Question

Square P, square Q, and square S are drawn

Answer 1

well going off of the pythagorean theorem

c^2 = a^2 + b^2 where c is the biggest side

try applying this logic to sides Q, P and S where Q is the biggest side

Answer 2

B

Answer 3

hm not quite

Q^2 = P^2 + S^2 so Q^2 is the sum, not half the sum
making A the better choice

Answer 4

good

Answer 5

A is correct ?

Answer 6

yes

Answer 7

D

Answer 8

hm not quite

if you put the triangles together you get 2 squares, right? so in total we have 2 + 4 = 6 squares with side length 5.9, what would be the total area?

Answer 9

B

Answer 10

area of a square = side length^2 right?

so 6 squares of side length 5.9 = 6 * 5.9^2 = ?

be careful w/ order of operations

Answer 11

C

Answer 12

209

Answer 13

good

Answer 14

volume of cone = pi * r^2 * h

so plugging things in gives us

16875pi = pi * r^2 * 25
solve for r

Answer 15

25m^2

Answer 16

hm check again

pi cancels out on both sides right?

so 16875 = r^2 * 25

you can divide both sides by 25 to get

16875/25 = r^2 then simply take the square root of both sides to solve

Answer 17

D.

Answer 18

16875/25 = r^2

675 = r^2

r = sqrt(675)

Answer 19

B

Answer 20

good

Answer 21

a^2 + b^2 = c^2 where a and b are the legs, and c is the hypotenuse

therefore

12^2 + b^2 = 37^2 solve for b

Answer 22

35, -35

Answer 23

good

since we are talking about the side lengths of a triangle we would only consider the positive value 35 to be the solution

Answer 24

f

Answer 25

forget the F

Answer 26

the three angles make up a perpendicular angle right?

so x + 2x + 42 = 90

first, solve for x

Answer 27

16

Answer 28

good

now, it wants the angle <QTR which equals 2x

so 2x = 2 * 16 = 32 = your solution

Answer 29

d

Answer 30

hm not quite

it says he wants to prove that "the exterior angle is equal to the sum of the two remote interior angles", right?

in this case exterior angle = x and two remote interior angles = p and q

so he must somehow prove that x = p + q

Answer 31

B

Answer 32

hm not quite

let's try looking at choice A

he starts with the original two statements he makes (p + q + r = 180 and x + r = 180 and uses them to prove that x = p + q, right? so choice A is the most logical solution here

Answer 33

if we try drawing a right triangle between points G and H such that GH is the hypotenuse we get

Answer 34

using the pythagorean theorem

5^2 + 10^2 = GH^2

solve for GH

round to the nearest tenth

Answer 35

5.0

Answer 36

D

Answer 37

hm not quite

remember order of operations, exponents before addition

so 5^2 + 10^2 = GH^2
becomes
25 + 100 = GH^2

125 = GH^2

so GH = ?

Answer 38

hm not D either, check your calculations again

Answer 39

Fg = 125/h^2

Answer 40

GH

Answer 41

let's replace GH with a generic variable x

x^2 = 125
x = ?

Answer 42

5√5

Answer 43

C

Answer 44

good, C

Answer 45

the third side of any triangle must be larger than the sum of the two other sides

so the third side must be larger than (9+37) and there's only one choice that satisfies this requirement

Answer 46

C

Answer 47

hm not quite

9 + 37 = 46 so the answer must be larger than 46

Answer 48

D. 54

Answer 49

good

Answer 50

we can set up a proportion where

2 inches/7 feet = 3 inches/x feet
and
2 inches/7 feet = (2 + 1/2)/y feet

solve for x and y

Answer 51

B

Answer 52

good

Answer 53

well we have two points (0,5) and (-4,0) try to apply the slope formula on these two points

(y2-y1)/(x2-x1) where
x1 = 0
x2 = -4
y1 = 5
y2 = 0 (taken from the coordinates of the two points)

Answer 54

A.

Answer 55

hold on

Answer 56

i think A

Answer 57

i think that's correct

Answer 58

hm not quite, you might have switched the numerator and denominator

using the slope formula gives us

(5-0)/(0 - (-4)) which simplifies to 5/4 not 4/5

so B is the better solution

Answer 59

any ideas? as a hint you are ~not~ given any information about the sides so you can only use the angle measurements as part of the proof

Answer 60

C

Answer 61

B and D are out of the picture

Answer 62

good, C

Answer 63

wait

Answer 64

actually I believe B might be a better choice

you have two pairs of angles (<L + <J) and (<R + <P) that are said to be congruent which implies the third must also be congruent making the two triangles similar

C is insufficient b/c knowing the angles sum to 180 doesn't necessarily prove similarity

Answer 65

weird question

Answer 66

this next question is kind of a pain in the butt but you have to draw lines from the origin to each point and calculate the length using the pythagorean theorem

Answer 67

as a hint let's start w/ point D and work our way backwards

if you draw a line from pt D to the origin you get

Answer 68

so if we have a right triangle with legs 3 and 2, and hypotenuse equal to the distance between D and the origin we have

D^2 = 3^2 + 2^2 solve for D
leave your solution in radical form

Answer 69

sqr13

Answer 70

good and that matches the original question so D is the best solution

Answer 71

this is kind of a pain but you have to split the shape into its three component rectangles

Answer 72

A is simple, it's a 12 * 4 rectangle which has area 48 sqr inch. since 12 * 4 = 48

Answer 73

for B, it has width 2 but we need to figure out the length by looking at the other sides of the shape

Answer 74

if the total length is 12 and the length of that side on the right is 5

thus x + 5 = 12

what must x, the side length of B, be?

Answer 75

7

Answer 76

good so B is a 5 * 2 = 10 sqr inch rectangle

lastly rectangle C

the bottom side is 12 as indicated by the drawing but we don't know what the width is yet

Answer 77

the total width of the entire shape is 10

the two segments on the right side are 4 and 2

so 4 + 2 + y = 10

solve for y, the width of rectangle C

Answer 78

4

Answer 79

good so the last rectangle is a 4 * 12 rectangle, or 48 inch sq

adding up all the area gives us

48 + 48 + 14 = 110 sqr inches

however it wants the area of the real garden not the drawing so we must use the conversion factor they give us

if 1 inch = 3 feet

then 1 inch^2 = 3^2 feet, or 9 feet ^2

so total area = 110 * 9 = 990 ft^2 = choice C

Answer 80

so as stated before, any side of a triangle must be greater than the sum of the other two sides

so for example, we can try choice A to see if it works

9 < 9 + 9 in all cases, so A is eliminated

try testing this logic for choices BCand D

Answer 81

*just had to correct a small typo

Answer 82

C

Answer 83

hm not quite

9 + 12 > 15
9 + 15 > 12
12 + 15 > 9

so c is a valid triangle

try choice D

9 + 12 > 25
is this a true statement?

Answer 84

no false

Answer 85

good so d is not a triangle making D the best solution

Answer 86

you must use the quadratic formula for this one

for a generic equation ax^2 + bx + c = 0
the quadratic formula is given by



so for your equation

2x^2 + 13x - 1 = 0

identify your a, b, and c values and plug them into the formula

** be careful with positive/negative signs **

Answer 87

a = 2, b = 13, c = -1

Answer 88

good, then just plug them into the quadratic formula

Answer 89

D

Answer 90

good

Answer 91

well since it crosses (0,0) that means it must be y = mx with no b value which eliminates choices C and D

to decide between A and B let's pick point (3,5) and plug them into y = mx

5 = m(3)

m = ?

Answer 92

5/3

Answer 93

good

so y = (5/3)x which is choice A

Answer 94

two intersecting lines create two pairs of equal angles
therefore
8x - 4 = 110
solve for x

Answer 95

57/4

Answer 96

good but the answers are in decimals so 57/4 = 14.25 = your solution

Answer 97

so we have a right triangle with legs 6 and 5 and hypotenuse LM

so 6^2 + 5^2 = LM^2 solve for LM

Answer 98

61

Answer 99

close, that's LM^2 so LM is just sqrt(61) d

Answer 100

to find out how many cones he can make he will calculate

volume of clay cube/volume of each cone tree

volume of a cube is s^2 where s = the side length = 3 inch

volume of a cone = (1/3) * pi * r^2 * h where h = height = 2 and radius = 0.75 inches (since the diameter is given as 1.5, divide by 2 to get 0.75 as the radius)

with that being said calculate volume of clay cube/volume of each cone tree

Answer 101

ugh made a typo

volume of a cube is s^3 not s^2

Answer 102

anyway we can break it down into steps

if volume of a cube = s^3 and s = 3 inch then volume = ?

Answer 103

did you get a solution for part A yet?

Answer 104

3

Answer 105

3 is a bit too low

volume of the cube is 3^3 = 27 inch^3

volume of the cone is (1/3) * pi * r^2 * h = (1/3) * pi * (0.75^2) * 2

so volume of cube/volume of cone = ?

Answer 106

1.17

Answer 107

27/((1/3) * pi * (0.75^2) * 2) = 22.9 when i chuck it into a calculator

we round down to 22 since we only want to know how many complete trees he can make

so for part A, 22 trees = your solution (make sure to show all your calculations)

Answer 108

sqr2

Answer 109

that's it for B

Answer 110

but could i rewrite for part A i'm a bit confused

Answer 111

the artist wants to know how many trees he can make with his cube

to find that, he must divide

volume of cube/volume of one tree

so simply show the calculations for the volume of the cube and the volume of the tree

Answer 112

also we may need to re-do part B because it wants an actual equation. hm.

Answer 113

yeah sorry I kind of misunderstood what part b was asking whoops

but in the meantime are you making any progress with part A?

Answer 114

@mikewwe13 still there?

Answer 115

Part A

to find out how many cones he can make he will calculate

volume of clay cube/volume of each cone tree

volume of a cube is s^3 where s = the side length = 3 inch

volume of a cone = (1/3) * pi * r^2 * h where h = height = 2 and radius = 0.75 inches (since the diameter is given as 1.5, divide by 2 to get 0.75 as the radius)

with that being said calculate volume of clay cube/volume of each cone tree

we round down to 22 since we only want to know how many complete trees he can make

then, volume of the cube is 3^3 = 27 inch^3

volume of the cone is (1/3) * pi * r^2 * h = (1/3) * pi * (0.75^2) * 2

so volume of cube/volume of cone = 22

so that would be 22 trees

Part B

the artist wants to know how many trees he can make with his cube

to find that, he must divide

volume of cube/volume of one tree

so simply show the calculations for the volume of the cube and the volume of the tree

Answer 116

am i correct ?

Answer 117

make sure the steps are logical and concise and you're not just copy-pasting things I've said (that can set off plagiarism detectors and that's no fun)

you just need to show:

1) # of trees = volume of cube/volume of cone
2) the calculations for the cube volume
3) the calculations for the cone volume
4) the calculation for dividing cube volume/cone volume
5) rounding down to 22

Answer 118

also part B is asking something entirely different, erase what you have so far for part B

Answer 119

FOR A i'm good ?

Answer 120

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
make sure the steps are logical and concise and you're not just copy-pasting things I've said (that can set off plagiarism detectors and that's no fun)

Answer 121

no into my own words

Answer 122

the content itself is fine

Answer 123

Part A

First, to find out how many cones he can only make he will have to calculate

the volume of clay cube/volume of each cone tree

the volume of a cube is s^3 where s = the side length = 3 inch

the volume of a cone = (1/3) * pi * r^2 * h where h = height = 2 and radius = 0.75 inches (since the diameter is given as 1.5, divide by 2 to get 0.75 as the radius)

with that being said calculate volume of clay cube/volume of each cone tree

we round down to 22 since we only want to know how many complete trees he can make

then, volume of the cube is 3^3 = 27 inch^3

volume of the cone is (1/3) * pi * r^2 * h = (1/3) * pi * (0.75^2) * 2

so therefore the volume of cube/volume of cone = 22

so that would be 22 trees

Answer 124

that's in my words

Answer 125

they not gonna know anyway but i want to be fair

Answer 126

and you're right

Answer 127

good but you don't need this sentence

"with that being said calculate volume of clay cube/volume of each cone tree"

the sentence "we round down to 22 since we only want to know how many complete trees he can make" needs to be before "so therefore the volume of cube/volume of cone = 22"

Answer 128

otherwise its fine

Answer 129

i could leave that out

Answer 130

anyway for part B idek what they want but here's my best attempt

x = the height of the tree since each piece of yarn goes from the top to the base

volume of cone = (1/3) * pi * r^2 * x = (1/3) * pi * (0.75)^2 * 2 from the part A calculations

solving for x gives x = 2 inch = the length of each piece

Answer 131

ok