Answer: U = 600 m/s
Step-by-step explanation:
Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.
After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.
From the first statement
Speed = distance/ time
Distance = speed × time
1500 = Ut
Make t the subject of the formula
t = 1500/U ..... (1)
From the second statement
Distance = speed × time
1500 = (U + 100) × ( t - 0.5 )
Open the bracket
1500 = Ut - 0.5U + 100t - 50
Collect the like terms
1550 = Ut - 0.5U + 100t .... (2)
Substitutes equation 1 into 2
1550 = 1500U/U - 0.5U + 100(1500/U)
1550 = 1500 - 0.5U + 150000/U
1550 - 1500 = (150000 - 0.5U^2)/U
Cross multiply
50U = 150000 - 0.5U^2
0.5U^2 + 50U - 150000 = 0
Divide all by 0.5
U^2 + 100U - 300000 = 0
Using completing the square method
U^2 + 100U = 300000
U^2 + 100U + 50^2 = 300000 + 50^2
(U + 50)^2 = 302500
U + 50 = sqrt(302500)
U + 50 = +/-(550)
U = 50 + 550 or 50 - 550
U = 600 or - 500
Since U is of the same direction, it is
positive. Therefore, the previous speed of the aeroplane is 600 m/s
Answer:
500km/hr
Step-by-step explanation:
The formula for Speed (km/hr) = Distance / Time
Where S = Speed
D = Distance
T = Time
S = D/T
From the question, the aeroplane covered a distance of 1500 km
S = 1500/ T
ST = 1500
Time taken( T ) = 1500/S ......... Equation 1
We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time
This is expressed mathematically as:
The new speed =S + 100km/hr
The new Time taken = 1500/ S - 1/2....... Equation 2
Also since Time = Distance / Speed
The new Time taken also = 1500/ S + 100 ......... Equation 3
Step 1
We would simplify Equation 2:
Time = 1500/S - 1/2
Find the Lowest common multiple = 2
Time = (2 × 1500 - S )/ 2S
Time = 3000 - S / 2S ......... Equation 4
Step 2
Equate Equation 4 and 3 together since they are both equal to time taken
1500/ S + 100 = 3000 - S / 2S
We cross multiply
2S × 1500 = (S + 100) ( 3000 - S)
3000S = 3000S - S² + 300000 - 100S
3000S - 3000S + S² - 300000 + 100S = 0
S² + 100S - 300000 = 0
Step 3
We solve for S = Speed by using factorisation method.
S² + 100x - 300000 = 0
S² - 500S + 600S - 300000 = 0
(S² - 500S) + (600S - 300000) = 0
S(S - 500) + 600(S - 500) = 0
(S - 500) (S + 600) = 0
S - 500 = 0, S = 500
S + 600 = 0 , S = -600
Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr
If -3/x = x/-27 , What is the positive value of x
Answer:
-3=x^2/-27
x^2=(-3)(-27)
x=9 or x=-9
Step-by-step explanation:
can sumone help with this pls
Answer:
D
Step-by-step explanation:
The range means the possible values of the y coordinate which is y ≥ 1 in this function
Determine the number of solutions for the quadratic function f(x) = -x^2 + 3x - 9.
Answer:
0
Step-by-step explanation:
Rewrite the equation as x^2-3x+9=0
find the determinant.
D = b^2-4ac = (-3)^2-4*1*9 <0
no solution
Question 14 (1 point)
John is collecting vintage baseball cards and has about 25 he got from his dad. He is collecting
about 2 cards per month. Write a function, C(x), that represents how many cards John has
after x months.
N
Answer:
C(x) = 25 + 2x
Step-by-step explanation:
He already has 25 cards.
He is collecting 2 cards per month. In x months, he will have collected:
2 * x = 2x cards
That means that the number of cards he will have after x months will be the sum of the cards he already has and the cards he collects per month:
C(x) = 25 + 2x
Associative
Property
Answer:
Below
Step-by-step explanation:
The associative property states that you can add or multiply numbers in any group.
Ex:
x + y + z = x + y + z
(x + y) + z = x + (y + z)
x * y * z = x * y * z
(x * z) * y = (x * y) * z
Addition: According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped or arranged. Here's an example of how the sum does NOT change irrespective of how the addends are grouped.
Multiplication: According to the associative property of multiplication, the product of three or more numbers remains the same regardless of how the numbers are grouped. Here's an example of how the product does not change irrespective of how the factors are grouped.
Division and Subtraction = NO ASSOCIATIVE PROPERTY
can 2x + 3y be simplified?
Answer:
no
Step-by-step explanation:
PLZ PLZ PLZ HELP HELP HELPPP 14 Find the area of the semicircle. Either enter an exact answer in terms of π πpi or use 3.14 3.143, point, 14 for π πpi and enter your answer as a decimal.
Answer:
The area of semi-circle is 2π units²
Step-by-step explanation:
13. What is the circumference of a circle with a diameter of 6 cm. Leave your answer in terms of tt.
O 6 cm
O 247 cm
O 12 cm
O 9 cm
Answer:
C = 6pi cm
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 6pi cm
Please I need help with this I’m stuck I need to get it right
Answer:
b
Step-by-step explanation:
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!
Answer:
see below
Step-by-step explanation:
(x + 1.5)² - 2.25 - 28 = 0
(x + 1.5)² - 30.25 = 0
(x + 1.5)² = 30.25
What is the best approximate of the square root of 50
Answer:7
Step-by-step explanation:
7^2 = 49 (or square root of 49 is 7)
8^2 = 64 (or square root of 64 is 8)
please help me on this!
Answer:
The rocket reached its maximum height at 1.25 seconds.
Step-by-step explanation:
What is the slope of the line represented by the points in the table? x y –2 –0.35 –1 –0.3 0 –0.25 1 –0.2 2 –0.15 Negative 0.05 Negative .005 0.005 0.05
Answer:
its a
Step-by-step explanation:
the slope goes from point a to , in this case is subtracting -.05
Answer:
its A - 0.05
Step-by-step explanation:
edge 2020!
Rate and give me a thanks if you want me to answer more of your guys questions.
Please solve 1/3 ÷ 2/3
Answer:
1/2
Step-by-step explanation:
[tex]\dfrac{1}{3}\div \dfrac{2}{3}=\\\\\dfrac{1}{3}\times\dfrac{3}{2}=\\\\ \dfrac{3}{6}=\\\\\dfrac{1}{2}[/tex]
Hope this helps!
Use the quadratic formula to solve the equation. 9x2−7x+1=0 Enter your answers, in simplified radical form. x = x =
Answer:
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
Step-by-step explanation:
I'm not too good with the quadratic formula so I'm going to complete the square.
First divide everything by 9 and move the 1 to the other side.
[tex]x^2-\frac{7}{9}=-\frac{1}{9}[/tex]
Then take half of [tex]\frac{7}{9}[/tex] and square it and add it to both sides.
[tex]x^2-\frac{7}{9} +\frac{49}{324}=\frac{13}{324}[/tex]
Now you can factor it.
[tex](x-\frac{7}{18})^2=\frac{13}{324}[/tex]
Square root:
[tex]x-\frac{7}{18}=\frac{\sqrt{13} }{18}[/tex]
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
How to factor 3x^2-10x-8?
[tex]answer \\(x - 4)(3x + 2) \\ solution \\ {3x}^{2} - 10x - 8 \\ = {3x}^{2} - (12 - 2)x - 8 \\ = {3x}^{2} - 12x + 2x - 8 \\ = 3x(x - 4) + 2(x - 4) \\ = (x - 4)(3x + 2) \\ hope \: it \: helps[/tex]
Answer:
Step-by-step explanation:
Describe the solution of g(x) shown in the graph. parabola opening down passing through 0 comma 2, negative 1.5 comma 4.25, and negative 3.5 comma 0 All real solutions All negative solutions All whole number solutions All solutions that lie on g(x)
Answer:
(A)All real solutions
Step-by-step explanation:
Given the function g(x) shown on the graph
One of the points of the parabola is (-3.5, 0).
The point x=-3.5 is one of the solution of the parabola since it intersects the x-axis at that point.
The other point of intersection is on the positive side between 0 and 1.
Therefore, g(x) has two solutions: One negative real number and one positive real number.
Therefore, g(x) has all real solutions.
The correct option is A.
Answer:
All solutions that lie on g(x)
Step-by-step explanation:
I took the test and that's the correct answer...
a builder has to fix 3 Walls that have fallen down.He needs 2kg of cement for each wall.How much will he need altogether in kilograms
Answer: 6 kilograms
Step-by-step explanation:
3 walls * 2 kilograms each = 6 kilograms in total
why is 8.8 a rational number
Answer:
See below
Step-by-step explanation:
8 is classified as a rational number because it can be made into a fraction. 8.8 = 8 8/10 = 88/10
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 3) ← 2 points on the line
m = [tex]\frac{3-2}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]
r(s+t)=u
options:
t=u−s/r
t=u/r−s
t=u/r+s
t=ru−s
Answer:
t = u/r -s
Step-by-step explanation:
r(s+t)=u
Divide each side by r
r/r(s+t)=u/r
s+t = u/r
Subtract s from each side
s+t-s = u/r -s
t = u/r -s
Someone please help me :( I’m struggling
Answer:
ax - by = k
Step-by-step explanation:
A literal equation is an equation made up of variables representing numbers that can be changed
ax - by = k is a literal equation because there are no numbers
Letters stand for each item
Nishchal was listening to a song. Shown above are the views of his player showing 'Time elapsed' and 'Time remaining' for the song in minutes and seconds. What is the total duration of the song?
Answer: T = time remaining + time elapsed.
Step-by-step explanation:
Time elapsed means the time that he has been listening to the song (the minutes passed since he hits the play button)
Time remaining is the time left to finish the song.
Then the total duration of the song will be:
T = time remaining + time elapsed.
"Time Elapsed" simply refers to the time which has been spent listening to the music track. The "time remaining" on the other hand is the time left on for the song to come to an end. Song duration is the addition of both.
How to calculate the total duration of the songPlease note that the information from the question required to give a well-rounded answer is incomplete. Hence the general answer.
To calculate the time duration of the song (which is the total length of the song in terms of time) the Time Elapsed must be added to the Time Remaining.
That is:
Total Duration = Time Elapsed + Time Remaining.
See the link below for more about Song Duration:
https://brainly.com/question/14701526
If /61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang
answer in simplest radical form.
A. 5
B. 6
C. 2V15
D. 6V10
Answer:
A. 5
Step-by-step explanation:
The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.
From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:
(√61)² = (x)² + (x + 1)²
x² + x² + 2x + 1 = 61
2x² + 2x + 1 - 61 = 0
2x² + 2x -60 = 0
Dividing through by 2 gives:
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x-5)(x+6) = 0
x-5 = 0 or x+6 = 0
x = 5 or x = -6
Since the length of a side cannot be negative, x = 5 units
Answer:
The correct answer is A.
Step-by-step explanation:
X=5
Paul needs to find 310% of 72%. which expression should he use?
Answer:
2.232, or 223.2%
Step-by-step explanation:
(3.1)(0.72)
Answer:
B
Step-by-step explanation:
i took the test and got it right
Draw a diagram for (x+2)(x+4)
Answer:
Download this mm file
Find an equation for the line that passes through the points (2, 3) and (-6,5).
Please I need help
Answer:
work is shown and pictured
write 10 examples of cyllnder in your daiy life
Step-by-step explanation:
milk container
a room spray
coke can
Answer:
Pipes
Cold drink cans
Water tanks
Battery
Gas cylinder
Candle
Test tube
Beaker
Fire extinguisher
Need help , can’t find this one
The expression sin^-1(4/5) has and infinite number of values. True or false?
It is indeed false.
[tex]\sin^{-1}x[/tex] is a function that takes values of [tex]x[/tex] between -1 and 1, and takes on values between -π/2 and π/2. Most importantly, it's a function that takes *one* value in its domain and assigns it to exactly *one* value in its range. Hence [tex]\sin^{-1}x[/tex] is one-to-one.
It's true that [tex]\sin x=\frac45[/tex] has infinitely many solutions, but [tex]\sin x[/tex] itself is not one-to-one.
Answer:
False
Step-by-step explanation:
