1.5 m
7.1 m
7.1 m
V=

Given:

A set of composite numbers less than 12.

To find:

The set by listing and set builder methods​.

Solution:

Composite number: A positive integer is called a composite number if it has at least one divisor other than 1 and itself.

Composite numbers less than 12 are 4, 6, 8, 9, 10.

By using the listing method , the given set can be expression as:

Set = {4, 6, 8, 9, 10}

The numbers 4, 6, 8, 9, 10 are greater than 1, less than 12 and non prime numbers.

By using set builder method, the given set can be expression as:

Set = [tex]\{x|x\neq P,1<x<12\}[/tex]

Therefore, the list and set builder notation of the given set are {4, 6, 8, 9, 10} and [tex]\{x|x\neq P,1<x<12\}[/tex] respectively.

Answer:

Step-by-step explanation:

According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. For us, in our triangle:

a + 2b + 70 = 180 so

a + 2b = 180 -70 and

a + 2b = 110. That's why.

Answer:

3

Step-by-step explanation:

Answer:

D. y = 3·x² - 2·x + 11/12

Step-by-step explanation:

The coordinates of the focus of the parabola, f = (1/3, 2/3)

The directrix of the parabola, y = 1/2

The standard form of the equation of a parabola is (x - h)² = 4·p·(y - k)

The coordinates focus = (h, k + p)

The y-coordinates of the directrix, y = k - p

By comparison, we have;

h = 1/3...(1)

k + p = 2/3...(2)

k - p = 1/2...(3)

Adding equation (3) to equation (2) gives;

k + p + (k - p) = k + k + p - p = 2·k = 2/3 + 1/2 = 7/6

k = (7/6)/2 = 7/12

k = 7/12

From equation (2), we get;

p = 2/3 - k

∴ p = 2/3 - 7/12 = 1/12

p = 1/12

The equation of the parabola is therefore;

(x - 1/3)² = 4·(1/12)·(y - 7/12) = y/3 - 7/36

y = 3 × ((x - 1/3)² + 7/36) = 3 × ((x² - 2·x/3 + 1/9) + 7/36) = 3·x² - 2·x + 11/12

y = 3·x² - 2·x + 11/12.

Answer:

Step-by-step explanation:

f(x) = (x + 3)(x - 2​) has two zeros:  One stems from (x + 3) = 0 and is (-3, 0); the other stems from (x - 2) = 0 and is (2, 0).  

The axis of symmetry is a vertical line located halfway between -3 and 2:  

x =  -1/2.

The graph opens up because the given (x + 3)(x - 2) has a positive leading coefficient (+1).

With this information we can eliminate the last two possible answers.  Note that the x-intercepts of the first graph are -3 and 2,  Thus, the first graph is the correct one.

Answer:

1/3

Step-by-step explanation:

3÷6/1 is the same thing as 3÷6

and when reducing to the lowest term gives 1÷3 or 1/3

Answer:

Amar will need 48 teaspoons of sugar to make lemonade

Step-by-step explanation:

If u need 4 teaspoons to make one tablespoon, then you just can do

4 x 1 = 4

so, having that now you can do

4 x 2 = 8

there you get 8 teaspoons

Now you do

4 X 12 = 48

Answer:

angle B is 38°

Step-by-step explanation:

all angles in a triangle has to equal 180°.

So first find the measurement of angle BAD. This is done by subtracting angle of CAD=46° from the total angle CAB=78° to get 32° for angle BAD. So if angle ADB is 110° and angle BAD is 32° which equals (110+32=) 142.

Then take 180 - 142 = 38°

Answer:

38

Step-by-step explanation:

We can see that A is equal to 78. We can also see that CAD is equal to 46. Therefore BAD is equal to 32. Add 32 and 110 together to get 142. Subtract 142 from 180 to get 38.

Hope that this helps!

Answer:

x = 6+5y

Step-by-step explanation:

x - 5y = 6

Add 5y to each side

x - 5y+5y = 6+5y

x = 6+5y

Answer:

x = 6 + 5y

Step-by-step explanation:

x - 5y = 6

Solve for x.

x - 5y = 6

Add 5y to both side

x - 5y + 5y = 6 + 5y

x = 6 + 5y

Answer:

1,3 3,1

Step-by-step explanation:

35°..

can also be 145° but not in this case since the angle is less than 90°

Answer:

the answer is $50.00

Step-by-step explanation:

okay so first u gave to subtract $80.00 from $430 u will get $350.00 then divide it by 7 and then you will get your answer

Answer:

ok

Step-by-step explanation:

Answer:

No. of sweets = 123

No. of children = 7

then

sweets per children =123/7 =17. 57

Answer: =17.57

Step-by-step explanation:

Divide the no. of sweets by the no. of children

=123/7

=17.57

Answer:

2r^2 + 3r^2 + 7r - 1 = 0

5r^2 + 7r - 1

Answer: 0.0833 or 83/1000

Hope this helps :)

Answer:

d(x)  =  6.68*x  +  765

Step-by-step explanation:

The demand function is a linear function of the price, then:

demand function d(x), is an equation of the type:

d(x)  = p*x  + b

In that equation we have two parameters  p  and  b

and we have two points of the straight line:

P ( 1500 ;  110 )

Q ( 750  ;  125 )

1500  =  p*110  +  b       (1)

750    =  p*125 + b        (2)

Subtracting  (1)  -  (2)  

1500  -  750  =  (110- 125 ) +  b

750  + 15  =  b

b  =  765     intercept on y-axis

1500  =  110*p  + 775

1500  -  765  =  110 *p

p  =  735/110

p  =  6.68

The equation of demand is:

d(x)  =  6.68*x  +  765

Answer:

Options : 1 , 2 , 4 , 5

Step-by-step explanation:

Rational numbers are numbers of the form

                                                                 [tex]\frac{p}{q}[/tex],

where p and q are integers and q≠0

A decimal number is a rational number , if its :

A) Terminating.

       Example : 0.5

B) Non Terminating and Recurring(repeating).

      Example : 0.111111111.....

Option 1 : True

Option 2 : True

Option 3 : False             [ denominator cannot be zero ]

Option 4 : True

Option 5 : True

Answer:

using trigonometry first find the height I mean the dotted line

then use the formular 1/2*h*(a+b)

where h is the height you just found

a is 10

b is 6

Answer:

Part A

x + y ≤ 460

2.5·x + 1.25·y ≥ 600

Part B

192 bottles

Step-by-step explanation:

The given parameters are;

The selling price of a can of lemonade = $2.50

The selling price for each bottle of water = $1.25

The amount the club needs to raise to cover the cost of renting costumes, A = $600

The maximum acceptable cans and bottles = 460

Part A

Let 'x', represent the number of cans of lemonade accepted by the students, and let 'y' represent the number of bottles of water accepted, we have;

The situation can be represented by the following system of inequalities

x + y ≤ 460

2.5·x + 1.25·y ≥ 600

Part B

The number of cans of lemonade sold, x = 144

Therefore, we have;

2.5 × 144 + 1.25·y ≥ 600

1.25·y ≥ 600 - 2.5 × 144 = 240

1.25·y ≥ 240

y ≥ 240/1.25 = 192

y ≥ 192

The least number of bottles of water that must be sold to cover the cost of renting costumes, y = 192 bottles

Answer:

Step-by-step explanation:

B. Because adding 2 moves you to the left when inside the parentheses.

not so sure about your question. please check.

Answer:

lol sorry for answer what's that

Answer:

Non of the given options

A function that represent an exponential decay and 2 as the y-intercept is y = 0.85ˣ + 1

Step-by-step explanation:

An exponential decay function is a function that reduces in magnitude at a constant percentage rate, r (< 1)

An exponential decay can be represented by the formula, y = a·(1 - r)ˣ

Therefore, the growth factor, (1 - r) = b is less than 1 for an exponential decay

Therefore the function that represent an exponential decay is y = 0.85ˣ, while a function that represent an exponential decay and has a y-intercept of 2 is y = 0.85ˣ + 1. therefore, non of the options

Answer:

11.6a + 880.2b - 477.2c

Step-by-step explanation:

Given:

length of the court = (5.8a+6.1b-3.6c) feet

width of the court = (434b-235c) feet

Since the court is said to be rectangular in shape :

The perimeter of a rectangle = 2(length + width)

Perimeter = 2(5.8a+6.1b-3.6c + 434b-235c)

Perimeter = 2(5.8a+6.1b+434b-3.6c-235c)

Perimeter = 2(5.8a + 440.1b - 238.6c)

Perimeter = 11.6a + 880.2b - 477.2c

Answer:

don't know about this question

Answer:

D. g(x) = 3·x²

Step-by-step explanation:

The given parent function, f(x) = x²

The graph of the function, g(x) is narrower than the graph of the function f(x)

Therefore, the coefficient of the quadratic function is larger than 1

The given point on the parabola, g(x) = (1, 3)

Therefore. when x = 1, g(x) = 3

However, when x = 1, f(x) = 1

Therefore, given that g(x) = a·f(x), we get;

a = g(x)/(f(x)) = 3/1 = 3

g(x) = 3·x²

Answer:

x≤2

Step-by-step explanation:

-6(4 - x) ≤-4(x + 1)

Distribute

-24 +6x≤ -4x-4

Add 4x to each side

-24 +6x+4x≤-4x-4+4x

-24 +10x≤ -4

add 24 to each side

-24+10x+24≤-4+24

10x≤20

Divide by 10

10x/10 ≤20/10

x≤2

Answer:

D. x ≤ 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

-6(4 - x) ≤ -4(x + 1)

Step 2: Solve for x