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nalin [4]
3 years ago
8

Biking at 10 mph, it takes Kristen 1/4 hour to reach the train station to go to work. Kristen then takes the train to work, and

it takes another 1/4 hour for her to get to work when the train travels 20 mph. How far does Kristen travel to work?
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
3 0

Answer:

Kirsten travels 7.5 miles to go to work.

Step-by-step explanation:

Bike: 10 MPH

Time: 1/4 Hour

1/4 of 10 = 2.5

Distance travelled on bike: 2.5 miles

Train: 20 MPH

Time: 1/4 Hour

1/4 of 20 = 5

Distance travelled by train: 5 miles

Add the distances together.

5 + 2.5 = 7.5

7.5 miles

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a_sh-v [17]
The root of 77 is 8.774 so the answer is C

Answer: C
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2 years ago
4.) 960 meters in 15 seconds<br> Write the following rate as a unit rate
murzikaleks [220]

Answer:

64

Step-by-step explanation:

960 divided by 15 is 64. The unit rate means one so you are trying to get it to 1 second so just do 15 divided by 15 which is 1, then 960 divided by 15 which is 64

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2 years ago
To change knots per hour, use the expression 1.15k, where k is the speed in in knots per hour. A plane is flying at 300 knots pe
Free_Kalibri [48]
1.15(300).
Substitute k for 300, since the plane is flying 300 knots per hour, and k=knots per hour.

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8 0
3 years ago
Read 2 more answers
Find the midpoint of the line segment with the endpoints (1, 0) and (2, -10).
Mariulka [41]

Answer:

\bigl(\frac{3}{2},-5\bigr)

or in decimal form

(1.5,-5)

Step-by-step explanation:

The midpoint of the line with endpoints (x_1,y_1) and (x_2,y_2) is \bigl(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigr). just take the average between the points

so given the points (1,0) and (2,-10)

x_1=1

y_1=0

x_2=2

y_2=-10

the midpoint is found as follows:

\bigl(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigr)

\bigl(\frac{1+2}{2},\frac{0-10}{2}\bigr)

\bigl(\frac{3}{2},\frac{-10}{2}\bigr)

\bigl(\frac{3}{2},-5\bigr)

or in decimal form

(1.5,-5)

7 0
3 years ago
Can someone help me with this? Please this would mean so much.
Paha777 [63]

Answers:

x = angle MLN = 35 degrees

angle FLJ = 55 degrees

=================================================

Explanation:

This problem is fairly tricky if you're not sure what to look for. A slight clue is that they've marked a red point that strangely doesn't have a label on it. It's a fairly small point but it's definitely there if you look closely. While this point's location isn't exactly what we want, we're fairly close. Start at point L and draw a ray through the center point P. Ray LP will intersect the circle at point A, as shown in the diagram below.

From here, draw segments FA and MA. Now notice that inscribed angle LMF = 55 and inscribed angle FAL both subtend the same arc. The term "subtend" basically means "cut off". This arc that the inscribed angles subtend is minor arc FL. A minor arc is where you travel the shorter path around the circle, which indicates its measure is less than 180 degrees.

Since inscribed angles LMF and FAL subtend the same minor arc, this makes the inscribed angles to be congruent.

In short: angle FAL is 55 degrees

----------------------

Segment LA goes through the center P. Through Thales theorem, we know that inscribed angle LFA is 90 degrees. Consequently, we can determine that inscribed angle FLA is 90-55 = 35 degrees.

Segment JL is tangent to the circle, meaning that angle ALJ is 90 degrees. So angle FLJ is 90-35 = 55 degrees.

It's not a coincidence that angle FLJ, angle FAL, and angle LMF are the same measure.

----------------------

We found that angle FAL was 55 degrees. Applying Thales theorem again shows that angle MAF is 90 degrees. Therefore, angle LAM is 90-55 = 35 degrees.

Focus now on triangle LMA. This is also a right triangle (Thales Theorem). The upper acute angle we found was angle LAM = 35, so the lower acute angle is ALM = 55.

Then we can find angle MLN = (angle ALN) - (angle ALM) = 90 - 55 = 35

In short, angle MLN = 35 degrees

Similar to the previous section, it is not a coincidence that angles LFM, LAM and MLN are the same measure.

------------------------

As an alternative, since we know angle FLJ = 55, and angle FLM is 90 degrees, this means...

(angle FLJ)+(angle FLM) + (angle MLN) = 180

55 + 90 + angle MLN = 180

145 + angle MLN = 180

angle MLN = 180 - 145

angle MLN = 35 degrees

7 0
2 years ago
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