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2 years ago

Which conjunction is disjunction is equivalent to the given absolute value inequality? |x+2|<18

Mathematics

1 answer:

a_sh-v [17]2 years ago

6 0

Answer: conjunction and -20<x <16 is answer.

Step-by-step explanation:

It is a conjunction because it is and statement

|x+2|<18 gives

[Since l x-a l <b means x-a lies between -b and b ]

-18<x+2<18

subtracting 2 in the whole inequality ,we get

-18-2 <x +2-2 < 18-2

-20 < x < 16

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Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.

ivann1987 [24]

Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

7 0

2 years ago

Help with simple interest rate P=$18,000, r= 7.5%, t=18 months

n200080 [17]

=2025
change 18months to years=1.5 years then you use the formula
PRT÷100
$18000 \times 7.5 \times 1.5 = 202500 \div 100 = 2025$

7 0

3 years ago

Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2

Sloan [31]

-3x²-2 .................

4 0

3 years ago

Increase £30 by 15% what is the answer

zheka24 [161]

30X15=450. 450:100= 4,50. 30+4,50= 34,50

7 0

2 years ago

Suppose two $20 bills, three $10 bills, one $5 bill, and seven $1 bills are placed in a bag. If you were to pull a bill at rando

Korolek [52]

Answer:

Assuming that the $1 bill was pulled at random, then the expected value of the amount chosen is $\frac{7}{13}$ .

Step-by-step explanation:

From the given question, the bag contains;

$1 bill = 7

$5 bill = 1

$10 bill = 3

$20 bill = 2

Total number of bills in the bag = 13

Pulling a bill at random, the bills would have an expected value as follows:

For $1 bill, the expected value = $\frac{7}{13}$

For $5 bill, expected value = $\frac{1}{13}$

For $10 bill, expected value = $\frac{3}{13}$

For $20 bill, the expected value = $\frac{2}{13}$

Assuming that the $1 bill was pulled at random, then the expected value of the amount chosen is $\frac{7}{13}$ .

6 0

2 years ago