Simplify. 1/4n - 1/2 / n/5

What are the zeros of the polynomial function y=2x^3-7x^2+2x+3?

zlopas [31]

$y = 2 {x}^{3} - 7 {x}^{2} + 2x + 3$

By inspection 1 is a root of y ,
Hence , (x-1) is a factor of y ,

$\dfrac{2 {x}^{3} - 7 {x}^{2} + 2x + 3 }{x - 1} = 2 {x}^{2} - 5x - 3 \\ \\ 2 {x}^{2} - 5x - 3 = (2x + 1)(x - 3)$

Hence , the 2 other roots are -1/2 and 3 , and the above graphs confirms the same.

Hope it helps you :)

7 0

3 years ago

Judy spent 3 hours driving 165 miles She thinks

sasho [114]

Step-by-step explanation:

she drove already 165 miles.

she will reach her destination, if she drives 4 more hours by going 65 miles/hour.

that would mean she would travel

65×4 = 260 miles

in these 4 hours.

so, the total trip is then 165 + 260 = 425 miles.

but what I find strange is that your teacher specified how long it took her to drive the first 165 miles.

as you can see above, it would make no difference for the calculation of the total trip length in miles.

this is either an attempt to confuse us, or the message is that Judy has to achieve an average of 65 miles/hour for the whole trip, and the problem definition was just imperfectly phrased.

if that is the case, then things look a bit different, as her average speed was only 165/3 = 55 miles/hour for the first 3 hours and 165 miles.

so,

(165 + x)/(3 + 4) hours = 65/hour

(165 + x)/7 hours = 65/hour

165 + x = 65 × 7 hours / hour = 65×7 = 455 miles

x = 455 - 165 = 290 miles

she would have to go

290 miles / 4 hours = 72.5 miles/hour

for these next 4 hours (and 290 miles) to reach an overall average speed of 65 miles/hour.

and the total trip would be then

165 + 290 = 455 miles

I am not sure, which your teacher wants here.

65 miles/hour average speed just for the next 4 hours, or to speed up that much for the next 4 hours that the overall trip average is then 65 miles/hour.

again, the phrasing of the problem definition suggests the first case, but the fact that the travel time for the first part of the trip is given could suggest the second case (as this information is not needed for the first case).

6 0

2 years ago

Suppose that you buy a two-year 8% bond at its face value.

Juliette [100K]

Answer:

Real Rate of Return = 4.9% and Nominal rate = 0.08 or 8%

Real Rate of Return = 2.9% and Nominal rate = 0.081 or 8.1%

real rate = 5 % and Nominal rate = 0.0815 or 8.15%

real rate = 3% and Nominal rate = 0.0815 or 8.15%

Step-by-step explanation:

given data

time period = 2 year

Coupon rate = 8% = 0.08

Inflation rate 1st year = 3% = 0.03

Inflation rate 2nd year = 5% = 0.05

solution

we get here Real Rate of Return that is express as

Real Rate of Return = (Coupon Rate - Inflation rate) ÷ (1+Inflation rate) .........1

so that here 1st year Real return will be

Real Rate of Return = (0.08 - 0.03) ÷ (1+0.03)

solve it we get

Real Rate of Return = 4.9%

and

(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ............2

(1 + nominal rate) = (1 + 0.049) × (1 + 0.03)

Nominal rate = 0.08 or 8%

and

for 2nd year Real return will be

Real Rate of Return = (0.08 - 0.05) ÷ (1+0.05)

solve it

Real Rate of Return = 2.9%

and

(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ............3

(1 + nominal rate) = (1 + 0.029) × (1 + 0.05)

Nominal rate = 0.081 or 8.1%

and

now for the bond Treasury Inflation-Protected Securities, we get real and nominal return that is

for 1st year

Real rate = Coupon rate - Inflation ...............4

Real rate = 0.08 - 0.03

real rate = 0.05

and

(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ................5

(1 + nominal rate) = (1 + 0.05) × (1 + 0.03)

so

Nominal rate = 0.0815 or 8.15%

and for 2nd years it will be

Real rate = Coupon rate - Inflation ....................6

Real rate = 0.08 - 0.05

real rate = 0.03

and

(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ...................7

(1 + nominal rate) = (1 + 0.03) × (1 + 0.05)

so

Nominal rate = 0.0815 or 8.15%

4 0

3 years ago

The sum of 367 and 863 is equal to the sum of 863 and another number. what is that number?

oksian1 [2.3K]

The other no is
863-367 =496

4 0

2 years ago

Read 2 more answers

How do you write the equation for intercept (4,-3), m=-1

nata0808 [166]

Answer:

y=-1x+-3

Step-by-step explanation:

y=mx+b

y=-1x+-3

6 0

3 years ago

Simplify. 1/4n - 1/2 / n/5 - 1/20n