A quadratic equation that opens up, is compressed by a factor of ¼ , and is shifted right by 5 units

labwork [276]

G is equivalent to 3

4 0

3 years ago

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph t

natulia [17]

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway $d_1$ = 60 mph

Let the time taken to travel on highway = $t_1$ hours

Distance traveled = $60t_1$ miles

Speed in the city = 40 mph

Let the time taken = $t_2$ hours

Distance traveled in the city = $40t_2$ miles

Speed on the construction = 20 mph

Let the time spend on the construction = $t_3$ hours

Distance traveled on the construction = $20t_3$ miles

Since, total distance covered = 380 miles

$d_1+d_2+d_3=60t_1+40t_2+20t_3$

He spends one half the time on the highway as he does on the construction,

$t_3=2t_1$

Total time spent in the trip = 11 hours

Therefore, $t_1+t_2+t_3=11$

$t_1+t_2+2t_1=11$

$t_2=11-3t_1$

From equation (1),

$60t_1+40(11-3t_1)+20(2t_1)=380$

$60t_1-120t_1+40t_1+440=380$

$440-20t_1=380$

$20t_1=440-380$

$t_1=\frac{60}{20}$

$t_1=3$ hours

$t_2=11-3t_1=2$ hours

$t_3=2t_1=6$ hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

3 0

3 years ago

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Leviafan [203]

-x^2+2x+3=x^2-2x+3 add x^2 to both sides

2x+3=2x^2-2x+3 subtract 2x from both sides

3=2x^2-4x+3 subtract 3 from both sides

2x^2-4x=0 factor

2x(x-2)=0

So x=0 and 2

3 0

3 years ago

Read 2 more answers

A health study tracked a group of person for five years. At the beginning of the study, 20% were classified as heavy smokers, 30

Aleks04 [339]

Answer: 0.421

Step-by-step explanation:

Heavy smoker = 20%

Light smoker = 30%

Non smokers = 50%

We can assume that the probability that a non-smoker is going to die in the next 5 years be y.

Since light smokers were twice as likely as nonsmokers to die during the five-year study, the probability will be:

= 2 × y = 2y

Probability for the Heavy smokers will be:= 2 × 2y = 4y

The expected number of people that will die for each in the next 5 years will be:

Non smoker:

= 50% × y

= 0.5 × y

= 0.5y

Light smoker:

= 30% × 2y

= 0.3 × 2y.

= 0.6y

Heavy smoker:

= 20% × 4y.

= 0.2 × 4y

= 0.8y

Total = 0.5y + 0.6y + 0.8y = 1.9y

The probability that the participant was a heavy smoker will be:

= 0.8y/1.9y

= 0.421

3 0

3 years ago

Directions: Find the value of x and each arc measure.<br>I need answers to both. 7 & 8

asambeis [7]

Answer:12(x-360)=120

Step-by-step explanation:

7 0

4 years ago