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Temka [501]
2 years ago
9

George took a nonstop flight from Dallas to

Mathematics
1 answer:
In-s [12.5K]2 years ago
5 0

It is given in the question that,

George took a nonstop flight from Dallas to Los Angeles, a total flight distance of 1,233 miles. The plane flew at a speed of 460 miles per hour for the first 75 minutes of the flight and at a speed of 439 miles per hour for the remainder of the flight.

Let for x hours, the flight travelled with a speed of 439 miles per hour .

So we have,

460* \frac{75}{60} + 439*x = 1233

575 + 439x =1233
\\
439x = 1233 - 575
\\
439x = 658
\\
x = \frac{658}{439} hours

And to convert it in minutes, we have to multiply by 60. And on doing so, we will get

x = \frac{658}{439}*60 =approx \ 90  \ minutes

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A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of th
Digiron [165]

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets  explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

 the line which represent the equation and c is the y-intercept

- The slope of the line m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

  where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

  the linear equation between the cars' numbers and the weeks

  numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ m=\frac{175-200}{15-10}=\frac{-25}{5}=-5

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

  two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

  x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

7 0
2 years ago
Read 2 more answers
Ne Friday night, a group of friends bought 5 containers of popcorn and 4 granola bars at the movie theatre for $42.50. The next
Tomtit [17]

In this question , it is given that p represents cost of 1 container of popcorn . Therefore cost of 5 containers of popcorn = 5p and cost of 3 containers of popcorn = 3p .

And g represents cost of 1 container of granola bars. THerefore cost of 4 containers of granola bars = 4g and cost of 6 containers of granola bars = 6g .

According to the given question, the required linear equations are

5p+4g=42.50 , 3p+6g =34.50 .

And these are the the required system of linear equation .

4 0
2 years ago
The quotient of 9.2 x 10 6 and 2.3 x 10 2 expressed in scientific notation is
Virty [35]
What we know:
quotient 9.2 x 10^6/ 2.3 x 10²
in quotients exponents are subtracted of they have the same base, for example 10^6 and 10² have the same base of 10

What we need to find: quotient 9.2 x 10^6/ 2.3 x 10²
9.2 x 10^6        
--------------  =    4 x 10^4    
 2.3 x 10²

Here in this problem I divided 9.2 by 2.3 and got 4, since the solution was simple and clean meaning no repeated decimals I went ahead and divided the 10^6 by 10^2 and got 10^4.


Another method would be to expand both numbers then divide and do scientific notation again.
Remember to change to normal notation you move the decimal to the right using the number of the exponent.

9.2 x 10^6= 9200000
2.3 x 10²= 230

920000/230=40000

40000= 4 x 10^4 scientific notation

Use the method that is best for you or just know you can use either method to check your work.

4 0
2 years ago
The pizza has an area of 78.5 in². What is the minimum width of a placemat that can be placed underneath it so that the pizza do
xz_007 [3.2K]

Answer:

The minimum width of the placemat is 10 inches.

Step-by-step explanation:

Let suppose that placemat has a square form, whose width must be at least equal to the diameter of the pizza, so that pizza does not touch the table. Hence, the following relationship is obtained:

w = D

Where:

w - Width of the placemat, measured in inches.

D - Diameter of pizza, measured in inches.

The area of the pizza, measured in square inches, is determined by this formula:

A = \frac{\pi}{4} \cdot D^{2}

The diameter is cleared afterwards:

D = \sqrt{\frac{4\cdot A}{\pi} }

If A = 78.5\,in^{2} and \pi = 3.14, then:

D = \sqrt{\frac{4\cdot (78.5\,in^{2})}{3.14} }

D = 10\,in

The minimum width of the placemat is 10 inches.

4 0
2 years ago
Read 2 more answers
Perpendicular segments are best described as being which of the following
KatRina [158]
It's A. Segments that intersect at the right angle
5 0
2 years ago
Read 2 more answers
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