answer key - clarkstown central school district
TRANSCRIPT
RealIntegerInteger
Integer
Integer
Natural
Natural
Whole
Whole
Rational
RationalRational
Rational
Irrational
Irrational
Rational
Rational
Rational
RealRealRealReal
RealReal
RealReal
AlwaysSometimes
AlwaysNever
11
102 2 = 100 |102 + 2||104| = 104
10 2 = 12 |40|40
(9)9
the opposite of 3 squared 9 3 3
9negative 3 squared
(9)9
32 12 14 7
99 105 5 6
110 + 85 = x25 = x 25 feet below sea level
22 (8) = x30 = x 30 degree difference
16 + 9 = x7 = x
7
6 + 3 106 + 30 36
8 6 + 248 + 2 50
25 (9 4) 25 5
=
=
5
213 (5)
31
2
6 + 3 +
3 + 5
(6)2 + (5)3
36 + 1255 6 2 5
36 125161
4030 + 10
3 + 1
4
undefined undefinedzero zero022
220
5x x2y 3y 75x x 2y 3y5 1 2 3
7
1
4a 10c 8 2a 74a 2a 8 74 10 28 7
21 28x + 8 + 10x 18x 13 10 18x 12 + 9x 9x 2
19x + 24 + 9x 13 19x 2610x + 11 12x 17 + 7x 9
1
15x 12y + 34 167x 140 19x 5
12x 145 15x 12y + 18
3 2x + 5 + x 7 5
2
4x 2
2 3
1 4x y x y 1
2 2 5
3 20 x 1 y 1
6
√ √4
-5 16 7
√-20 7√11
-33 -3 121
√-3 121
√ √3
9 7 x4
√3x2 7√
x2
√ √5
x 25 6 x4 x1
√5x3 6x
√x2
√ √ √3
-3 9 5 y4 y1
√-9y2 5y√
y2
√ √2
-2b 4 34 b8
√-4b5 34
√b4
√
√√ √6 36 5
√6 5
180 √
√12
2 144 2 √24 22 288
√√
√7
-4 49 6 √-28 6-4 294
√
√60n3
√ √2
4 15 n2 n1 √2n 15n
√n
√√-6 2240x6
√ √8
-6 64 35 x6
√-48x3 35√
x3 34√240x6
√ √416 15 x6
√3x3 15√
x3
34
36
49
√√
= 67 √ √
2 4 2
3 √√ √
x2
49 x4 x1
√5x
7x2 x
25 x2
√√x5
7
= √3
2 2 √
√ √y3
225 y6 y1
√8x2
15y3 y
64 x4
√√ x28
15
12 3 √
√ √√4
8 3 + 2 16 3
3 11 -3 7√ √1 1
√ √8 3 + 8 3 16 3 √
√ √3
3 4 5 + 2 9 5
√ √6 5 + 6 5 12 5 √
√ √ √2
√5
4 3 - 7 25 3
√ √2 3 - 35 3 -33 3 √
√ √2
24 s7 a5b2
1 32
= 19
1 41
= 14
41= 1 x8
x8 =
29 46 105
k9 a6c7 10w5x5
21x6 16y7 30x9
42y416w10z6
6x3y7
a8c4 x6y8 m6n9
16x4y4 27x12y21 100x2y10
34 = 81 1 26
= 1 64
26 = 86 3n3
4x6 9y5 5x3y2
7w4m2
15 x
2y8 1 5x2y8
13 w
4x2 x2 3w4
2.204 x 1096.59 x 1034.7338 x 106
8.331 x 10-42.9 x 10-1 5.71 x 10-6
0.335
67 61,000 1600
0.0000291 0.0000008651
polynomial 5x3 3x2 + 14x + 2 3
binomial
polynomial
polynomial
trinomial
monomial
9z3 2z
7y5 + 3y2 + 2y + 2
3
5
5
2
2
7x5 + x3 2x2 + 4
5x2 + 2x 7
3x2
x2 - 7x - 20 5x4 - 15x3 + 10x2 -6y + 21y2 - 24 - 5y
21y2 - 11y - 24
4x + 16 - 3x4 + 9x2 - 2x + 5 n2 + 5n + 6n 2x2 + 3x + 4x2 - x + 1
-3x4 + 9x2 + 2x + 21 n2 + 11n 6x2 + 2x + 1
2x + 4y - 1 - x - 7 - 6yx - 2y - 8
5x2 + 12x - 17 - 13 + 4x2 - 8x9x2 + 4x - 30
3x + 10 + 6x - 159x - 5
x2 + 9x - 5x2 + 3x-4x2 + 12x
-5x2 + 8x + 12 + 3x2 - 4x + 8
-2x2 + 4x + 20
6x2 - 11x - 17 - 9x2 + 8x + 12
-3x2 - 3x - 5
5x + 3 + 2x + 5x + 3 + 2x
14x + 6 units 8y - 4 + 9y - 5 + 3y
20y - 9 units
x2 - 3x + 2 + x2 - 3x + 2 + 3x - 7 + 3x - 72x2 - 10 units
5x3 + 3y + 5x3 + 3y + 5x3 + 3y15x3 + 9y units
x5y - x2y2 -112m2n + 64mn2 -24mn x3z4 - 5x3z2
x3a5 - 8xa4ca5x3 - 8a4cx
8x5y2 + 60x2yz - 28x2y 3x3y2 + 6x4 + 3x3z
2x + 2x + 5x 2 + 5x 214x 4
Perimeter = 14x 4 feet
A = 2x (5x 2)
A = lw
Area = 10x2 4x feet2
P = add up all sides
A = 10x2 4x
x2 + 1x + 5x + 5x2 + 6x + 5
y2 7y + 4y 28y2 3y 28
x2 + 3x 10x 30x2 7x 30
a2 5a 4a + 20a2 9a + 20
2x2 2x + 6x 62x2 + 4x 6
12x2 + 2x + 12x + 212x2 + 14x + 2
25x2 35x + 35x 4925x2 49
6x2 + 18x + 12x + 366x2 + 30x + 36
4x3 + 12x2 8x + x2 + 3x 2
4x3 + 13x2 5x 2
GCF: 5 GCF: 3x GCF: 4 GCF: 4y
x (1 y) 5 (3m + 10) 6 (3n + 4) 7y (3x 4)
2x (2x3 11x + 9) 7x2 (3x3 + 5x + 7)
c3 (2c2d4 3c + 4) y (23y9 46y6 + 68y + 10)
x2 + 6x + 6x + 36
(x + 6) (x + 6)
x2 + 12x + 36
(x 6) (x 6)
x2 6x 6x + 36x2 12x + 36
x3 + 4x2 + 2x + 3x2 + 12x + 6x3 + 7x2 + 14x + 6
3x + 1 5a2 + ab 2b6z2 3y + 2z
4 + 5vw 4w5vw 4w + 4
x2 2x xy2z
2z + 6z2 3y
xy2z + x2 2x
Same Signs both positive Same Signs both negativeDifferent Signs Bigger positivemult. to 40, add to 14
(x + 10) (x + 4) mult. to 24, add to 5(x + 8) (x 3)
mult. to 20, add to 9(x 5) (x 4)
Same Signs both positive Same Signs Both negativemult. to 15, add to 16
(x + 15) (x + 1)mult. to 14, add to 9(x 7) (x 2)
mult. to 24, add to 11
(x 8) (x 3)
Same Signs both negative
4 (6x 5)24x 20 Perimeter = 24x 20 units
A = (6x 5)2A = s2
Area = 36x2 60x + 25 units2
P = add up all sides
A = 36x2 30x 30x + 25A = (6x 5) (6x 5)
36x2 60x + 25 36(2)2 60(2) + 25 36(2)2 60(2) + 25 144 120 + 25
49
The puppy will have 49 square feet of space to play.
2x 2x2x 7 = 15
+ 7+ 72x = 222 2 x = 11
22c + 88 = 22 88 88
22 22c = 5
22c = 110
20x + 16 2x = 14x 2822x + 16 = 14x 28
8 8x = 5.5
8x = 44
. . .
+12+ 12
x = 35
37
73
x = -15 73
2x - 53
= 5 (3)3
2x - 5 = 15+ 52x = 20
+ 5
2 2x = 10
4x + 8 = 2x 16 2x 2x
6x + 8 = 16 8 86x = 24-6 -6x = 4
0.4y 3.6 = 0.3y + 1.23 (x + 2) = 7 (x 2)
4 4x = 5
4x = 20
. . .
+1.8x+1.8x5x 7.1 = 6.8+ 7.1 +7.15x = 13.95 5x = 2.78
3x + 6 = 7x 140.1
x = 48
0.1y = 4.8
. . .
0.1
3x + 7 = 3x + 6 3x
ContradictionNo Solution
3x7 ≠ 6
2x + 9 = 2x + 8 + 12x + 9 = 2x + 9 2x 2x
9 = 9Identity
Infinite Solutions
√x2 = 49√x = ± 7
x2 = 81-10 -10
√x2 = 81√ x = ± 92x2 = 50
+5+5
2 2√x2 = 25√
x = ± 5
x = 2q
3x = 6q3 3
x = 6a
5x = 30a
. . .
5 5
5 r - 10y = x
r = 5x + 10yr - 10y = 5x y - z = 2x
2 y - z = x
Let c = the # of cups $7.50 + $2.50c = $12.50
7.50 + 2.50c = 12.50c = 2
You can buy 2 cups of food.
Let c = the # of chocolates $3c - $45 = $105
3c - 45 = 105c = 50
You must sell 50 chocolates.
Let w = the # of weeks $100 + $20w = $280
100 + 20w = 280
w = 9It will take you 9 weeks.
Let x = cost of 1st item Let x + 8 = cost of 2nd item x + x + 8 = $130
x + x + 8 = $1302x + 8 = $130
x = 61
The items cost $61 and $69.
Let n = 1st odd integer Let n + 2 = 2nd odd integer n + n + 2 = 84
n + n + 2 = 842n + 2 = 84
n = 43The integers
are -43 and -41.
0.5x + 6 < 9x < 6
60 -5 0
x ≤ -5
x ≤ -1
-1 0
4x 3 > 21
x > 6
60
5n + 3 ≥ 382x 4 > 17
2 + 7 ≤ 40 x
e ≤ 3600a ≥ 45a ≤ 50
Let x = # of tickets 12x + $2157 ≥ $4500
12x + 2157 ≥ 450012x ≥ 2343
x ≥ 195.25
They must sell at least
196 tickets.
Let x = # of boxes 3x + $12.75 ≤ $38
3x ≤ 25.25x ≤ 8.41666...
They can buy at most8 boxes.
3x + 12.75 ≤ 38
Let x = # of tickets 12x + $2157 ≥ $4500
12x + 2157 ≥ 450012x ≥ 2343
x ≥ 195.25
They must sell at least
196 tickets.
Let x = # of boxes 3x + $12.75 ≤ $38
3x ≤ 25.25x ≤ 8.41666...
They can buy at most8 boxes.
3x + 12.75 ≤ 38
0.5 pounds /week$20 /ticket
16x = 9
16x = 1441612
x = 2
12x = 2512
12 1
50 n =1 3.2 1x = 160
1n = 1601 The actual distance between
the cities is 160 km.
Let n = the actual distance
14 ounces
10 teaspoons2 1
= 0.75 teaspoons/ ounce
6 laps
4 minutes2 1
= 0.75 minutes/ lap
20 pounds$14.99 = 0.7495 $0.75/ pound
50 pounds$37.99 = 0.7598 $0.76/ pound
The 20 pound bag is a better buy because it costs less per pound.
2 DVD's$26.50 = 13.25 $13.25/ DVD
3 DVD's$40.00 = 13.3333... $13.33/ DVD
The 2 pack of CD's is a better buy because it
costs less per DVD.
0.75 lb$6 $8/ pound
1 lb$8.50 $8.50/ pound
A
B
0.25 lb$2.25 $9/ poundC
4 oz = 0.25 lb
y
x
The graph repersents a proportional relationship because it is a straight line that passes through the origin. (0, 0)
28
y = 2x b = 2c36
b = 2c b = 2 18b = 36
y = 0.99x c = 0.99a
21
n = 121.9047 ...
21n = 25602121 512 = 5 n You would expect
about 122 people to have green eyes.
Let n = # of people expected with green eyes
n = 4.5731 ...
1230n = 562512301230 375 = 15 n
You would expect about 5 cars to have headlight problems.
1230
Let n = # of cars expected with headlight problems
y 9
6 15
=
3.6 = y
54 = 15y15 15
3.6 ft
little big x
9 28 12
=
21 = x
252 = 12x12 12
21 m
big little
0.875 87.5%
215% 220 3
2043OR
0.0425 1
0.666.6 %66 %3
2 OR
2%50 1
0.2825 7
p 192
25 100
=48 = p
4800 = 100p100100 Mary earned $48 commission.
Let p = amount of commission
p 85
15 100
=12.75 = p
1275 = 100p100100 Jenny paid $72.25 for the boots.
discount = $12.75Sale Price = 85 - 12.75 = 72.25
Let p = amount of discount
p 99.50
7.5 100
=
7.4625 = p
746.25 = 100p100100
The bicycle costs $106.96.
tax = $7.46Total = 99.50 + 7.4625 = 106.9625
Let p = amount of tax
p 350
12 100
= 42 = p
4200 = 100p100100 42 people will
win a door prize.Let p = # of people who will win
p 22
5.25 100
= 1.155 = p
bill = 22+1.155 = 23.155
p 23.155
15 100
=
3.47325 = p
Total = 23.155 + 3.47325= 26.62825
= $26.63
Let p = tax Let p = tip
Find the discount first:
n 300
= 30 100
90 = n$300 - $90 = $210
Now find the sales tax on the discounted price:
n 210
= 8 100
16.8 = n
Let n = taxLet n = discount
discount = $90tax = $16.80
Total = 210 + 16.80= 226.80
= $226.80
I = PRTI = (1750)(0.0875)(2.5)I = 382.8125I = $382.81
Total = P + IT = 1750 + 382.81
Total = $2132.81
She started her bank account with $800.
I = PRT147 = P (0.1225)(1.5)147 = 0.18375P
0.18375 0.18375
800 = P
65 x
70 100
=92.8571 . . . = x
6500 = 70x7070 The original price
is $92.86.
Let x = original price
52 8
r 100
=650 = r
5200 = 8r8 It's a 650% increase
in weight.8
R = 650%
Let R = % increase
Percent error = 12.5%
Percent error = x 100 5 40 Percent error = 12.5%
Let R = % error
Percent error = 25%
Percent error = x 100 100 400 Percent error = 25%
Let R = % error
13.49 75.99
r 100
= 17.7523... = r
1349 = 75.99r
The price decreased about 17.8%.R ≈ 17.8%
75.99 75.99Let R = % increase
Total = 20 pens
7 20
1 40 (impossible)
1 (certain)3 + 4
3 80
= 3 20
5 20
#5 1 20
= 4 20
5 20
#6
1 19
= 4 19
5 20
#7
1 57
= 3 20
8 19
#8 3 50
= 8 20
3 20
#9 5 18
6 20
3 10
=
6 20
n 150
=
45 = n
900 = 20n20
Let n = # of times expected to land on the sun
20n = x 150 6
20
You would expect the spinner to land on the sun 45 times
n = 45
Total = 50 rolls
34 50
x 10,000 = 6800
skirtsblousesx3 4 = 12 12 outfits
coin #2coin #1x2 2 = 8 8 outcomesx
coin #32
158 9
= 17.5
11, 12, 15, 17, 18, 19, 20, 21, 25
median = 18mode = none
meanmean = 17.5
median
range 25 - 11 = 14
range = 14
1, 2, 3, 3, 4, 4, 5, 6, 6, 7 median = 4lower extreme = 1upper extreme = 7
1st Quartile = 33rd Quartile = 6
Title
# of items
Electronics World
AIt's median time is 5 minutes faster, it also has a lower range and IQR (interquartile range)
50%75%
time is 5 minutes faster, it also has a lower range and IQR (interquartile range) so it's data are more clustered together.
A It's median
C = πdC = π 20C = 20π
C ≈ 62.8 mm
A = πr2
A = π (10)2
A = 100π
d = 20, so r = 10
A ≈ 314.2 mm2C = 62.8318... A = 314.1592...
C = πdC = π 10C = 10π C = 10π m
C = 2πr C = 2 π 10C = 20π C = 20π in
A = πr2 A = π (6)2
A = 36πd = 12, so r = 6
A = 36π in2
6 = rThe radius is 6 meters.
C = 2πr 12π = 2 π r 2π 2π
12π = 2 π r
radius = 6 in
√√A = πr2 36π = πr2
π π
36π = πr2
36 = r2
±6 = r
The diameter is 12 inches
18 = d
C = πd18π = π d18π = πd π π
d = 18 so r = 9 A = πr2
A = π (9)2
A = 81πA = 81π cm2
AB
A A = lwA = 9 8 A = 72
BA = 5 2A = 10
Total Area = 72 - 10Total Area = 62 yd2
A = lw
Total Area = A - B8 yd
SA = 550 m2
l w
h
V = lwhV = (15)(5)(10)V = 750 m3
SA = 2lw + 2wh + 2hl = 2(15)(5) + 2(5)(10) + 2(10)(15) = 150 + 100 + 300
= 550
SA = 2πr2 + 2πrhSA = 2π(5)2 + 2π(5)(4)SA = 50π + 40πSA = 90π SA = 90π in2 SA ≈ 282.7 in2
V = πr2hV = π(5)2 4 V = 100π
V = 100π in3
V ≈ 314.2 in3
13
V = πr2h13
V = π(4)2 25
V = 133.3π
diameter = 8, so radius = 4
V = 133.3π ft3 V ≈ 418.9 ft3
Maxwell should find its volume because volume is the amount of space a 3dimensional figure occupies.
Area of front/backA = lw A = 3 x 2A = 6
frontside
top Area of Sides (2)A = lw A = 2 x 1A = 2
SA = 6 + 6 + 2 + 2
SA = 16 ft2
V = lwhV = (6)(2.5)(4)V = 60 in3
Volume of 1 box of crayons
240 60 = 14,400They need 14,400 cubic inches of space to store the crayons.
V = πr2h81π = π(3)2 h height = 9m81π = 9πh
81π = 9πh 9π9π
9 = h
V = lwh40 = 4 2 h 40 = 8h
885 = h
height = 5m
50125
135
48 + 37 + 111 = 196No
10 + 70= 80
8 10 = 80
180 - 80= 100
100 3 21 + 12= 75
21 - 6= 15 7 22 - 38
= 116
3 22 - 2= 64
vertical angles
x = 10
7
- x- 1x
7
8x = x + 70
7x = 70
complementary
x = 214
3x + 12 + x - 6 = 90
- 6
4
4x + 6 = 90- 64x = 84
supplementary
x = 2210
7x - 38 + 3x - 2 = 180
+ 40
10
10x - 40 = 180+ 4010x = 220
38 + 68 + y = 180106 + y = 180
- 106 - 106y = 74
The other angle is 74
Let y = the measure of other angle
36
2x90 + 36 + 2x = 180
126 + 2x = 180- 126 - 126
2x = 542 2x = 27
x = 27
45 + 110 + 65 + x = 360220 + x = 360
- 220 - 220x = 140
The m W is 140
Let y = m W
x + x + 5 + x + 15 + 2x = 3605x + 20 = 360
- 20 - 20
x = 68
5x = 3405 5
m A = 68
m B = 68 + 5 = 73
m C = 68 + 15 = 83
m D = 2(68) = 136
12 - 21.
12)
30
Vertical to 2 OR supp. to 4 or 1150 It is supplementary to 4 or 1
Alt. interior to 4 OR corresponding to 1 150
17 *The sum of the 3 angles of a triangle is 180
30Vertical to 5 OR alt. exterior to 1 OR
corresponding to 430
They are alternate exterior
They are correspondingThey are alternate interior
AC CAor
AB BAorB
Cscaleneobtuse
6 + 8 > 914 > 8 (True) Yes
Sum: 6 + 9 = 15Difference: 9 6 = 3
The third must be greater than 3 inches, but less than 15 inches.
√
a2 + b2 = c2
162 + b2 = 302
256 + b2 = 900
b2 = 644- 256 - 256
√ b = ± 2 161 2 161 meters √√
a2 + b2 = c2
102 + 122 = c2
100 + 144 = c2
244 = c2√√ ± 2 61 = c √
2 61 feet√
50 fthouse
40 ftground
x
tree
√
a2 + b2 = c2
402 + b2 = 502
1600 + b2 = 2500
b2 = 900- 1600 - 1600
√ b = ± 30
The tree hit the house 30 feet
above the ground.
y2 y1x2 x1
ΔyΔx
slope = =x1 y1 x2 y2
5 - 14 - -3 = 7
4
slope = 74
y2 y1x2 x1
x1 y1 x2 y2
5 - 63 - 2 = 1
-1
slope = -1
y2 y1x2 x1
slope = -2y-intercept = 7
slope = y-intercept = -5
21 slope = 5
y-intercept = 1
xintercept (let y=0)
12 = 6x6
xint = 2
12
yintercept (let x=0)
y = 6x + 12
y = 122 = xyintercept = 12
y = 6(0) + 12
y = 6x + 120 = 6x + 12
12
6
xintercept (let y=0)
4 4x = 4
3
xintercept = 4
3
yintercept (let x=0)
y 4x = 3
y = 3yintercept = 3
y 4(0) = 3
y 4x = 30 4x = 34x = 3
y = x + 521 y = 5x 3 y = x 6
slope = -2y-intercept = 3up 2 left 1
2-1
-21
down 2 right 1
ORslope = -2y-intercept = -4
up 2 left 1
2-1
-21
down 2 right 1
OR
y = 2x + 3
y = 2x + 3 TP
Test Point (3,2)x, y
True
y ≥ -2x - 4
2 ≥ -2(3) - 41 ≥ -10
xintercept (let y=0)
12 = 6x6
xint = 2
12
yintercept (let x=0)
y = 6x + 12
y = 122 = xyintercept = 12
y = 6(0) + 12
y = 6x + 120 = 6x + 12
12
6
xintercept (let y=0)
4 4x = 4
3
xintercept = 4
3
yintercept (let x=0)
y 4x = 3
y = 3yintercept = 3
y 4(0) = 3
y 4x = 30 4x = 34x = 3
y = x + 521 y = 5x 3 y = x 6
slope = -2y-intercept = 3up 2 left 1
2-1
-21
down 2 right 1
ORslope = -2y-intercept = -4
up 2 left 1
2-1
-21
down 2 right 1
OR
y = 2x + 3
y = 2x + 3
TP
Test Point (3,2)x, y
True
y ≥ -2x - 4
2 ≥ -2(3) - 41 ≥ -10
y = x + 131
1
1 11
-1-1
OR
1
1
y = x 1slope = 1yintercept = 1
y = x 131y = x + 1
slope = yintercept = 1
31
1
3 13
-1-3
OR
1
3
(3, 2)
2 = 22 = 22 = (3) + 12 = 3 1Check (3, 2)
y = x 1 31y = x + 1
31
x y
y = x + 2
down 2 right 3
-23
∆y∆x
Slope23-
yintercept 2
23-
up 2 right 1
21
∆y∆x
Slope
yintercept 3
2
y = 2x 3
down 2 right 3 up 2
right 1
Yes, every input has exactly one output
Not a function, the input -2 has 2 outputs
(2, 5)(2, -2) (4, 1)(3, 3) (6, 1){2, 3, 4, 6}{-2, 1, 3, 5}
Not a function, because the input 2 has 2 outputs.
y = 128 - 8x
If bottle is unopened, no servings have been poured, so x = 0.
y = 128 - 8(0)y = 128 - 0y = 128
has exactly one output.
Yes, every input
I agree with the boys claim. shown in the table is NOT a function
The relation
because some inputs have 2 outputs.If we reverse the x (input) and y (output),
the relation would be a function becauseeach inputs would have exactly 1 output.
Using the vertical line test -- Each vertical line drawn through the graph intersects at only 1 location.
A
Remember: The y-intercept is the value of y when x = 0
ΔyΔx
=slope = 44 = 1
+4 +4
Function Rule: y = x - 5
ΔyΔx
=slope = 24 = 2+2 +4
y-intercept = 1
y-intercept = -5 Function Rule y = 2x + 1
translationreflectionrotation
dilationlarger
smaller
translations, reflections and rotations are isometries
Rule: (x,y) (x, y) A' (3, 5)
Rule: (x,y) (x, y) A' (3, 5)
Rule: (x,y) (x 2, y + 6) A' (5, 11)
Rule: (x,y) (2x, 2y) B' (4, 16)
Rule: (x,y) (y, x) R' (7, 4)
Rule: (x,y) (x, y) T' (3, 9)
A' (2, 8)T' (2, 2)
A (1, 4)T (1, 1)
M (3, 3)
H (3, 1)
M' (6, 6)
H' (6, 2)
Rule: (x,y) (2x, 2y)
H'
A'M'
T'