PERTANYAAN :
1.A law firm seeks to recruit top-quality experienced lawyers. The total package offered is
the sum of three separate components: a basic salary which is 1.2 times the candidate’s
current salary together with an additional $3000 for each year worked as a qualified
lawyer and an extra $1000 for every year that they are over the age of 21.
Work out a formula that could be used to calculate the total salary, S, offered to
someone who is A years of age, has E years of relevant experience and who currently
earns $N. Hence work out the salary offered to someone who is 30 years old with five
years’ experience and who currently earns $150 000.
2.Write down a formula for each situation:
a. A plumber has a fixed call-out charge of $80 and has an hourly rate of $60. Work out the total charge, C, for a job that takes L hours in which the cost of materials and parts is $K.
b.An airport currency exchange booth charges a fixed fee of $10 on all transactions and offers an exchange rate of 1 dollar to 0.8 euros. Work out the total charge, C, (in $) for buying x euros.
c. A firm provides 5 hours of in-house training for each of its semi-skilled workers and 10 hours of training for each of its skilled workers. Work out the total number of hours, H, if the firm employs a semi-skilled and b skilled workers.
d. A car hire company charges $C a day together with an additional $c per mile. Work out the total charge, $X, for hiring a car for d days and travelling m miles during that time.
Without using a calculator, evaluate
(a) 10 × (−2)
(b) (−1) × (−3)
(c) (−8) ÷ 2
(d) (−5) ÷ (−5)
(e) 24 ÷ (−2) (f) (−10) × (−5)
(f) (−6) × 5 × (−1)
3.Without using a calculator, evaluate
(a) 5 − 6 (b) −1 − 2
(c) 6 − 17
(d) −7 + 23
(e) −7 − (−6)
(f) −4 − 9
(g) 7 − (−4)
(h) −9 − (−9)
(i) 12 − 43 ( j) 2 + 6 − 10
4.Without using a calculator, evaluate
(a) 5 × 2 − 13 (b) 5 × (1 − 4)
(c) 1 − 6 × 7 (d) −5 + 6 ÷ 3 (e) 2 × (−3)2 (f) −10 + 22 (g) (−2)2 − 5 × 6 + 1 ( j)
5.Simplify each of the following algebraic expressions:
(a) 2 × P × Q (b) I × 8 (c) 3 × x × y
(d) 4 × q × w × z (e) b × b (f) k × 3 × k
STATUS :100%
KETERANGAN : Saya sudah mengerjakan assignment ini dengan baik dan benar
BUKTI :
1.
Step 1: Define the formula
We are told:
Basic salary = 1.2×N1.2 \times N1.2×N
Experience bonus = 3000×E3000 \times E3000×E
Age bonus = 1000×(A−21)1000 \times (A – 21)1000×(A−21) (only counts years over age 21)
So, the total salary SSS is:
S=1.2N+3000E+1000(A−21)S = 1.2N + 3000E + 1000(A – 21)S=1.2N+3000E+1000(A−21)
Step 2: Substitute the values given
A=30A = 30A=30
E=5E = 5E=5
N=150,000N = 150,000N=150,000
S=1.2(150,000)+3000(5)+1000(30−21)S = 1.2(150,000) + 3000(5) + 1000(30 – 21)S=1.2(150,000)+3000(5)+1000(30−21)
Step 3: Calculate step by step
Basic salary:
1.2×150,000=180,0001.2 \times 150,000 = 180,0001.2×150,000=180,000
Experience bonus:
3000×5=15,0003000 \times 5 = 15,0003000×5=15,000
Age bonus:
30−21=9⇒1000×9=9,00030 – 21 = 9 \quad \Rightarrow \quad 1000 \times 9 = 9,00030−21=9⇒1000×9=9,000
Step 4: Add them up
S=180,000+15,000+9,000=204,000S = 180,000 + 15,000 + 9,000 = 204,000S=180,000+15,000+9,000=204,000
✅ Final Formula:
S=1.2N+3000E+1000(A−21)\boxed{S = 1.2N + 3000E + 1000(A – 21)}S=1.2N+3000E+1000(A−21)
✅ Salary Offered:
S=$204,000\boxed{S = \$204,000}S=$204,000
2.
(a) Plumber: fixed call-out $80, hourly rate $60, job takes LLL hours, materials cost $KKK.
C=80+60L+K\boxed{C = 80 + 60L + K}C=80+60L+K
(b) Currency booth: fixed fee $10, exchange rate 1$ =0.8 euros1\$\ = 0.8\ \text{euros}1$ =0.8 euros. To buy xxx euros you need x0.8=1.25x\dfrac{x}{0.8}=1.25×0.8x=1.25x dollars plus the fee:
C=10+x0.8=10+1.25x\boxed{C = 10 + \dfrac{x}{0.8} = 10 + 1.25x}C=10+0.8x=10+1.25x
(c) Training hours: 5 hours per semi-skilled worker, 10 hours per skilled worker. If firm employs aaa semi-skilled and bbb skilled workers:
H=5a+10b\boxed{H = 5a + 10b}H=5a+10b
(d) Car hire: $CCC per day and $ccc per mile. For ddd days and mmm miles:
X=Cd+cm\boxed{X = Cd + cm}X=Cd+cm
Without calculator — evaluate:
Work carefully, step by step:
(a) 10×(−2)=−2010 \times (-2) = -2010×(−2)=−20
(b) (−1)×(−3)=+3(-1)\times(-3)=+3(−1)×(−3)=+3
(c) (−8)÷2=−4(-8)\div 2 = -4(−8)÷2=−4
(d) (−5)÷(−5)=+1(-5)\div(-5)=+1(−5)÷(−5)=+1
(e) 24÷(−2)=−1224\div(-2) = -1224÷(−2)=−12
(f) (−10)×(−5)=+50(-10)\times(-5)=+50(−10)×(−5)=+50
You listed (f) twice; I’ll label the last one as (g):
(g) (−6)×5×(−1)(-6)\times 5 \times (-1)(−6)×5×(−1). First (−6)×5=−30(-6)\times 5=-30(−6)×5=−30, then −30×(−1)=+30-30\times(-1)=+30−30×(−1)=+30.
So final results:
(a) −20-20−20, (b) 333, (c) −4-4−4, (d) 111, (e) −12-12−12, (f) 505050, (g) 303030
3.
(a) 5−6=−15 – 6 = -15−6=−1
(b) −1−2=−3-1 – 2 = -3−1−2=−3
(c) 6−17=−116 – 17 = -116−17=−11
(d) −7+23=16-7 + 23 = 16−7+23=16
(e) −7−(−6)=−7+6=−1-7 – (-6) = -7 + 6 = -1−7−(−6)=−7+6=−1
(f) −4−9=−13-4 – 9 = -13−4−9=−13
(g) 7−(−4)=7+4=117 – (-4) = 7 + 4 = 117−(−4)=7+4=11
(h) −9−(−9)=−9+9=0-9 – (-9) = -9 + 9 = 0−9−(−9)=−9+9=0
(i) 12−43=−3112 – 43 = -3112−43=−31
(j) 2+6−10=8−10=−22 + 6 – 10 = 8 – 10 = -22+6−10=8−10=−2
4.
(a) 5 × 2 − 13
5×2=105 × 2 = 105×2=10
10−13=−310 − 13 = -310−13=−3
✅ Jawaban: -3
(b) 5 × (1 − 4)
Hitung dalam kurung: 1−4=−31 − 4 = -31−4=−3
5×−3=−155 × -3 = -155×−3=−15
✅ Jawaban: -15
(c) 1 − 6 × 7
Kali dulu: 6×7=426 × 7 = 426×7=42
1−42=−411 − 42 = -411−42=−41
✅ Jawaban: -41
(d) −5 + 6 ÷ 3
Bagi dulu: 6÷3=26 ÷ 3 = 26÷3=2
−5+2=−3−5 + 2 = -3−5+2=−3
✅ Jawaban: -3
(e) 2 × (−3)²
Kuadrat dulu: (−3)2=9(−3)² = 9(−3)2=9
2×9=182 × 9 = 182×9=18
✅ Jawaban: 18
(f) −10 + 22
−10+22=12-10 + 22 = 12−10+22=12
✅ Jawaban: 12
(g) (−2)² − 5 × 6 + 1
Kuadrat dulu: (−2)2=4(−2)² = 4(−2)2=4
Kali: 5×6=305 × 6 = 305×6=30
4−30+1=(4+1)−30=5−30=−254 − 30 + 1 = (4 + 1) − 30 = 5 − 30 = -254−30+1=(4+1)−30=5−30=−25
✅ Jawaban: -25
5.
(a) 2 × P × Q
Tidak ada angka atau variabel yang sama untuk dikalikan, jadi kita cukup menuliskannya berurutan:
✅ Jawaban: 2PQ
(b) I × 8
Urutkan angka di depan huruf:
✅ Jawaban: 8I
(c) 3 × x × y
Gabungkan:
✅ Jawaban: 3xy
(d) 4 × q × w × z
Gabungkan:
✅ Jawaban: 4qwz
(e) b × b
Variabel sama → dijadikan pangkat:
✅ Jawaban: b²
(f) k × 3 × k
Gabungkan angka dulu: 333
k×k=k2k × k = k²k×k=k2
✅ Jawaban: 3k²