Geometric Applications: For the next three questions, use the information below:
A rectangle has a side with a length of 8ft and a width of (2x+4)ft.
Label the rectangle
15 pts
a) Find the perimeter of the Rectangle:
b) Find the area of the rectangle:
c) If the total Area is 80 square feet, find the width in feet.

The temperature of the body after 60 minutes is  60.5° F.

Using the Newton's law of cooling;

T(t) =[tex]Ts + (To - Ts)e^-kt[/tex]

T(t) = temperature at time t

Ts = temperature of the surrounding

To = Temperature of object

t = time taken

k = cooling constant

Now;

[tex]T(t) -Ts=(To - Ts)e^-kt\\45 - 67 = (34 - 67)e^-15k\\-22 = -33e^-15k\\-22/-33 = e^-15k\\0.667 = e^-15k\\ln(0.667) = ln( e^-15k)\\-0.405 = -15k\\k = -0.405/ -15\\k = 0.027[/tex]

At t = 60 min

[tex]T(t) = Ts + (To - Ts)e^-ktT(60) = 67 + (34 - 67)e^-( 0.027*60)\\T(60) = \\67 + (-33)e^-( 0.027 * 60)\\T(60) = \\60.5 F[/tex]

T(60) = 60.5° F

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Answer:

T≈169

Step-by-step explanation:

Enter only the final temperature into the input box.

T_a = 67\hspace{50px}T_0=210

T  

a

​

=67T  

0

​

=210

\text{Write Formula:}

Write Formula:

T=67+(210-67)e^{-kt}

T=67+(210−67)e  

−kt

Plug in givens

\color{blue}{T}=67+143e^{-k\color{green}{t}}

T=67+143e  

−kt

Simplify

\text{Plug in given time and temperature:}

Plug in given time and temperature:

\color{blue}{193}=67+143e^{-k(\color{green}{1.5})}

193=67+143e  

−k(1.5)

Simplify

\text{Solve for }k\text{:}

Solve for k:

193=

193=

\,\,67+143e^{-1.5k}

67+143e  

−1.5k

-67\phantom{=}

−67=

\,\,-67

−67

126=

126=

\,\,143e^{-1.5k}

143e  

−1.5k

\frac{126}{143}=

143

126

​

=

\,\,\frac{143e^{-1.5k}}{143}

143

143e  

−1.5k

​

Divide by 143

0.8811189=

0.8811189=

\,\,e^{-1.5k}

e  

−1.5k

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,\ln\left(e^{-1.5k}\right)

ln(e  

−1.5k

)

Take ln of both sides

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,-1.5k

−1.5k

\frac{\ln\left(0.8811189\right)}{-1.5}=

−1.5

ln(0.8811189)

​

=

\,\,\frac{-1.5k}{-1.5}

−1.5

−1.5k

​

Divide by -1.5

0.0843751=

0.0843751=

\,\,k

k

k\approx

k≈

\,\,\color{blue}{0.084}

0.084

Round k to nearest thousandth

\text{Complete Formula:}

Complete Formula:

T=67+143e^{-\color{blue}{0.084}t}

T=67+143e  

−0.084t

Plug in k

\text{Find temperature after }\color{green}{4}\text{ minutes:}

Find temperature after 4 minutes:

T=67+143e^{-0.084(\color{green}{4})}

T=67+143e  

−0.084(4)

Plug in time

T=67+143e^{-0.336}

T=67+143e  

−0.336

Multiply

T=169.1911041

T=169.1911041

Plug into the calculator

T\approx 169

T≈169

Step-by-step explanation:

you really don't see this ?

this is rotated by 180 degrees around the origin.

do you see how the different points change positive from one shape to the other ?

think what happens when you rotate a disk (like a plate) with something on it. how does that something on it change is position and orientation ?

this here is the same thing. look at H and how it turns into O.

Answer: This is B.) -9

Step-by-step explanation:

Step-by-step explanation:

All of those numbers are greater than -5 except for B.

Answer:

A: 2400

B: 600

C: 1800

Step-by-step explanation:

A= x+3x=4x

C = x+2x= 3x

4x+x+3x = 4800

8x= 4800

x= 600

share of A= 2400$

share of B= 600$

share of C= 1800$

Answer:

A. Solution

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Step-by-step explanation:

*Note:

A coordinate is a solution if both the left side and right side of the equation is equal.

Step 1: Define

Identify.

-6x + 6y = 9

(1/2, 2)

Step 2: Verify

Since 9 does indeed equal 9, the coordinate (1/2, 2) is a solution.

Answer:

Step-by-step explanation:

C I took the test

The equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.

The percentage is defined as ratio expressed as a fraction of 100.

Finley was paid an annual salary of $57,000

with a 4% raise for each following year

Finley's annual salary, during the 2th year

⇒ 4% of 57,000 + 57,000

⇒ (0.04)57,000 + 57,000

⇒ 2280 + 57,000

⇒ 59280

Finley's annual salary, during the 2th year

Determine the difference between year 2 and year 1 salary.

Rate of change = 4% of 57,000 - 57,000

Rate of change = (0.04)57,000 - 57,000

Rate of change = 57,000(0.04 - 1)

Finley's annual salary, during the 5th year

Determine the difference between year 5 and year 4 salary

⇒ 57,000(0.04(5) - 1)

That's the constant.

Finley's annual salary, during the nth year

So, f (n) = 57,000(1.04n – 1)

Hence, the equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.

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Answer:

no entiendo tu pregunta xD !?

Answer:HOLA

Step-by-step explanation:Mi casa su casa , come estas , si uno

Answer:

6 red balls

Step-by-step explanation:

The probability in the first pick

6/21

The probability in the second pick (without replacement)

5/20

the requested probability

(6/21)(5/20) = 30/420

simplification

30/420 = 3/42 = 1/14

Hope this helps

Answer:

6 red balls.

Step-by-step explanation:

If there are x red balls then

probability of 2 red balls

= x/21 * (x - 1)/20 = 1/14

x^2 - x / 420 = 1/14

x^2 - x = 30

x^2 - x - 30 = 0

(x - 6)(x + 5) = 0

x = 6.

Answer:

7

12-5=6 this helps you''';

Answer:

  x = 15

Step-by-step explanation:

Corresponding sides have the same ratio:

  UV/PR = TV/QR

  (x +6)/14 = (x -3)/8

  4(x +6) = 7(x -3) . . . . . . multiply by 56

  4x +24 = 7x -21 . . . . . . eliminate parentheses

  45 = 3x . . . . . . . . . . . add 21-4x

  15 = x . . . . . . . . . . . .divide by 3

_____

Alternate solution

The long-side : short-side ratios for the two triangles are ...

  14 : 8 = (x +6) : (x -3)

If we look at the differences between the ratio numbers we see ...

  14 -8 = 6

  (x +6) -(x -3) = 9

That is, the numbers in the second ratio must be 9/6 = 3/2 times the numbers in the first ratio. In other words, ...

  x -3 = (3/2)(8) = 12

  x = 15

Check: x +6 = 3/2(14) ; 15 +6 = 21

Answer:

1.8?

Step-by-step explanation:

Answer:

its 1 4/5 your welcome

Step-by-step explanation:

Answer:

Its either A or C

Step-by-step explanation:

Answer:

whats the question.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

x(48 - 2x) = 32

Hope it helps.

Answer:

c

Step-by-step explanation:

Answer:

18 minutes and 45 seconds

Step-by-step explanation:

[tex]\frac{1}{50}[/tex] + [tex]\frac{1}{30}[/tex] = [tex]\frac{3+5}{150}[/tex] = [tex]\frac{4}{75}[/tex]

1 ÷ [tex]\frac{4}{75}[/tex] = [tex]\frac{75}{4}[/tex] = 18' 45''

Answer:

18.75 minutes If A and B work together

Answer:

[tex]I(-2,0) \to\\ I \ ' \ (-0.5,0)\\\\J(3,2) \to\\ J \ ' \ (0.75,0.5)\\\\K(1,-1) \to\\ K \ ' \ (0.25,-0.25)\\\\[/tex]

==================================================

Explanation:

For each point, multiply each x,y coordinate by 0.25 (the scale factor) to dilate the preimage to the image. This will shrink the image because the positive scale factor is less than 1.

So for instance, point J(3,2) will have this scratch work

meaning J(3,2) moves to J ' (0.75, 0.5)

----------

Side notes:

Answer:

that means you have a 5000 dollar debt

Hope This Helps!!!

Answer: (-7,-5)

Step-by-step explanation:

Because when you mark point M and A if you mirror point M and A on the x Axis then you will get (-7,-5)

Answer:

y = -30

Step-by-step explanation:

3 (y + 8) = 2y - 6

3y + 24 = 2y -6                Distribute the 3

y + 24 = -6                       Subtract 2y on both sides

y = -30                              Subtract 24 on both sides

Answer: 29

Step-by-step explanation:

29 ÷ 8 = 3 remainder: 5

I solved using long division.

Answer:

29

Step-by-step explanation:

30

24

5

8x3=24

24+5= 29

Beacuase it had to be smaller than 30

Answer:

1) x > -2

2) x < -1

Step-by-step explanation:

1) 2(x - 2) + 7 > -1

2x - 4 + 7 > -1

2x + 3 > -1

2x > -4

x > -2

2) 5 - 4x > 9

-4x > 4

x < -1

Answer:

13. STR

14. VY

Step-by-step explanation:

I hope this helps!

4 3/4 = 19/4

133/(19/4) = 133(4/19) = 1197/19 = 63 mph

Answer:

10

Step-by-step explanation:

"Least" means smallest.

"Common" means same.

"Denominator " means the bottom number in a fraction.

Something/2 can be changed to something/10

AND something/5 can also be changed to

something/10

1/2 >>>> 5/10

3/5 >>>> 6/10

10 is the least common denominator.

Answer:

5 feet + 12 inches = 2 yards

48 inches = 1 foot + 1 yard

5 feet = 3 feet + 24 inches

Step-by-step explanation:

To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:

1 feet = 12 inches

3 feet = 1 yard

To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.

12 inches = 1 feet

Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.

Blank inches = 1 foot + 1 yard

To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.

Blank feet = 3 feet + 24 inches

Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.

Answer:

  width: 37.9 ft

  height: 39.7 ft

Step-by-step explanation:

Sometimes it is easier to work these problems by finding the average of the length and width. If that value is x, then the length is x+0.9, and the width is x-0.9. The area is ...

  A = LW

  1504.6 = (x +0.9)(x -0.9) = x^2 -0.81

  1505.41 = x^2

  x = √1505.41 ≈ 38.7996

  width = x -0.9 = 38.8 -0.9 = 37.9

  height = 38.8 +0.9 = 39.7

The width of the door is approximately 37.9 ft; the height is about 39.7 ft.

Answer:

1/4

Step-by-step explanation:

1/4 because it is one piece out of the four cuts. if it were yellow, than it would be 2/4, or 1/2

Answer:

a) 8/17

b) 4/17

c) 5/17

d) 48/187

Step-by-step explanation:

a) P(silver) = 16/34 = 8/17

b) P(blue) = 4/17

c) P(red) = 5/17

d) P(silver, not silver) = 8/17 × 18/33 = 144/561 = 48/187

The probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have 16 silver cars, 8 blue cars and 10 red cars in a parking lot.

[A] -

P{silver} = 8/(16 + 8 + 10) = 8/34

[B] -

P{blue} = 16/(16 + 8 + 10) = 16/34

{C} -

P{red} = 10/(16 + 8 + 10) = 10/34

D) -

P{not silver} = 1 - 15/33 = 18/33

Therefore, the probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

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