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irina [24]
3 years ago
11

5.2412 2x+3y=-5 5x-y=-12

Mathematics
1 answer:
cupoosta [38]3 years ago
4 0

Answer: 5.2412 = 5.2412 = 2x + 3y = −5 = 2x + 3y = -5 = 5x − y= -12

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PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwi
il63 [147K]
To solve our questions, we are going to use the kinematic equation for distance: d=vt
where
d is distance 
v is speed  
t is time 

1. Let v_{w} be the speed of the wind, t_{w} be time of the westward trip, and t_{e} the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so d=2400. We also know that the speed of the plane is 450 mi/hr, so v=450. Now we can use our equation the relate the unknown quantities with the quantities that we know:

<span>Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
</span>d=vt
2400=(450-v_{w})t_{w}

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
d=vt
2400=(450+v_{w})t_{e}

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:450-v_w Time:t_w
Going eastward -Distance: 2400 Rate:450+v_w Time:t_e

2. Notice that we already have to equations:
Going westward: 2400=(450-v_{w})t_{w} equation(1)
Going eastward: 2400=(450+v_{w})t_{e} equation (2)

Let t_{t} be the time of the round trip. We know from our problem that the round trip takes 11 hours, so t_{t}=11, but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so t_{t}=t_w+t_e. Using this equation we can express t_w in terms of t_e:
t_{t}=t_w+t_e
11=t_w+t_e equation
t_w=11-t_e equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns: 
2400=(450-v_{w})t_{w}
2400=(450-v_{w})(11-t_e) 

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

3. Lets solve our system of equations to find the speed of the wind: 
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

Step 1. Solve for t_{e} in equation (2)
2400=(450+v_{w})t_{e}
t_{e}= \frac{2400}{450+v_{w}} equation (3)

Step 2. Replace equation (3) in equation (1) and solve for v_w:
2400=(450-v_{w})(11-t_e)
2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} )
2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}}
2400(450+v_{w})=1147500+2400v_w-11(v_w)^2
1080000+2400v_w=1147500+2400v_w-11(v_w)^2
(11v_w)^2-67500=0
11(v_w)^2=67500
(v_w)^2= \frac{67500}{11}
v_w= \sqrt{\frac{67500}{11}}
v_w=78

We can conclude that the speed of the wind is 78 mi/hr.
6 0
3 years ago
Find the distance between the two points (-7, 5) (-7, -4)
Sveta_85 [38]

Answer:

Step-by-step explanation:

d^2=(x_2-x_1)^2+(y_2-y_1)^2\\ \\ d^2=(-7+7)^2+(5+4)^2\\ \\ d^2=81\\ \\ d=9

5 0
2 years ago
How could you rewrite (-3 + 5) + 8 + (-1)
vagabundo [1.1K]

(-3 + 5) + 8 + (-1)=

2 + 8 - 1 =

= 9

7 0
2 years ago
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
insens350 [35]

(2y² + 7y + 11) - (8y² - 5y + 7) you can distribute the negative sign to the second expression and then combine the like terms

new expression: (2y² + 7y + 11) (-8y² + 5y - 7)

2y² and -8y² equals -6y²

7y and 5y equals 12y

11 and -7 equals 4

The answer is -6y² + 12y + 4

5 0
3 years ago
A random sample of 49 statistics examinations was taken. the average score, in the sample, was 84 with a variance of 12.25. the
tester [92]

Since in this case we are only using the variance of the sample and not the variance of the real population, therefore we use the t statistic. The formula for the confidence interval is:

<span>CI = X ± t * s / sqrt(n)                      ---> 1</span>

Where,

X = the sample mean = 84

t = the t score which is obtained in the standard distribution tables at 95% confidence level

s = sample variance = 12.25

n = number of samples = 49

From the table at 95% confidence interval and degrees of freedom of 48 (DOF = n -1), the value of t is around:

t = 1.68

 

Therefore substituting the given values to equation 1:

CI = 84 ± 1.68 * 12.25 / sqrt(49)

CI = 84 ± 2.94

CI = 81.06, 86.94

 

<span>Therefore at 95% confidence level, the scores is from 81 to 87.</span>

6 0
3 years ago
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