Solution:
We have:
f(x) = √x
g(x) = 7x + b
y = f(g(x)), Given point on the graph (x, y) = (4, 6)
Use: f(x) = √x
f(g(x)) = √(g(x))
y = √(7x + b), x = 4, y = 6
6 = √(7(4) + b)
6² = (7(4) + b)
36 = 28 + b
36 - 28 = b
8 = b
b = 8
Let the length of the rectangle is x. units , accordingly :
2.(x+3) = x×3.
2x + 6 = 3x.
x = 6 units is the answer :)
Answer:
Step-by-step explanation:
4) ΔSTW ≅ ΔBFN . So, corresponding parts of congruent triangles are congruent.
a) BN = SW d) m∠W = m∠N
BN = 9 cm m∠W = 82°
b) TW = FN e) m∠B = m∠S
TW = 14 cm m∠B = 67°
c) BF = ST f) m∠B + m∠N + m∠F = 180°
BF = 17 cm 67 + 82 + m∠F = 180
149 + m∠F = 180
m∠F = 180 - 149
m∠F = 31°
5) ΔUVW ≅ ΔTSR
UV = TS
12x - 7 = 53
12x = 53+7
12x = 60
x = 60/12
x = 5
UW =TR
3z +14 = 50
3z = 50 - 14
3z = 36
z = 36/3
z = 12
SR =VW
5y - 33 = 57
5y = 57 + 33
5y = 90
y = 90/5
y = 18
7) ΔPHS ≅ ΔCNF
∠C = ∠P
4z - 32 = 36
4z = 36 + 32
4z = 68
z = 68/4
z = 17
∠H = ∠N
6x - 29 = 115
6x = 115 + 29
6x = 144
x = 144/6
x = 24
∠P + ∠H + ∠S = 180 {Angle sum property of triangle}
36 +115 + ∠S = 180
151 + ∠S = 180
∠S = 180 - 151
∠S = 29°
∠F = ∠S
3y - 1 = 29
3y = 29 + 1
3y = 30
y = 30/3
y = 10
8) ΔDEF ≅ ΔJKL
DE = 18 ; EF = 23
DF = 9x - 23
JL= 7x- 11
DF = JL {Corresponding parts of congruent triangles}
9x - 23 = 7x - 11
9x - 7x - 23 = -11
2x - 23 = -11
2x = -11 + 23
2x = 12
x = 12/2
x = 6
JK = DE {Corresponding parts of congruent triangles}
3y - 21 = 18
3y = 18 + 21
3y = 39
y = 39/3
y = 13
Answer:
$67.20
Step-by-step explanation:
"30% off" translates into multiplying the original price by 1.00 - 0.30, or 0.70.
0.70($96) = $67.20 is the sales price
Split the second term in 5x^2 + 12 - 32 into two terms
5x^2 + 20x - 8x - 32
Factor out common terms in the first two terms, then in the last two terms
5x(x + 4) - 8(x + 4)
Factor out the common term: x + 4
<u>(x + 4)(5x - 8) </u>
