We want to find the average speed of the plane in still air, we will get that the average speed of the plane in still air is 355.3 km/hr
So we know that the total trip is 9900km, so from Texas to Frankfurt the distance is half of that:
9900km/2 = 4950km
Now, The speed of the plane in still air is x km/hr
The speed of the air is 50 km/hr, and it flows from Frankfurt to Texas.
So in the first part of the trip, the wind blows in opposite direction to the motion of the plane, thus the speed of the plane will be:
(x - 50) km/hr
While in the return trip the wind blows in favor of the plane, in this case, the speed is:
(x + 50)km/hr
Then if the first part of the trip lasts for T hours (the second for T - 4 hours) we can write the system of equations:
(x - 50)*T = 4950
(x + 50)*(T - 4) = 4950
Where I removed the units so it is easier to read.
If we isolate T in the first equation we get:
T = 4950/(x - 50)
Now we can replace this in the other equation to get:
(x + 50)*(4950/(x - 50) - 4) = 4950
If we multiply both sides by (x - 50) we get:
(x + 50)*4950 - 4*(x + 50)*(x - 50) = 4950*(x - 50)
Now we can solve this for x:
(x + 50)*4950 - 4*(x^2 - 2500) - 4950*(x - 50) = 0
100*4950 - 4*(x^2 - 2500) = 0
495000 - 4*x^2 + 10000 = 0
505000 = 4*x^2
√(505000/4) = x = 355.3
The average speed of the plane in still air is 355.3 km/hr
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13476446
A2 + B2
Best answer gets a brainliest and thank and 5 star
Answer:
a+b)(a-b)
(Step-by-step explanation:
The area of a square pond is 1000m2.A path of uniform width is surrounded outside the pond and its area is 369m2.find the outer length of the path
Answer:
631 m²
Step-by-step explanation:
Outer length of park = Total area - Area of pond
Outer length of park = 1000 - 369
Outer length of park = 631 m²
Answer:
Hope it will help you a lot.
A car is traveling at 20 miles per hour during rush hour. How far does the car travel in 1 minute and 45 seconds?
Answer: 7/12 miles
Step-by-step explanation:
20mph = 20/60 miles per minute = 1/3 miles per minute
1 min 45s = 1 min + 3/4 min = 7/4 min
1/3 x 7/4 = 7/12 miles
The distance travelled by car with the given speed and time is 7/12 miles.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a car is traveling at 20 miles per hour during rush hour.
Time =1 minute and 45 seconds
= [tex]1\frac{45}{60}=1\frac{3}{4}[/tex]
= 7/4 minutes
Now, 20 miles per minute
= 20/60 miles per minute = 1/3 miles per minute
We know that, Distance =Speed×Time
= 1/3 ×7/4
= 7/12 miles
Therefore, distance travelled by car is 7/12 miles.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ2
A tree of unknown height casts a shadow that is 18 feet long. If a person that is 5 ft 7 in casts a shadow that is 4 ft long, then how tall is the tree in feet?
Round your answer to the nearest integer. Do not include feet in your answer.
Answer:
25.
Step-by-step explanation:
5 ft 7 in = 5.583 ft.
We have 2 similar triangles here.
If h is the height of the tree, then:
h / 5.583 = 18/4
h = 18*5.583/4
h = 25.12 ft
The height of the tree is approximately 25.12 feet.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The ratio of the shadow lengths is equal to the ratio of the object heights.
In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:
H/h = 18/4
We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.
Substituting this value into the equation above and solving for H, we get:
H = (18/4) x 5.58 feet
= 25.12 feet
Therefore, the tree is around 25.12 feet tall.
Learn more about the Ratio here:
brainly.com/question/1504221
#SPJ2
Given f(x)=9-2x, find f(10).
A.-11
B.11
C.29
D.-29
Answer:
the answer is A
Step-by-step explanation:
9-2(10) 9-20
The given function is a linear function that decreases as the value of the
input x increases.
The value of f(10), given f(x) = 9 - 2·x is option A. -11Reasons:
The given function is f(x) = 9 - 2·x
The output of the function is the value of f(x) for a given input x of the function.
The input value, x is substituted into the function to obtain the output value, f(x).
Given that the input, x = 10
We have;
f(10) = 9 - 2×10 = -11
Therefore, the correct option for f(10) is A. -11
Learn more about functions here:
https://brainly.com/question/10781304
Convert 62% into a fraction
Answer:
62% = 31 / 50
Step-by-step explanation:
62/100
if you need to simplify then it would be 31/50
An elevator company claims "for every 15 inches of cable, we can hold up to 32 pounds". Each elevator comes with a standard length of 18 inches for their cable. If an elevator has a
weight limit of 800 lbs, how many additional inches of cable were used?
375 inches of cable were used for an elevator with weight limit of 800 lbs
Let y represent the weight in pounds and x represent the inches of cable.
Since y and x are proportional:
y = kx,
k is the constant of proportionality.
15 inches of cable, we can hold up to 32 pounds. Hence:
32 = 15k
k = 2.13 pounds per inch
y = 2.13x
For a weight of 800 lbs, y= 800:
800 = 2.13x
x = 375 inches
375 inches of cable were used for an elevator with weight limit of 800 lbs
Find out more on equation at: https://brainly.com/question/2972832
What is the measure of angle DCE? Use numbers only.
Answer:
156 degrees
Step-by-step explanation
First we need to figure out what X is. To do that we set up the equation 7x+3=8x because vertical angles are congruent. After solving that we get x=3. We plug 3 back into each equation and we get that angle ACE equals 24. Since angle ACE and angle DCE are supplementary we know that they will equal 180 so we subtract 24 from 180 and get 156 as the final answer.
Hope this helps!
What positive acute angle is
Зл/4
related to?
Answer:
[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]
[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]
[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]
[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]
2...
25. Which is a solution of the inequality y
(3,-5)
(2,-1)
(4,1)
(6,-4)
Step-by-step explanation:
B
D
A
с
2
2-1
1
2
3 4 5
2 1
2
2 4 5
A
B
2-1
1
2
B
5 4 3 2 1
1
2 3 4 5
Find the value for x.
Answer:
4x + 22
Step-by-step explanation:
Need help. I don't understand this question.
Answer:
The first is 1 and the second is 28 i believe
Step-by-step explanation:
Hope this helps:)
Elsa is selling bracelets at craft shows to raise money for an animal shelter.
She is also accepting additional cash donations. She plans to give 75% of the
money from all bracelet sales and donations to the shelter. She will use the
remaining money to buy more supplies. Bracelet sales and donations from
the first craft show are represented by the expression 24n + 32, where n
represents the amount Elsa charges for each bracelet. The second craft
show sales and donations is represented by the expression 40n + 56. If Elsa
charges $4 for each bracelet, how much money will she donate to the
Answer:
$258
Step-by-step explanation:
75% = 0.75 when we divide by 100 to convert a percentage to a decimal
75% of total sales = money donated
Total sales = sales from first show + sales from second show
= 24n+32 + (40n+56)
= 64n + 88
0.75 of (64n+88) = money donated
= 0.75 * (64n+88)
= 48n + 66
substitute 4 for n, as she charges $4 for each bracelet
money donated = 48*4 + 66 = 258
It is for my final, please help!
Answer:
The answer will be the third one.
Step-by-step explanation:
Hope it helps
which among the following
We have:
[tex]1-\frac{1}{3} >0[/tex] ; [tex]1- \frac{11}{17}>0[/tex] ; [tex]1-\frac{132}{157}>0[/tex] ⇒ right
[tex]\frac{-1}{7}, \frac{-51}{107},\frac{-347}{949} <0[/tex] ⇒ wrong
[tex]\frac{7}{5}, \frac{131}{47} ,\frac{945}{711} >1[/tex] ⇒ wrong
ANSWER: [tex]\frac{1}{3} ,\frac{11}{17} ,\frac{132}{157}[/tex]
ok done. Thank to me :>
The kinetic energy, k, the amount of energy that a moving object has, can be found for a particular roller coaster by the radical function v equals the square root of the quantity 2 times k over the 1,000 period If the velocity, v, of the roller coaster is 10 meters per second, what is the kinetic energy?
200,000 Joules
10,000 Joules
50,000 Joules
5,000 Joules
The kinetic energy of the roller coaster is 2000Joules
Given the formula for expressing the velocity of the roller coaster is given as:
[tex]v = \sqrt{\frac{2k}{1000} }[/tex]
Given the following parameter:
v = 10m/s
Substitute the given parameter into the formula to have:
[tex]10 = \sqrt{\frac{2k}{1000} }[/tex]
Square both sides of the equation:
[tex](10)^2=(\frac{2k}{1000} )^2\\100=\frac{4k^2}{1,000,000} \\4k^2=100,000.000\\k^2=\frac{100,000,000}{4} \\k^2=4,000,000\\k=2000Joules[/tex]
Hence the kinetic energy of the roller coaster is 2000Joules
Learn more on subject of formula here: https://brainly.com/question/657646
Answer:
You need to use √2k/1000 formula.
2000 joule is the correct answer.
Learning Task 2 B. Perform the indicated operations. Write your solution in the box below. Add Subtract: 1. (5x4 - 3x2 + 4) + (6x3 - 4x2 - 7) 6. (5x3 - 7x2 + 3x - 4) -(873 + 2x2 32-7) 2.-7x3y + 4x2y2 - 2 and 4x3y + 1 - 8x2y2 7. (2x2y - 5xy + 3y2 -- (7xy -- 672 - 5729) 3. (5 + 24y3 - 7y2) + (-6y3 + 7y2 + 5) 8. (9x5 - 623 + 712) - (773 4. (2xs - 6x3 - 12x2 - 4) + (-11x + 8x + 2x2 + 6) 9. Subtract 4x3.5x - 8 from 672 - 3x + 8 5. (3y5 - 2y + y* + 2y3 + 5) and (238 + 3y8 + 2+ 7) 10. (1.599 + 4.8y2 + 12) - (ya - 1.742 + 2y) Solution and Answer 67 + 2x2) -
- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p.
Step-by-step explanation:
For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:
5(3) - 2y = 7
15 - 2y = 7
2y = 8
y = 4 => k =4
2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:
-2y = -5x + 7
y = (5/2)x + 7/2 => the gradient is 5/2
3) the condition of perpendicularity is expressed by the following relation:
a * a' = -1
Where a is the slope of the first line and a' of the second line. We need to find a' that will be:
-1/a = -1/(5/2) = -2/5
The perpendicular line will be:
y = (-2/5)x + b
We need to find b, and we know that this line passes through A (1,-1):
-1 = (-2/5)*1 + b
b = -1+(2/5) = -3/5
The equation will be:
y = (-2/5)x - 3/5.
4) I don't know what that symbol means (pV2).
-PLEASE HURRY
8. Given: x2 – 2x + 5, find :
1.f(2)
2.f(-3)
3.f(0)
4.f(5) - f(-2)
5.f(1) + f(6)
-
Answer:
Step-by-step explanation:
f(x) = x² - 2x + 5
1) f(2) = (2)² - 2(2) + 5 = 5
2) f(-3) = (-3)² - 2(-3) + 5 = 20
3) f(0) = (0)² - 2(0) + 5 = 5
4) f(5) - f(-2) = (5)² - 2(5) + 5 - [(-2)² - 2(-2) + 5 = 20 - 13 = 7
5) f(1) + f(6) = (1)² - 2(1) + 5 + [(6)² - 2(6) + 5 = 4 + 29 = 33
A complex shape with measurements 6 inches, 5 inches, 4 inches, 3 inches, 4 inches, 2 inches, 6 inches, 10 inches. What is the perimeter of the shape?
Answer: 40
Step-by-step explanation: do 6 add 5 add 4 add 3 add 4 add 2 add 6 add 10
Solve the equations below exactly. Give your answers in radians, and find all
possible values for t in the interval 0 (less than or equal to ) t (less than or equal to) 2 pi
If there is more than one
answer, enter your solutions in a comma separated list.
(a) sin (t) = - square root of 3 divide by 2
when t=
(b) cos (t) = 1/2
when t=
Answer:
See below (along with unit circle attached)
Step-by-step explanation:
[tex]sin(t)=-\frac{\sqrt{3}}{2}[/tex]
[tex]t=\frac{4\pi}{3},\frac{5\pi}{3}[/tex]
[tex]cos(t)=\frac{1}{2}[/tex]
[tex]t=\frac{\pi}{3},\frac{5\pi}{3}[/tex]
It really helps to use the unit circle! I've attached it below for your convenience. Keep in mind that a point on the unit circle is defined by [tex](cos(\theta),sin(\theta))[/tex] where [tex]\theta[/tex] is measured in radians.
Marsha is driving 630 total miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?
Answer:
Marsha has driven 252 miles
Step-by-step explanation:
In order to figure out the problem, you take the total distance and multiply it by the fraction she has gone. This would be 630*(2/5) which would equal 252. Thus, Masha has driven 252 total miles.
Hope this helps!
Answer: 252 miles
Step-by-step explanation:
12. TEKS 21
A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were
black-and-white coples, and the rest were color copies.
.
Each black-and-white copy cost $0.08.
Each color copy cost $0.15.
.
Which system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop?
The system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop is
b + c = 68
b + c = 680.08b + 0.15c = 6
Given:
Total amount paid = $6.00
Total copies = 68
cost of black-and-white copy = $0.08
cost of color copy = $0.15
let
number of black-and-white copies = b
number of color copies = c
The equation:
b + c = 68
b + c = 680.08b + 0.15c = 6
Therefore, the system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop is
b + c = 68
b + c = 680.08b + 0.15c = 6
Learn more about equation:
https://brainly.com/question/4916384
It cost Faith $9.10 to send 91 text messages. How many text messages did she send if she spent $17.60?
Answer:
176
Step-by-step explanation:
9.10 / 91 = 1/10
17.60 x 1/10 = 176
Th stalest tree in the world is a red wood in red wood national and state parks .it is 379feet tall .how many yards is this
Answer:
126 1/3 yards
Step-by-step explanation:
1 foot = 1/3 yard
379 feet = 379/3 yard= 126 1/3 yards
G(x)=4.8x -5
I needed help finding the slope
Answer:
Slope is 4.8
Step-by-step explanation:
[tex]{ \tt{G(x) = 4.8x - 5}} \\ [/tex]
Answer: The Answer is 4.8
A square is a quadrilateral with four equal sides and four 90 degree angles. Is quadrilateral ABCD a square?
Answer: yes
Step-by-step explanation:
I NEED HELP FOR MY FINALS PLS N TY!!!
1. Compute the length of a rectangle with a perimeter 40.2 in and width of 6.7 in.
Answer:
13.4
Step-by-step explanation:
You would take the width x 2 which is 13.4. Now you subtract the combined width from 40.2. From here you are left with 26.8. Since this is a rectangle the length would be the same on both sides. You divide 26.8 by 2 and you get 13.4.
21
4x + 5
E
חו
What is the value of x?
Answer:
don't know
Step-by-step explanation:
Find the equation that represents the proportional relationship in this graph, for y in terms of x.
Answer:
y = 0.4 x
Step-by-step explanation: