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klemol [59]
3 years ago
6

Dana has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the ra

ce and walking back the same distance to cool down. If she run at a speed of 8 mph and walks back at a speed of 2 mph, how long should she plan to spend walking back
Mathematics
1 answer:
Sedaia [141]3 years ago
8 0

Answer:

2hrs 40 minutes

Step-by-step explanation:

The formula for distance is expressed as:

d=st, s=speed, t=time

#The time taken to run:

d=st\\\\t=d/s\\\\t_r=d/8

#The time taken to walk:

d=st\\\\t=d/s\\\\t_w=d/2

#Since the distances are the same:

d_r=8t_r,d_w=2t_w\\\\8t_r=2t_w\\\\t_r+t_w=4->t_w=4-t_r\\\\\therefore8t_r=2(4-t_r)\\\\8t_r=8-2t_r\\\\t_r=1\frac{1}{3} \hrs\\\\t_w=4-1\frac{1}{3}=2\frac{2}{3}\ hrs

Hence, Dana spends 2hrs 40 minutes walking back

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determine if each polygons are similar, if so, write the similarity statement and the similarity ratio. if not explain why.
Delicious77 [7]

Answer:

They are not similar

Step-by-step Explanation:

For two polygons to be considered similar, two conditions must be met:

1. The ratio of their corresponding sides must be equal, and must have the same scale factor.

2. Their corresponding angles must be the same. That is, the corresponding angles must be congruent.

Now let us examine the two polygons ( ∆AYP and ∆BOX) given to ascertain if they are similar.

First, we can observe that only two of their corresponding sides were given. The third corresponding side, "YP/OX" is not given. This makes it difficult for us to tell if the polygons are similar, if we are to base our conclusion on merely considering the ratio of their corresponding sides.

Although, the two given corresponding sides (AY/BO & AP/BX), both have equal ratio ⅖, i.e. AY/BO = AP/BX = ⅖. This is not enough to tell both polygons are similar, as we cannot tell if the third corresponding side would give us same ratio, since it wasn't given in the diagram.

==>Next is to examine the interior angles of the polygons, whether the measure of their corresponding angles are the same.

Thus, from the diagram, we can see that two angles of the each triangle were given. We can find the measure of the third angle not given since we know that sum of the interior angles of a triangle = 180°

Thus, <P in ∆AYP = 180 - (90+20) = 180 - 110

<P = 70°

Thus, <B in ∆BOX = 180 - (90+80) = 180 - 170

<B = 10°

From the above calculation, comparing both polygons having known the measures of their corresponding angles, we can conclude that both polygons given in the question are not similar.

This is because the measure of their corresponding angles are not congruent.

<A is not congruent to <B, so likewise with <P and <X.

4 0
3 years ago
Please please helpppp.
padilas [110]

There are 3 ways of solving a simultaneous problem, substitution method, elimination method and Gauss-Jordan method. I'm gonna use the substitution method since it's easier and i think it would suit your level more.

First let's try solving for y since it's easier to start with.

Firstly we have to find an equation for x:

x-2y=2\\x-2y+2y=2+2y\\x=2+2y

Great, now we can use the substitution method to find the value of y using the first equation:

2x+3y=11\\2(2+2y)+3y=11\\4+4y+3y=11\\7y=7\\y=1

Now we know that y=1 we can solve the first equation we made:

x=2+2y\\x=2+2(1)\\x=4

And the answer is x=4 , y= 1\\(4,1)

Double check:

2x+3y=11\\2(4)+3(1)=11\\8+3=11\\11=11\\\\x-2y=2\\(4)-2(1)=2\\2=2

And that's our final answer! (4,1)

7 0
3 years ago
Justify each step in solving the equation 4X equals seven times X -3
torisob [31]
4x = 7(x-3)

1.  Distribute that multiplicand 7:  4x = 7x - 21

2.  Group the x terms together:  Subtract 4x from both sides:  0 = 3x - 21

3.  Solve for x:  Add 21 to both sides:  21 = 3x

4.  Divide both sides by 3 to obtain x = 7 (answer)
5 0
3 years ago
Read 2 more answers
A wildlife conservancy maintains a ratio of 2 squirrels for every 8 birds how many birds would there be if there were 15 squirre
GrogVix [38]

Answer: 16 birds


Step-by-step explanation:

Acording to the info we know that: for every 1 squirrel there are 4 birds

=> the number of the birds if there were 15 squirrels: 15*4=60 (birds)


7 0
3 years ago
PLEASE I NEED HELP CLICK ON THIS IMAGE
lesantik [10]

Answer:

261

Step-by-step explanation:

I took each number and divided each of them by 9 until I got a whole number with no decimals.

261 ÷ 9 = 29

6 0
2 years ago
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