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Shtirlitz [24]
2 years ago
7

In the diagram below , what is the value of a?

Mathematics
1 answer:
ipn [44]2 years ago
5 0

Step-by-step explanation:

solution

let,

AB = 9

AC = 9 + 3a - 6

AD = 12

AE = 12 + 20

now

AB/AD = AC/AE

or, 9/12 = 3 + 3a / 22

by cross multiply

or, 9×22 = 12×(3 + 3a)

or, 198 = 36 + 36a

or, (198 - 36)/36 = a

or, 4.5 = a

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A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
Kitty [74]

Answer: ab =6

have:

\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\\frac{a+b+1}{ab}=1

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

4 0
2 years ago
Two friends are hiking in Death Valley National Park. Their elevation ranges from 228 ft below sea level at
monitta

Answer:

x - 231 ≤ 459

Step-by-step explanation:

Given:

Elevation ranges below sea level  = 228 ft

Elevation ranges above sea level  = 690 ft

Elevation = x

Computation:

Ideal range = [690-228] / 2 = 231

Tolerance range = [690+228] / 2 = 459

So,

x - 231 ≤ 459

6 0
3 years ago
Solve the equation -3 + 1/2n = 1/2 (-n + 14) in two different ways.
Lemur [1.5K]

Answer:

Step-by-step explanation:

-3 + 1/2n = 1/2 (-n + 14)

distribute

-3 + 1/2n = -1/2n + 7

                 -1/2n

cancel out -1/2n

-3 = n + 7

-10 = n

subtract 7

n =  -10

4 0
2 years ago
Ian can buy bottles of water in packages of 6 for $9.24 or in packages of 4 for $8.80. How much money does he save by buying 12
kati45 [8]

Answer:

Ian saves 7.92

Step-by-step explanation:

9.24/6=1.54

2*9.24= 18.48

8.80/4=2.20

3*8.80= 26.40

26.0 - 18.48 = 7.92

7 0
3 years ago
Help plsssssssssssssssssssssss
bonufazy [111]

Answer:

54 in

Step-by-step explanation:

because 6 times 5 is 30 plus 4 times 6 is 24 equals 54

7 0
3 years ago
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