For what values of r will the area of the shaded region be greater than or equal to 12 square units? Write your answer as an inequality.

Answer:

see the attachment

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

First, we factorize each integer:

[tex]12 = 2^{2}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex]

Then the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]36 = 2^{2}\times 3^{2}[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3}\times 3^{2} = 72[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 72, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]32 = 2^{5}[/tex], [tex]40 = 2^{3}\times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{5}\times 5 = 160[/tex], [tex]HCF = 2^{3} = 8[/tex]

The highest common factor and the least common multiple are 8 and 160, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex], [tex]60 = 2^{2}\times 3 \times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 \times 5 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]42 = 2\times 3 \times 7[/tex], [tex]56 = 2^{3}\times 7[/tex], [tex]70 = 2\times 5\times 7[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3} \times 3 \times 5 \times 7 = 840[/tex], [tex]HCF = 2\times 7 = 14[/tex]

The highest common factor and the least common multiple are 14 and 840, respectively. [tex]\blacksquare[/tex]

To learn more on prime numbers, we kindly invite to check this verified question: https://brainly.com/question/4184435

Answer:

(4 − 3)(−3 + 6) − (2 )

1(3)-2

3-2

1

Hope This Helps!!!

Answer:

y = | x - 3 | is graphed on the attachment below ↓

Step-by-step explanation:

If you ever need an equation graphed, here's a useful site called Desmos that can do that really well and for free.

Answer:

1. 2.5 miles/hour

2. 24 minutes

Step-by-step explanation:

1. 5/6 of mile in 1/3 of an hour. In 1 hour, Bianca can walk 5/6 x 3 = 15/6 miles or 2.5 miles/hour

2. 5/6 of mile in 1/3 of an hour, hour in 1 mile = (1 x 1/3)/(5/6) = 2/5 = 0.4 hour = 24 minutes

Answer:

Well your Hypotenuse is 10 and your other angle is 8 so it is most likely 6 because you see a change in 2 each time and it is about 2 units smaller because all right triangles follow a pattern

Step-by-step explanation:

if it was too go even higher it would go to 12,14,16 etcetera

[tex]\rule{2000pt}{1000000pt}[/tex]

Answer:

OD 60 in by 45 in

Step-by-step explanation:

Answer:

L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

Answer:

Rational

Step-by-step explanation:

It isnt whole because its a decimal,

It isnt an Integer because its a decimal

It isnt natural because its a decimal

Meaning it can only be rational

Answer:

2+2=4................

Answer:

you are wrong because 2+2=4

Answer:

it depends how much the god snores within a certain time period

Answer:

1/3

Step-by-step explanation:

-2-4 = -6

-7-11 = -18

Answer:

[tex]-37\frac{3}{4}[/tex]

Step-by-step explanation:

0.75 is equivalent to three quarters, or (3/4).

3/4 would be the fraction. -37 would be the whole number.

[tex]-37.75 = \boxed{-37\frac{3}{4}}[/tex]

Hope this helps.

Answer:

- 37 3/4

Step-by-step explanation:

Answer:

y = m x + b    standard form of straight line

y = 2 x + 5

The slope is m and = 2

the y intercept is 5  because when x = o y = 5

if y = 0 then x = -2/5 and would be the x intercept

x is the independent variable and y is the dependent variable

I am not familiar with your definitions for domain and range but

both x and y can vary from -∝ to = ∝

Answer:

4.546, rounded

Step-by-step explanation:

pls mark brainliest!

Answer:

huh

Step-by-step explanation:

by-step explaAnswer:

by-step epla

Step-nation:

a

Answer:

$2,025.78

Step-by-step explanation:

I = Prt ⇒ P = [tex]\frac{I}{rt}[/tex]

2.25% = 0.0225

P = 45.58 ÷ ( 0.0225 × 1 ) ≈ $2,025.78

Answer:

Step-by-step explanation:

Find c if ∠PQR = 90°?

I will ASSUME you mean point P is at (3. c)

slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6

slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)

perpendicular lines have negative reciprocal slopes.

(2 - c) / 6 = -1(3c - 9)/9

9(2 - c) = -6(3c - 9)

18 - 9c = -18c + 54

       9c = 36

         c = 4

Answer:

x=  47 18+2  201  i  ≈0.382978723+0.603295612i x=  47 −2  201  i+18  ≈0.382978723−0.603295612i  Hopefully this makes just the same amount of sense as this question

Answer:

7 hours

Step-by-step explanation:

Answer:

she could park there for 7 hours

Step-by-step explanation:

13-4=9 9/1.50=6

Answer:

y € R i guess

Step-by-step explanation:

I hope it correct

Answer:

23 seconds later Erin will catch up

Erin will run 115 meters

Step-by-step explanation:

23+4x=5x

x=23

23 seconds later Erin will catch up

Erin will run 115 meters

Answer:

6.78

Step-by-step explanation:

Answer:

6.78 pounds

Step-by-step explanation:

Add: 3.18+1.35+2.25=6.78

(If you wanted the cost for the whole thing then you need to include the price for each of the pounds)

Answer:

start at 5 on the number line and move 8 to the left.

Step-by-step explanation:

Answer:

[tex]-2^{-2} = \frac{1}{-2^{2} } = \frac{1}{4} = 0.25[/tex]

[tex]-2^{-1} = \frac{1}{-2 } = -0.5[/tex]

[tex]-2^{0} = 1[/tex]

[tex]-2^{1} = -2[/tex]

[tex]-2^{2} = 4[/tex]

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

x/2 - 3 = 5

x/2 = 5+3

x/2 = 8

x = 8×2

x = 16

[tex]x = 23[/tex]

Step-by-step explanation:

First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:

[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]

but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as

[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]

Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get

[tex]-6x - 15y = -105\;\;\;\;\;(3)[/tex]

Adding Eqn(3) to Eqn(2), we get

[tex]-5x = -115[/tex]

or

[tex]x = \dfrac{-115}{-5} = 23[/tex]