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3 years ago

Twice a number is 16 greater than two times the opposite of the number. What is the number

Mathematics

1 answer:

kodGreya [7K]3 years ago

6 0

Answer:

Step-by-step explanation:

Let's say our number is n.

First, we have two times a number. This can be represented by 2 times our number, n, or 2*n

Next, we have that is 16 greater than ... It is hard to conceptualize what 2*n is 16 greater than, so we can move on and save this for later.

Furthermore, we have two times the opposite of the number. Opposite represents the opposite side of a number line, e.g. if the number was 5, the opposite would be -5. This can be represented by multiplying our number n by -1, or -1 * n = -n. We then take two times of this opposite, or 2 * -1 * n = -2 * n.

So far, we have 2*n is 16 greater than -2 * n. We can then say that if a first number is 16 greater than a second number, we must add 16 to the second number to get the first number. Applying that here, we can say that 2*n = -2*n + 16

We then have

2*n = -2*n + 16

We then want to separate the n from the real number(s) (16 in this case). To do that, we can add 2*n to both sides, making our equation

2*n+2*n = 16

4*n = 16

Then, we can finally divide both sides by 4 to get

n = 4

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Textbooks are exempted from PST in Ontario. If the total cost of a book

Andrei [34K]

Answer:

4.24

Step-by-step explanation:

Total price = price of the book + 5% of the price of the book

T = total price P = price of the book G = GST

T = P + G

and

G = 5% of P = 0.05P

therefore

T = P + 5%P = 1P + 0,05P = 1.05P

P = T/1.05 = 89/1.05 ≅ 84.76 (it is 84.7619047619)

G = 89 - 84.76 = 4.24

8 0

3 years ago

One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone

valina [46]

Answer:

Both plans would cost $100 if 6 gigabytes of data are used.

Explanation:

From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:

c = 52 + 8d ........................... (1)

c = 82 + 3d ........................... (2)

Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:

52 + 8d = 82 + 3d

8d - 3d = 82 - 52

5d = 30

d = 30 / 5

d = 6

Substituting d = 6 into equation (1), we have:

c = 52 + (8 * 6)

c = 52 + 48

c = 100

Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.

5 0

2 years ago

On any given day, the probability that a large local river is polluted by carbon tetrachloride is 0.12. Each day, a test is cond

babymother [125]

Answer:

a) 0.2416

b) 0.4172

c) 0.0253

Step-by-step explanation:

Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .

denoting event a A=the test proves correct and B=the river is polluted

a) the test indicates pollution when

- the river is polluted and the test is correct

- the river is not polluted and the test fails

then

P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416

b) according to Bayes

P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)

then

P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172

c) since

P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584

the rate of false positives is

P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253

4 0

3 years ago

What is the gcf of 12 and 36

timofeeve [1]

The gcf would be 12 because both 12 and 36 can be divided by 12 and it is the highest number

4 0

3 years ago

Graph the function.<br> [-X + 1, -10 6. f(x) = x2-9, -3 (2x+1, 3

lapo4ka [179]

Answer:

2x2 - 5x - 12 = 0.

(2x + 3)(x - 4) = 0.

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

6 0

3 years ago