Question

What is the length of the third side of the window frame below?

Answer 1

10
15
25
30

Answer 2

Can you use the Pythagorean Theorem? side length a squared + side length b squared = the hypotenuse length squared.

Answer 3

@asett i dont know how to im taking a 8th grade class in 7th grade.

Answer 4

Good for you! I'll walk you through!

Answer 5

@asett thank you :).

Answer 6

I apologize for asking this, but do you know what a hypotenuse is?

Answer 7

not really....

Answer 8

Okay, do you know how to identify a right triangle?

Answer 9

not really..

Answer 10

Cool. So, first, a right triangle is any triangle that has a 90 degree angle, indicated with a small square in the 90 degree corner such as in your illustration above. Does that make sense?

Answer 11

yes it does :).

Answer 12

Yay! So, in every triangle, there are three sides (duh), but the right triangle is a special case. One of its sides is always going to longer than the other two sides, and that side is always the side opposite of the 90 degree angle (where the little box is). You getting this?

Answer 13

yes i am :).

Answer 14

That side is called the hypotenuse...

Answer 15

now im getting it!

Answer 16

In Pythagoras Theorem, we see the equation\[a ^{2}+b ^{2}=c ^{2}\]There is a really cool story behind that equation, if you want to look it up later : ). Anywho, the c represents the length of the hypotenuse while a and b represent the remaining sides of the triangle. So, if we have three variables and we have two knowns with which we can replace two variables, we will be able to find our third variable. Still with me? (We're getting there!)

Answer 17

yes i am

Answer 18

Good, so now we can take what we know (two lengths: the length of c, the hypotenuse 65, and b, the length of one side 60). \[a ^{2}+60^{2}=65^{2}\]

Answer 19

ok

Answer 20

Do you think you can take it from there?

Answer 21

i think its 30

Answer 22

Not quite :). So, first will solve both the 60 squared and the 65 squared.\[a ^{2}+3600=4225\]

Answer 23

Then, subtract 3600 from both sides \[a ^{2}=625\]and take the square root of a to get ?

Answer 24

15?

Answer 25

Not quite. \[\sqrt{625}=25\] 25, then, is your answer!

Answer 26

@asett i was very close..

Answer 27

Yes you were. :). Keep up the good work!!

Answer 28

@asett do you mind helping me with more?

Answer 29

Not at all! I would be glad to.

Answer 30

@asett thank you so much!

Answer 31

np

Answer 32

Luke filled the glasses shown below completely with water. The total amount of water that Luke poured into the glasses is 90 cubic centimeters. What is the height of glass 1? Round your answer to the nearest hundredths. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.

Answer 33

2.63
3.82
4.04
5.62

Answer 34

3.82?

Answer 35

One sec, I'm going to work it out then help you...

Answer 36

thanks alot!

Answer 37

Okeydoke. No, it is not 3.82 :).

Answer 38

First, do you know the volume equations for a cylinder and a cone?

Answer 39

no.

Answer 40

That's where we'll begin.

Answer 41

ok it 3:00 here and i really need this turned in fast.

Answer 42

The answer is 4.04. Do you want to know how I got it?

Answer 43

yes please!

Answer 44

i still have seven questions to answer :( and schools in 4 hours.

Answer 45

First, take the equation for the volume of a cone - V= 1/3 * pi * radius squared * height. Now, we know everything about this cone (the glass on the right in the diagram) except for the volume, so will find its volume first! \[V = 1/3*3.14*(4.2/2)^{2}*5.6\]Then, we get the volume of this glass which is 25.8.

Answer 46

Then, subtracting 25.8 from the total volume the student poured into the two glasses (90 cubic centimeters), we are left with the knowledge that the glass on the left must have a volume of 64.2 cub. cm.

Answer 47

you're so good at explaining!

Answer 48

THANKS ALOT I SORTA UNDERSTAND. But you wouldn't mind if i asked you the questions and you just gave me the answer. Its really late and i need this done!

Answer 49

So, using the equation for volume of a cylinder (the glass on the left): V= pi * radius squared * height. We know what the volume is (64.2), pi is (3.14) and the radius is (4.5/2=2.25) squared (which is 5.0625), so we can plug everything into the equation to get our answer, which is the height of the glass on the left.\[64.2=\pi*5.0625*h\]

Answer 50

I'll do my best.

Answer 51

you're so nice!

Answer 52

The legs of a right triangle are 3 units and 10 units. What is the length of the hypotenuse? round your answer to the nearest hundredth. i believe its 7.00

Answer 53

1.00
7.00
9.54
10.44

Answer 54

10.44

Answer 55

thank love!The height of a cone-shaped container is 70 centimeters and its radius is 15 centimeters. Cathy fills the container completely with honey. Every day Cathy uses 500 cubic centimeters of honey from the container to make honey cookies. After how many days will the container be completely empty? Round your answer to the nearest whole number.

Answer 56

Hypotenuse must always be longer than either of the legs.

Answer 57

20

Answer 58

17
20
33
40

Answer 59

33

Answer 60

What is the length of the hypotenuse of a right triangle if each of the two legs is 6 units?
12 sqrt
6
72 sqrt
36

Answer 61

72 sqrt

Answer 62

The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle?
Are you sure you dont mind?

Answer 63

No problem!

Answer 64

5 sqrt
7 sqrt
5
7

Answer 65

7 sqrt

Answer 66

he figure below shows the location of 3 points around a lake. The length of the lake, BC, is also shown.

(Figure is not drawn to scale.)


Which of the following options is closest to the distance (in miles) between points A and B?

Answer 67

2.24
2.65
3.74
5.29

Answer 68

5.29

Answer 69

What is the length of leg y of the right triangle?

Answer 70

retain SOMETHING in your mind, i just read this thread, goodluck

Answer 71

10
14
24
26

Answer 72

10

Answer 73

@DanJS I most certainly will!

Answer 74

I mean you asked the same exact question about 5 times, and it was explained twice. , bahh sorry beg my pard

Answer 75

What is the length of segment AB?

Answer 76

72 sqrt
140 sqrt
12
36

Answer 77

72 sqrt

Answer 78

The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 112 miles due north of the warehouse.


A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?

Answer 79

112
154
224
252

Answer 80

224

Answer 81

thanks

Joel used candle molds, as shown, to make candles that were perfect cylinders and spheres:


What is the approximate difference in the amount of wax needed to make a candle from each of these molds

4.19
10.4
12.56
20.93

Answer 82

How many do you have?

Answer 83

20

Answer 84

its one more after this one.

Answer 85

Yay! 20.93

Answer 86

@ms.hi ?

Answer 87

yes? @asett

Answer 88

Oh. I thought you had another one for us to do.

Answer 89

you didn't answer the one above lol.