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2 years ago

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Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. K

elly ran at an average speed of 8 miles per hour. When will Ava and Kelly be 3/4 miles apart?

1 answer:

Serhud [2]2 years ago

7 0

Answer:

The answer is 0.375 hours

Step-by-step explanation:

You might be interested in

What is the length of segment XY?

Brilliant_brown [7]

Answer:

StartRoot 53 EndRoot units

XY = √53

Step-by-step explanation:

Choose which is point 1 and point 2 so you don't confuse the coordinates.

Point 1 (–4, 0) x₁ = –4 y₁ = 0

Point 2 (3, 2) x₂ = 3 y₂ = 2

Use the formula for the distance between two points.

$L = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$

$XY = \sqrt{(3-(-4))^{2} + (2-0)^{2}}$

$XY = \sqrt{49 + 4}$

$XY = \sqrt{53}$

Therefore the line of segment XY is √53.

6 0

2 years ago

Read 2 more answers

If a cone with a diameter of 10 meters has a surface area of 290.6 square meters, find its slant height.

Finger [1]

<h2>Hello!</h2>

The answer is:

The slant height is 13.43 m.

$l=13.43m$

<h2>Why?</h2>

To solve the problem, we need to use the following equations to calculate the total surface area and the lateral surface area of right cone:

$TotalSurfaceArea=LateralSurfaceArea+BaseArea$

$LateralSurfaceArea=\pi *r*l$

Where,

r, is the radius of the cone.

l, is the slant height of the cone.

We are given the following information:

$TotalSurfaceArea=290.6m^{2} \\Diameter=10m\\Radius=\frac{1}{2}d=\frac{1}{2}10m=5m$

So, calculating the area of the base(circle) in order to find the lateral surface area, we have:

$BaseArea=\pi *r^{2} \\\\BaseArea=\pi *5m^{2} =\pi *25m^{2}=79.54m^{2}$

Then, substituting the area of the base into the total surface area to calculate the surface area of the cone, we have:

$LateralSurfaceArea=TotalSurfaceArea-BaseArea$

$LateralSurfaceArea=290.6m^{2}-79.54m^{2}$

$LateralSurfaceArea=211.06m^{2}$

Now, calculating the slant height, we have:

$LateralSurfaceArea=\pi *r*l$

$l=\frac{LateralSurfaceArea}{\pi*r }$

Substituting, we have:

$l=\frac{211.06m^{2}}{\pi*5 }=\frac{211.06}{15.71m }$

$l=\frac{211.06}{15.71m }=13.43m$

Hence, we have that the slant height is 13.43 m.

$l=13.43m$

Have a nice day!

6 0

2 years ago

Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/2 , 2 1/4 ) and (−2 1

kotykmax [81]

Answer:

k=1.5

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A row of tiny red beads is placed at the beginning and at the end of a 20‐centimeter bookmark.

AlladinOne [14]

Answer:

51 rows

Step-by-step explanation:

Given

Length of bookmark = 20cm

Distance between beads = 4mm

Required

Number of rows of beads

First, the distance between the rows of beads must be converted to cm

if 1mm = 0.1cm

then

4mm = 4*0.1cm

4mm = 0.4 cm

This means that each row of beads is placed at 0.4 cm mark.

The distance between each row follows an arithmetic progression and it can be solved as follows;

$T_n = a + (n-1)d$

Where $Tn = 20cm$ (The last term)

$a = 0 cm$ (The first term)

$d = 0.4cm$ (The distance between each row of beads)

n = ?? (number of rows)

Solving for n; we have the following;

$T_n = a + (n-1)d$ becomes

$20 = 0 + (n-1)0.4$

$20 = (n-1)0.4$

DIvide both sides by 0.4

$\frac{20}{0.4} = \frac{(n-1)0.4}{0.4}$

$50 = (n-1)$

$50 = n-1$

Add 1 to both sides

$50 + 1= n-1 + 1$

$n = 51$

Hence, the number of rows of beads is 51

4 0

2 years ago

A set of positive integers {1, 2 , 3 , 4, 5 , 6 , 7 , 8 , 9} is used to form a pack of nine cards. each card displays one positi

ivanzaharov [21]

If the largest integer drawn among the four cards is 5, then that means that 3 of the cards drawn are from the set {1, 2, 3, 4}. The number of ways of selecting 3 cards from 4 cards is given by:

$^4C_3=4$

If the largest integer drawn among the four cards is 6, then that means that 3 of the cards drawn are from the set {1, 2, 3, 4, 5}. The number of ways of selecting 3 cards from 5 cards is given by:

$^5C_3=10$

If the largest integer drawn among the four cards is 7, then that means that 3 of the cards drawn are from the set {1, 2, 3, 4, 5, 6}. The number of ways of selecting 3 cards from 6 cards is given by:

$^6C_3=20$

Therefore, <span>the number of selections grace could make if the largest integer drawn among the four cards is either a 5, a 6 or a 7 is given by 4 + 10 + 20 = 34 selections.</span>

6 0

2 years ago