(6, 3), (7-4) find the slope<br>

Emma is training for a 10-kilometer race. She wants to beat her last 10-kilometer time, which was 1 hour 10 minutes. Emma has al

Mandarinka [93]

Answer:

$70 > 55 + t$

Step-by-step explanation:

Given

$Previous\ Time = 1\ hr\ 10\ mins$

$Current\ Time = 55\ mins$

Required

Represent the additional time needed as an inequality

Convert the previous time to minutes

$Previous\ Time = 1\ hr\ 10\ mins$

$Previous\ Time = 1 * 60\ mins + 10\ mins$

$Previous\ Time = 60\ mins + 10\ mins$

$Previous\ Time = 70\ mins$

Let the additional time be t

<em>This means that she needs to run at least t minutes to beat her previous record</em>

<em />

To beat her previous record, the sum of current time and x must be less than her previous time. i.e.

$55 + t < 70$

This can be rewritten as:

$70 > 55 + t$

7 0

3 years ago

Read 2 more answers

There are 105 calories in a glass and a half of lemonade. how many calories are in 2 1/2 glasses

ddd [48]

Answer:

175

Step-by-step explanation:

A glass and a half is 1+1/2 = 3/2 glasses.

2 1/2 glasses is 2/2 glasses more than that, or 5/2 glasses.

5/2 glasses is 5/3 times the size of 3/2 glasses, so there will be 5/3 the number of calories:

... (105 calories) × (5/3) = 175 calories

8 0

3 years ago

Read 2 more answers

a roller coaster car rapidly picksup seed as it rolls down a slope. AS it starts down its speed is 4m/s. 3 seconds later its spe

il63 [147K]

Change in speed = (end speed) - (start speed)

   =    (22 m/s)    - (4 m/s) = 18 m/s .

Magnitude of average acceleration =

   (change in speed) / (time for the change) .

   =    (18 m/s) / (3 sec) = 6 m/s² .

That's about 0.61 G.
If you weigh 150 pounds, then you would feel as if there's
a force of 92 pounds pushing you back against the seat !

7 0

3 years ago

Jackie makes an $800 deposit into a bank account earning 4.5% interest.

Pepsi [2]

Answer:

a. $1251.5

b. $1254.64

c. 15.4 years

d. 30.56 years

Step-by-step explanation:

Given the information:

Principle (P) = $800
Interest = 4.5%

As we know, the formula to find the future value of Jackie deposit with interest is compounded monthly, quaterly, ..is

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

P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time

Hence:

a. If the interest is compounded quarterly how much money will Jackie have in 10 years?

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

<=> $A=800(1+\frac{0.045}{4} )^{4*10}$

<=> A = $1251.5

d. If Jackie's money is compounded monthly, how long will it take her money to triple?

<=> $A=P(1+\frac{r}{n} )^{nt} = 3*800$

<=> $800(1+\frac{0.045}{12} )^{12*t} = 2400$

<=> $(1+\frac{0.045}{12} )^{12*t} = 3$

<=> t = 30.56 years

As we know, the formula to find the future value of Jackie deposit with interest is compounded continuously

A = P* $e^{rt}$ where e is the mathematical constant approximated as 2.7183.

b. If the interest is compounded continuously how much money will Jackie have in 10 years?

<=> A = 800* $2.7183^{0.045*10}$

<=> A = $1254.64

C. If Jackie's money is compounded continuously, how long will it take her money to double?

<=> P* $e^{rt}$ = 2*800

<=> 800* $2.7183^{0.045*t}$ = 1600

<=> $2.7183^{0.045*t}$ = 2

<=> t = 15.4 years

8 0

3 years ago

Find all the zeros of f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Andrews [41]

Answer:

x=-2 x=2 x = 1/2 x=3

Step-by-step explanation:

f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Graph

We see that there is a zero at -2

Using synthetic division

-2 2 -5 -5 20 -12

-4 18 -26 12

------------------------------

2 -9 13 -6 0

This gives us ( x+2) ( 2x^3 -9x^2 +13x -6)

We see that there is a zero at 2

Using synthetic division ( 2x^3 -9x^2 +13x -6)

2 2 -9 13 -6

4 -10 6

------------------------------

2 -5 3 0

This gives us ( x+2) ( x-2) ( 2x^2 -5x+3)

We can factor ( 2x^2 -5x+3)

( x+2) ( x-2) ( 2x -1) ( x-3)

Using the zero product property

( x+2)=0 ( x-2)=0 ( 2x -1)=0 ( x-3)=0

x=-2 x=2 x = 1/2 x=3

7 0

3 years ago

(6, 3), (7-4) find the slope​

(6, 3), (7-4) find the slope