Identify whether the following items best fit with a discrete or a continuous model. Then determine whether it is a linear (arithmetic) or exponential (geometric) relationship that is being described. Finally, write the function that represents the situation.
One square inch is infected by bacteria. For every hour that passes the amount of area infected by the bacteria doubles.

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)

Answer:

3(3+2b)

or

2b +9

Step-by-step explanation:

Answer:

Step-by-step explanation:

3b+5-9b-9+6b

=3b+6b-9b+5-9=-4

Answer:

B is the answer

Try all and see for yourself

Answer:

Part A: a. the point 3 units to the left of 7

Part B: b. -4

Step-by-step explanation:

Part A: The expression can be simplified into 7 - 3, and when you subtract a number, you go left on the number line, so the point 3 left of 7

Part B: 7 - 3 = 4, and to get to 0 from 4, you need to subtract 4 or add -4

Answer:

p = y+3

Step-by-step explanation:

Answer:

 [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Step-by-step explanation:

Explanation

Given function f(r) = r² log r  ....(i)

Apply derivatives formula

              [tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]

             [tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]

            [tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]

Differentiating equation (i) with respective to 'r' , we get

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]

Final answer:-                

               [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Answer:

8

Step-by-step explanation:

2(20-8x)=5x-2

40-16x=5x-2

42=21x

x=2

HK=5x-2 = 5(2)-2 = 10-2 = 8

Answer:

77,5

Step-by-step explanation:

13

. 75

_____

65

71

_____

77,5

Answer:

3 divided 5

Step-by-step explanation:

Edgar will get 3/5 or 0.6 part of pumpkin bread.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Total numbers of people in Edgar's family = 5

Total number of pumpkin bread = 3

Since, 3 bread are divided equally among 5 people,

implies that, bread will divide in the same ratio,

5 people = 3 bread

1 people= 3/5 bread

1 people= 0.6 part of bread

So Edgar will get 3/5 or 0.6 part of bread.

To know more about Ratio on:

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Answer:

D. Not factorable

Step-by-step explanation:

Answer:

for (f+g)(x): 7x + 3; x = -3/7

for (f-g)(x): -3x - 3; x = -1

Step-by-step explanation:

(f+g)(x) = (2x+7)+(5x-4)

Eliminate parentheses.

2x + 7 + 5x -4

Combine like terms.

7x + 3

If you are solving for x, move the 3 to the other side.

7x = -3.

Then divide each side by 7.

x = -3/7

(f-g)(x) = (2x+7) - (5x -4)

Distribute the negative.

(2x+7) + (-5x+4)

Eliminate parentheses.

2x + 7 - 5x - 4

Combine like terms.

-3x -3

If you are solving for x, move the -3 to the other side.

-3x = 3

Then divide each side by -3.

x = -1.

Answer:

Summarize the end of the story and explain the resolution— when the conflict is solved :

At the end of the story...

Step-by-step explanation:

Answer:

Hi...

59+4=63

63/7=9

So Nina will be 9 years old

Answer:

4x+20+2

4x+22

Step-by-step explanation:

4×x=4x then 4×5=20+2

Answer:

D. 10x - 5

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 2x + 5x

g(x) = 3x - 5

(f + g)(x) is f(x) + g(x)

Step 2: Simplify

f(x) = 7x

g(x) = 3x - 5

Step 3: Find

Answer:

The bubble on the left should be 0.01.  The bubbles on the right should be: (top to bottom) 7, 0.1, 0.07, 0.004.

Step-by-step explanation:

You're just supposed to break the decimal into parts.  It like breaking 178 into hundreds, tens, and ones (100 + 70 + 8)

Answer: 2 (x+5)

Step-by-step explanation:

Answer:

x+5

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The relation given as represented by the table of values is definitely not a function. This is because, 1 domain value (x-value), is having two range values (y-values), 2 and 5, that are assigned to it.

A function cannot have two y-values assigned to one x-values.

Answer:

1.48 miles

Step-by-step explanation:

If the trail is 14.8 miles and Rita has hiked 1/10 of it. Then just multiply 14.8 by 1/10.

14.8 * 1/10 = 1.48 miles.

Answer:

1.48

Step-by-step explanation:

I know the answer is correct

Answer:

Step-by-step explanation:

-x+5=9

-x=-9-5

-x=-14

x=14

coefficient of x is -1

Answer:

19

Step-by-step explanation:

The probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

P(Small | Cold) = n(Small and Cold)/n(Cold)

From the table:

P(Small | Cold) = 8/(8 + 12 + 5)

P(Small | Cold) = 0.32

or

P(Small | Cold) = 32%

Thus, the probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

Learn more about the probability here:

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Answer:

11/4

29/6

32/5

Step-by-step explanation:

Answer: 11/4, 29/6, 32/5

Step-by-step explanation:

This is going to help trust me

Answer:

you're scale is 1.6666667

Step-by-step explanation:

because if you do 30 decided by 18 it gives u 1.6666667

Answer:

The options are not shown, so i will solve this in a general way.

Let's suppose that there are N nuts

If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.

If we divide the N nuts into groups of 3, there is no remainder.

This means taht N is a multiple of 3. then we can write:

N = 3*k

where k is a random integer.

Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:

N = 5*j + 2

where j is a random integer.

Now we only need to find a pair of k and j (both positive integers) such that:

3*k = 5*j + 2

We can rewrite this as:

k = (5/3)*j + (2/3)

Now we could just input different values of j, and see if k is also an integer:

j = 2

k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4

Then the pair j = 2, k = 4 is a possible solution.

N = 3*k = 3*4 = 12

N = 5*j + 2 = 5*2 + 2 = 12

From this we can conclude that N = 12, so Scrat has 12 nuts.

Now with the equation

k = (5/3)*j + (2/3)

We can find other possible combinations of j and k, that will give different values for N.

for example, if j = 5:

k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9

Then the pair j = 5, k = 9 is also a possible solution:

N = 3*k = 3*9 =  27

N = 5*j + 2 = 5*5 + 2 = 27

In this case, Scrat has 27 nuts.

Answer: 55, 720

This is the answer. No doubt about it

Answer:

Opposites of each other?

Step-by-step explanation:

I am not sure, the only thing that is not making them equal to each other is that they have opposite signs.

Answer:

L= 11m

W= 7m

Step-by-step explanation:

Step one:

given data

Let the width W= x

Length = (2x-3)

P= 36 m

Required

The perimeter

P= 2L+2W

36= 2(2x-3)+ 2x

36= 4x-6+2x

collect like terms

36+6= 6x

42= 6x

divide both side by 6

x= 7

the width is 7 m

the length = 2x-3= 2*7-3= 14-3= 11 m