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4 years ago

Graph the relation shown in the table. Is the relation a function? Why or why not?

Mathematics

2 answers:

Bogdan [553]4 years ago

4 0

Answer: choice B) yes; only one range value exists for each domain value

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Explanation:

The inputs are x = -3, x = -1, x = 1, x = 5. They are the first coordinate listed of each point. We don't have any x values repeating so this means we have a function. Each input leads to exactly one output which is what choice B is stating. The domain is the set of allowed inputs, or x values. The range is the set of possible y outputs.

If we had something like (1,2) and (1,5) then the input x = 1 leads to more than one output (y = 2 and y = 5). This example means we don't have a function

If you graph the points (-3, -2), (-1,0), (1,0) and (5,-2) as shown in the attached image, then you'll notice that it is impossible to pass a single line through more than one point. Therefore this graph passes the vertical line test visually proving we have a function.

Going back to the example with (1,2) and (1,5), plotting these two points leads to the vertical line test failing implying we don't have a function.

lesya [120]4 years ago

3 0

The answer to this question is B

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

$A = P(1 + \frac{r}{n})^{nt}$

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

4 0

4 years ago

Help please.

kompoz [17]

The domain will be the numbers you can use for x and not get a undefined thing like division by 0 or square root of a negative number

(f*g)(x)=f(x) times g(x)=(3x+2) times (7x+6)=(3x+2)(7x+6)= $21x^2+14x+18x+12=21x^2+32x+12$

the domain is all real numbers because we can't find any values of x that make a division by 0 or square root of a negative

answer is C

3 0

3 years ago

What is the length to the nearest tenth, of the line segment joining the points (-4,2) and (146,52)

Vlad1618 [11]

Finding the distance between (-4,2) and (146,52)

Use the distance formula to determine the distance between the two points.
Distance= √(x2−x1)^2+(y2−y1)^2

Substitute the actual values of the points into the distance formula.
√((146)−(−4))^2+((52)−(2))^2

Simplify the expression.
√19400

Rewrite 19400 as 10^2⋅194.
√10^2⋅194

Pull terms out from under the radical.
10√194

The approximate value for the distance between the two points is 139.28389.

10√194≈139.28389

7 0

3 years ago

The Other Number Your first number was 8. Is the other one 0? How did we know that? Can we read your mind?

Mandarinka [93]

Answer:

???

Step-by-step explanation:

3 0

2 years ago

What is 1.5 divides by 0.25 also if you could can you set it up and show me hot to dived it plz whoever does it first and is rig

zhuklara [117]

Answer:

6 all u do is .25 + .25 etc until you 1.5

Step-by-step explanation:

8 0

3 years ago