Question

Which three angles measure could be used to form a triangle?

Answer 1

@Vocaloid

Answer 2

hint - which choice has all three angles add up to exactly 180?

Answer 3

C

Answer 4

check your calculations again

55 + 70 + 105 does not equal 180

try the other choices

Answer 5

A

Answer 6

good

Answer 7

for a square pyramid surface area = area of the 4 triangular sides + the base

the base is a square with side length 44, what's the area of the base?

Answer 8

1936

Answer 9

awesome

so each other side is a triangle with base 44 and height 33, what's the area of each triangle?

as a reminder area of triangle = (1/2)bh

Answer 10

726

Answer 11

good, and we have 4 of those so area of the four triangles = 4 * 726

so total area = 4 * 726 + 1936 = ?

Answer 12

4840

Answer 13

good so 4840 = your solution

Answer 14

since we have two adjacent angles on a straight line, the two angles add up to 180

which equation best represents this idea?

Answer 15

D

Answer 16

well done

Answer 17

sorry for the correction just had to fix the parentheses

hm

well, the radius of the cone is one half the radius of the cylinder

so volume of cylinder/volume of cone =

(pi * (2a)^2 * h)/(1/3 * pi * b^2 * h)

where 2a is the radius of the cylinder
and a is the radius of the cone

simplify the expression. as a hint, h, pi, and a cancel out

Answer 18

ugh I keep messing this up, it should be a instead of b in the denominator

Answer 19

(pi * (2a)^2 * h)/(1/3 * pi * a^2 * h)

Answer 20

12/x

Answer 21

so meaning D 12

Answer 22

yup

Answer 23

well the brace is the hypotenuse of a right triangle with legs 8 and 15 right? so try applying the pythagorean theorem

Answer 24

D

Answer 25

check your calculations again, you cannot simply add the legs w/o squaring them first

x^2 = 8^15 + 15^2 solve for x

Answer 26

15

Answer 27

*8^2 + 15^2

Answer 28

289

Answer 29

good, and if x^2 = 289 what is x?

Answer 30

17

Answer 31

C

Answer 32

good

Answer 33

start by distributing 9w(w-2)
add 27 to both sides
then factor or use the quadratic eqn

Answer 34

B

Answer 35

good

Answer 36

well the statement is that <3 and <7 are equal right?
so the statement must be factually correct and provide a reason why <3 and <7 are congruent and corresponding angles based on the diagram

that being said any ideas?

Answer 37

D

Answer 38

hm not quite

supplementary angles are usually not congruent

any thoughts on B or C?

Answer 39

B cause they are congruent

Answer 40

that's a good attempt but the key is "any two lines" vs "two parallel lines"

the angles are only congruent if the transversal cuts thru two parallel lines

therefore C is the factually correct statement that proves why <3 and <7 are congruent, and thus the best choice

Answer 41

if it's a straight line the points must be linear

so we would want the choice where the x-values and the y-values both change at a constant rate

Answer 42

A B or D

Answer 43

if you had to choose one which would be your best choice? remember, x and y must change at a constant rate

Answer 44

B

Answer 45

well let's look at B

x goes from 0 --> 4 --> 8 so it's increasing by 4 each time, so far so good

y goes from -4 ---> 0 ---> 0

see how it increases by 4 but then doesn't increase from 0 to 0? that means choice B is not linear and thus not the solution

any thoughts on A or D then?

Answer 46

D

Answer 47

good

Answer 48

we can set up a proportion where

1.5 inch/100 miles = 4.5 inch/x miles

and solve for x

Answer 49

7

Answer 50

check your calculations again

if you cross multiply the proportion you get

1.5 inch/100 miles = 4.5 inch/x miles

1.5x = 4.5*100 solve for x

Answer 51

0

Answer 52

1.5x = 4.5*100

x is being multiplied by 1.5 right? so divide both sides by 1.5 to solve for x.

Answer 53

300

Answer 54

good so 300 = your solution

Answer 55

we have another right triangle where legs are x and 28 and hypotenuse = 35

so x^2 + 28^2 = 35^2 solve for x (this is the first step)

Answer 56

21

Answer 57

good, now it wants the area of the rectangle which is just L*W so 21 * 28

Answer 58

588x

Answer 59

good so 588 = your solution

Answer 60

36.21

Answer 61

it just wants the area of the cone + the two spheres on top

so area of a cone = (1/3)*pi*r^3*h
area of sphere = (4/3)pi*r^3

let's start w/ the cone

(1/3)*pi*r^2*h
the diameter is 3 inch so the radius is 3/2 = 1.5

if r = 1.5 and h = 6 what's the area of the cone?

Answer 62

*made a typo, it should be r^2 not r^3

so you want to find (1/3)*pi*r^2*h

Answer 63

(1/3) * pi * (1.5)^2 * 6 = ?

Answer 64

14

Answer 65

good but let's keep it in terms of pi

(1/3) * pi * (1.5)^2 * 6 = (1/3) * 2.25 * 6 pi = 4.5pi

now let's move to the spheres

(4/3)pi*r^3 = ?

where r = 1.5

Answer 66

there was a problem and couldn't get back on, i wanted to answer but i had to refresh then it didn't act right so i tried again later

Answer 67

the site went down for a bit

anyway (1/3) * pi * (1.5)^2 * 6 = 4.5pi

then for the spheres simply calculate 2 * (4/3) * pi * (1.5)^3

Answer 68

28

Answer 69

good but let's leave it in terms of pi

2 * (4/3) * pi * (1.5)^3= 9pi

so adding what we have so far 9pi + 4.5pi = 13.5 pi = your solution

Answer 70

well fact 1 says that a linear pair (two angles on a line) add up to 180

the linear pair is z + y

fact 2 says that the exterior angle = the sum of the two remote interior angles
that gives us z = w + x

then you can substitute (w+x) into the first equation for z

which choice best describes these steps?

Answer 71

B

Answer 72

please try to review what I have said

the linear pair z + y = 180
the exterior angle z equals the sum of w and x

please try to pick the choice that matches this idea

Answer 73

no hold on

Answer 74

A

Answer 75

good

Answer 76

it's alittle hard to visualize but try imaginging a right triangle with MP as the hypotenuse

Answer 77

first step is to find this distance using the pythagorean theorem

Answer 78

you have a right triangle with legs 4 and 5

find the hypotenuse

Answer 79

5.7

Answer 80

hm not quite

let's let x = the hypotenuse

then x^2 = 4^2 + 5^2 solve for x

Answer 81

you can leave it in radical form for now

Answer 82

sqr41

Answer 83

good

then we want to find the length of MP by finding the hypotenuse of the bigger triangle

Answer 84

we have a right triangle with legs sqrt(41) and 4, find the hypotenuse MP

Answer 85

41.49

Answer 86

hm not quite

a^2 + b^2 = c^2

plug in the legs to get

( sqrt(41) ) ^2 + 4^2 = c^2 solve for c

Answer 87

sqr57

Answer 88

good

however the answers are in decimals so we just plug that into a calculator to get about 7.5 which is your solution

Answer 89

anyway let's start a fresh question if possible, this one is already 100+ replies