Segment AB is tangent to C. Find AB. 6 + 6 AB=

Directions: Answer true or false. If false, provide a counterexample.

Arisa [49]

Natural numbers are closed under division: false.

A set is closed under a certain operation if the results of that operation are always inside that set.

So, if natural numbers were closed under division, the division of two natural numbers would always be a natural number.

You have plenty of counterexamples, to pick one you may divide any odd number by 2: 5/2 is not a natural number.

Negative numbers are closed under addition: true.

Let $m,n$ be two positive numbers. So, $-m,-n$ are two negative numbers. Their sum is

$(-m)+(-n)=-(m+n)$

And since $m+n$ is positive, we deduce that $-(m+n)$ is negative, so the sum of two negative numbers is still negative.

Prime numbers are closed under subtraction: false.

This would mean that the subtraction of two primes is also a prime. Again, there are many counterexamples: 7 is prime and so is 3, but their difference 7-3 is 4, which is not prime.

7 0

3 years ago

A summer camp cookout is planned for the campers and their families. There is room for 525 people. Each adult costs $9, and each

vodomira [7]

Answer:

The System of Inequalities in this real-world scenario is:

x+y < = 525

9x+5y < = 1200

Step-by-step explanation:

In this question we are asked to to write a system of inequalities, thus a system of relating two variables, where the relationship will be of the form either greater > or less < or equal.

Given Information:

→ Maximum number possible in the summer camp: 525

→ People attending are Adults (lets call them $x$ and Campers (lets call them $y$ )

→ Ticket Cost for Adults is $9

→ Ticket Cost for Campers is $5

→ Maximum budget available for both Adults and Campers is $1200

From these information we can obtain 2 Inequalities to define our system of equation.

The first inequality will be with respect to the Maximum Number of People possible which reads as:

$x+y\leq 525$ [sum of adults and campers should be less or equal to maximum number of people possible]

The second will be with respect to the Maximum Budget available which reads as:

$9x+5y\leq 1200$ [sum of the cost per ticket for adults and campers should be less or equal to maximum budget available]

Thus the System of Inequalities in this real-world scenario is:

$x+y\leq 525\\9x+5y\leq 1200$

Which if solved can give us the values for $x$ and $y$ , thus the number of adults and numbe of campers attedning the summer camp.

5 0

4 years ago

a ships triangular signal flag has a base of 8 in and an area of 64 in. What is the height of the signal flag? SHOW WORK

patriot [66]

The formula in computing the area of the triangle is:

A = bh/2

Where A = area of the triangle

b = base of the triangle

h = height of the triangle

What is asked in the problem is the height of the triangle and you are already given the area so you substitute the given measurements to the formula:

64 = 8(h) / 2

2 (64) = 8h

8h = 128

h = 16

Therefore, the height of the signal flag is 16 in

5 0

4 years ago

Write an equation of the line from the table

stellarik [79]

Answer:

y=x+6

Step-by-step explanation:

x to y is always add 6.

This is why the equation is y=x+6

Hope this helps :)

4 0

3 years ago

I need this done fast

kramer

Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd

Step-by-step explanation:

4 0

3 years ago