadratic formula: x
OleMash [197]

ANSWER



x=1.39 to the nearest hundredth.



EXPLANATION



We have the equation,



0=2x^2+3x-8



Which can be rewritten as



2x^2+3x-8=0

The question demands the use of the quadratic formula.

Comparing this to the general quadratic equation;

ax^2+bx+c=0


a=2,b=3,c=-8


The quadratic formula is given by;


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


We now substitute all the values in to the formula;


x=\frac{-3\pm\sqrt{(3)^2-4(2)(-8)}}{2(2)}

We simplify to obtain;

x=\frac{-3\pm\sqrt{9+64}}{4}


x=\frac{-3\pm\sqrt{73}}{4}


We now split the plus or minus sign to obtain;


x=\frac{-3-\sqrt{73}}{4}


This implies that;


x=-2.89

Or

x=\frac{-3+\sqrt{73}}{4}


This will evaluate to;


x=1.39

Hence, the positive solution rounded to the nearest hundredth is

x \approx 1.39

6 0
3 years ago
Read 3 more answers
Simplify: -2/5 + 4/3
hoa [83]

Answer:

14/15

Step-by-step explanation:

1. Convert the fractions to have the same denominator

Remember that you can only add fractions with the same denominator

To find the common denominator, find the LCM of 5 and 3 which is 15.

-2/5 * 3/3 = -6/15 and 4/3 * 5/5 = 20/15

-6/15 + 20/15 = 14/15

hope this helps! <3

7 0
2 years ago
Read 2 more answers
Write an equation in slope-intercept form (0,2) (7,-1)
maksim [4K]

Answer:

y=-3/7x+2

Step-by-step explanation:

first formula (Slope): y2-y1/x2-x1

-1-2/7-0= -3/7

second formula (point slope): y-y1=m(x-x1)

y-2=-3/7(x-0)

(distribute the -3/7)

y-2=-3/7x-0

(add 2 to both sides)

y=-3/7x+2

6 0
3 years ago
Other questions:
  • julie goes to the park across the street from her house several times a day and jogs a total of six miles every day. she jogs th
    9·1 answer
  • 2.49 divied by 48 1/8 i will mark you brainlist
    10·1 answer
  • How many years does it take for an annuity of $ 1,000 to grow to $ 20,000, assuming k = 7%?
    7·1 answer
  • What are the solutions to the equation 0 = x2 – x-6? Select two options
    6·1 answer
  • Hello please help i’ll give brainliest pls
    11·1 answer
  • What is the surface area for the figure, in square centimeters?
    15·1 answer
  • If there are 32 boys and 24 girls in a room, fill out all the possible ratios of boys to girls​
    14·2 answers
  • A bit in a hurry here! Could anyone please help out here?
    6·1 answer
  • 1/4 xy if x = -2/3 and y = 3/5
    13·1 answer
  • 1. find measure of A.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!