A time/motion word problem"A plane leaves Denver heading due north at 500 mph. Simultaneously, another plane leaves Denver traveling due east at 1200 mph. After how many minutes will the planes be 650 miles apart?"

I know the answer is 30, but I have no clue how to solve the problem itself

Answers

Answer 1

Answer: The two planes are flying on the two legs of a right triangle.
The straight distance between them is the hypotenuse of the triangle.

Since the speeds are in mph, let's work the time in hours.
Call the time 'H' that we're looking for.
It's the number of hours after they both take off that they're 650 miles apart.

After 'H' hours, the first plane has gone 500H miles north.
After 'H' hours, the second plane has gone 1200H miles east.
After 'H' hours, they are 650 miles apart.

Do you remember this for a right triangle ? ==> A² + B² = C²

(500H)² + (1200H)² = (650)²

250,000H² + 1,440,000H² = 422,500

1,690,000 H² = 422,500

H² = (422,500) / (1,690,000) = 0.25

H = √0.25 = 1/2 hour = 30 minutes

Answer 2

Answer: $x^2=500^2+1200^2\n\nx^2=250000+1440000\ \ \ \Rightarrow\ \ \ \ x^2=1690000\ \ \ \Rightarrow\ \ \ \ x=1300\ [mph]\n\nthe\ distance=650\ miles\n\nthe\ speed= (the\ distance)/(the\ time) \ \ \ \Rightarrow\ \ \ 1300\ [mph]= (650\ [miles])/(the\ time)\n\nthe\ time= (650)/(1300) \ [hr]=0.5\ [hr]=30\ [min]\n\nAns.\ after\ 30\ minutes.$

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$F= (9)/(5) C+32\ /\cdot5\n \n5F=9C+160\ \ \ \Rightarrow\ \ \ 9C=5F-160\ /:9\n \nC= (5F-160)/(9) \ \ \ \Rightarrow\ \ \ Ans.\ 3)$

the answer to your question is number 3

Use the functions m(x) = 5x + 4 and n(x) = 6x − 9 to complete the function operations listed below.Part A: Find (m + n)(x). Show your work.

Part B: Find (m ⋅ n)(x). Show your work.

Part C: Find m[n(x)]. Show your work.

Answers

For this case we have the following functions:

For the sum of functions we have:

Substituting values:

Adding similar terms we have:

For the multiplication of functions we have:

Substituting values:

If we apply the distributive property we have:

Adding similar terms we have:

For the composition of functions we have:

Rewriting we have:

A. (m+n)(x)=
5x+4+6x-9=
11x-5

B. (mn)(x)=
(5x+4)(6x-9)=
30x^2+24x-45x-36=
30x^2-21x-36

C. basically sub n(x) for x in m(x)
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A sum of a number and 14 is at least of 28

Answers

a sum means we are adding.
a number and 14 means we are adding 14 and a number (x)
at least means <
and to balance the equation out they gave us 28
so our answer is....
14 + x < 28

Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.

Answers

When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.

Answer:Sample Response: When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.

Step-by-step explanation:

Two same-sized triangular prisms are attached to a rectangular prism as shown below.If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
a 1,208 square centimeters
b 1,592 square centimeters
c 1,004 square centimeters
d 1,400 square centimeters

Answers

Answer: a) 1,208 square centimeters

Step-by-step explanation:

The surface area would be the sum of the different areas separated in the figure.

The area of the front and back faces of the rectangular prism:

$a*c*2=20*12*2=480cm^(2)$

The area of the top and the base of the rectangular prism:

$a*e*2=20*8*2=320cm^(2)$

The area of the front and back faces of both triangular prisms:

$(d*c)/(2)*4=(5*12)/(2)*4=30*4=120cm^(2)$

The area of the side faces of both triangular prisms:

$e*b*2=8*13*2=208cm^(2)$

The area of the bases of both triangular prisms:

$d*e*2=5*8*2=80cm^(2)$

Finally, the surface area of the whole figure:

$480+320+120+208+80=1,208cm^(2)$

A*E*2= 20*8*2=320
A*C*2= 20*12*2=480
D*C/2*4 5*12*2=120
B*E*2 13*8*2=208
D*E*2 5*8*2=80
320+480+120+208+80=1208
so ur answer is A

A car with a cost of $25,000 is decreasing in value at a rate of 10% each year. The function g(t)= 25,000(0.9)^t gives the value of the car after t years. When will the value of the car be about $12,000? A) after 7 years B) after 9 years C) after 13 years Could you also explain how to do it?

Answers

12,000 = 25,000 $(0.9)^(t)$
Divide both sides by 25,000 → 0.48 = $(0.9)^(t)$
Convert to log form → $log_(0.9)$ 0.48 = t
Use the change of base formula → $(log 0.48)/(log 0.9)$ = t
Plug into the calculator → 6.966 = t

Answer: A

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Could someone help me with number 3?

A time/motion word problem"A plane leaves Denver heading due north at 500 mph. Simultaneously, another plane leaves Denver traveling due east at 1200 mph. After how many minutes will the planes be 650 miles apart?"I know the answer is 30, but I have no clue how to solve the problem itself

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A time/motion word problem"A plane leaves Denver heading due north at 500 mph. Simultaneously, another plane leaves Denver traveling due east at 1200 mph. After how many minutes will the planes be 650 miles apart?"

I know the answer is 30, but I have no clue how to solve the problem itself