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3 years ago

Domain and range of the function and it’s inverse

Mathematics

1 answer:

sineoko [7]3 years ago

8 0

Answer:

B (second table in list)

Step-by-step explanation:

The function is a quadratic with vertex and y-intercept at (0,-2). The parabola opens up meaning only y - values above -2 are a part of the function. Since range is the set of all y values, then the range is $y\geq -2$ .

The domain is not restricted and it is all real numbers.

The inverse of the function is where x and y are switched. So the range becomes the domain and vice verse.

This means the domain of the inverse is $x\geq -2$ and the range of the inverse is all real numbers.

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You deposit $300 in a savings account that pays 6% interest compounded semiannually. How much will you have at the middle of the

Otrada [13]

Answer:

Please check the explanation.

Step-by-step explanation:

a) How much will you have at the middle of the first year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 0.5 years

Total amount = A = ?

Using the formula

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

substituting the values

$A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}$

$A=300\cdot \frac{2.06}{2}$

$A=\frac{618}{2}$

$A=309$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.

Part b) How much at the end of one year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 1 years

Total amount = A = ?

Using the formula

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

so substituting the values

$A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}$

$A=300\cdot \frac{2.06^2}{2^2}$

$A=318.27$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.

7 0

3 years ago

A company has an annual electric bill of $495,000. Of that amount, 3/5 was billed

disa [49]

Answer:

$74,250

Step-by-step explanation:

495,000x0.6=297,000

297,000/4=74,250

7 0

3 years ago

What single decimal multiplier would you use to increase by 5% followed by a 20% increase?

sashaice [31]

Answer:

The single decimal multiplier is 1.26.

Step-by-step explanation:

Multipliers:

For a decrease of a%, we multiply by: $\frac{100-a}{100}$

For a increase of a%, we multiply by: $\frac{100+a}{100}$

For consecutive changes, we multiply the multipliers.

Increase of 5%

Multiply by $\frac{100+5}{100} = \frac{105}{100} = 1.05$

Increase of 20%

Multiply by $\frac{100+20}{100} = \frac{120}{100} = 1.2$

Consecutive:

1.05*1.2 = 1.26

The single decimal multiplier is 1.26.

8 0

3 years ago

lbvjy [14]

9514 1404 393

Answer:

Step-by-step explanation:

There can be any whole number of boys from 0 to 14. That's 15 different possibilities.

8 0

3 years ago

plz, help I don't know what I'm doing wrong. In the diagram, RSTU, and ABCD. Find the ratio of their perimeters.

Bogdan [553]

Answer:

3 : 2

Step-by-step explanation:

Note that the ratio of perimeters is equal to the ratio of the sides, thus

ratio of corresponding sides = 12 : 8 = 3 : 2

Thus the ratio of perimeters is 3 : 2

6 0

3 years ago