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klemol [59]
3 years ago
11

nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. in the first part of the race, her av

erage speed was 8.75 kilometers per hour. for the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. which expression represents nikita’s distance for the second part of the race?
Mathematics
1 answer:
Nataliya [291]3 years ago
5 0
Total distance 5 km; at 5km / 0.65 h =

Second part distance: x; at 6 km/h, during t2

First part distance: 5 - x; at 8.75 km/h, during t1

V = d/t ⇒ t = d/V

t2 = x/6
t1=[5-x]/8.75

t2 + t1 = 0.65

x/6 + [5-x]/8.75 = 0.65

x/6 + 5/8.75 - x/8.75 = 13/20

 x/6 - x/8.75 = 13/20 - 5/8.75

x/6 - 4x/35 =13/20 - 20/35

35x - 24x = (35*6)(35*13 - 20*20)/(20*35)

11 x = 16.5
x = 16.5/11 = 1.5 km












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Find the quotients. 25÷34 94÷-34 -57÷-13 -53÷16
Assoli18 [71]

Answer:

  • 25 ÷ 34 = 25/34
  • 94 ÷ -34 = - 94/34 = -2 28/34 = -2 14/17
  • -57 ÷ -13 = 57/13 = 4 5/13
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4 0
3 years ago
Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.
miss Akunina [59]

Answer:

Here's what I get.

Step-by-step explanation:

Part A. Equation in standard form

The question is asking you to find the equation of a straight line that passes through two points

Let x = the number of days

and y = the cost

Then the coordinates of the two points are (2,225) and (5,480).

(i) Calculate the slope of the line

\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}

In other words, the daily rental is $85/day.

(ii) Calculate the y-intercept

\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}

(iii) Write the equation for the line

y = 85x + 55

That is, the cost is $55  plus $85/day

Part B. Equation in function notation

Replace y with ƒ(x)

ƒ(x) = 85x + 55

Part C. Graphing

Let's say you want to plot a graph of the rental cost for up to ten days.

(i) Calculate two points on the graph.

When x = 0, y = 85; when x = 10, y = 905.

(ii) Scale your axes

A good number of intervals is about ten.

Your x-axis should have tick marks at 1-day intervals.

Your largest y-value is 905. Ten intervals would make about $90/interval. However, you should round that up to $100/interval for easy interpolation.

Your y-axis will run from 0 to $1000 in $100 intervals.

Plot your two points and draw a straight line through them.

(iii) Axis labels

x represents the number of days, so the label on the x-axis could be "No. of days."

y represents the cost of renting the boat, so the label on the y-axis could be "Rental cost."

Your graph should resemble the one below.

4 0
3 years ago
Don and Frank started from the same point and drove in opposite directions. Don's rate of travel was 50 miles per hour. Frank's
lozanna [386]

9514 1404 393

Answer:

  180 miles

Step-by-step explanation:

Don drove (50 mi/h)×(2 h) = 100 mi.

Frank drove (40 mi/h)×(2 h) = 80 mi.

Since they drove in opposite directions, the total distance between them is

  100 mi +80 mi = 180 mi.

6 0
3 years ago
Please help me thanks :)
KengaRu [80]

Answer:

1895.22 feet^2

Step-by-step explanation:

So starting off we will find the area of the hexagon.

The formula is complicated so I won’t write it.

The area is 509.22 feet^2.

Now for the triangles.

So the base is 14 feet and the height is 33 feet.

After multiplying them and dividing them by two I got 231 feet^2.

Then multiplying 231 by 6 I got 1386 feet^2.

So adding up 1386 and 509.22 I got 1895.22 feet^2.

8 0
3 years ago
Can anybody help me with this question...please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Vesna [10]

it's 72°, since move two point

5 0
3 years ago
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