Answer:
previous speed of the aeroplane is 500 km/hr
Step-by-step explanation:
Given: Distance covered by aeroplane = 1500 km
It covers the same distance in a time which is half an hour less than the previous time if the speed is increased by 100 km/hr
To find: previous speed of the aeroplane
Solution:
Let x denotes the previous speed of the aeroplane.
Time taken by an aeroplane if speed is x km/hr = distance/speed = [tex]\frac{1500}{x}[/tex] hours
If speed is increased by 100 km/hr, new speed = (x + 100) km/hr
Time taken by an aeroplane if speed is (x + 100) km/hr = [tex]\frac{1500}{x+100}[/tex] hours
According to question,
[tex]\frac{1500}{x+100}=\frac{1500}{x}-\frac{1}{2}\\ \frac{1500}{x}-\frac{1500}{x+100}=\frac{1}{2} \\\frac{1}{x}-\frac{1}{x+100}=\frac{1}{3000}\\ \frac{x+100-x}{x(x+100)}=\frac{1}{3000}\\ x^2+100x=300000\\x^2+100x-300000=0\\[/tex]
[tex]x^2+600x-500x-300000=0\\x(x+600)-500(x+600)=0\\(x-500)(x+600)=0\\x=500\,,\,-600[/tex]
As speed can not be negative, [tex]x=-600[/tex] is rejected.
So,
previous speed of the aeroplane is 500 km/hr
WILL MARK BRAINLIEST
The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
I assume you meant h(t) = 160t - 16t^2, as h(t) = 160t - 16t2 has no maximum.
There's two ways of solving this:
(i) By completing the square and finding the maximum turning point.
(ii) By using Calculus methods to find derivative and equating it to 0 in order to find maximum turning point.
(i) h(t) = 160t - 16t^2
h(t) = -16t^2 +160t
h(t) = -16(t^2-10t) (by taking out a common factor of -16)
h(t) = -16[(t-5)^2 - 25] (by completing the square)
h(t) = -16(t-5)^2 + 400 (on multiplying out by -16)
From this we see that the turning point is at (5;400), therefore the maximum height is 400 feet and is reached after 5 seconds.
Or...
(ii) h(t) = 160t - 16t^2
h`(t) = 160 - 32t (where h`(t) = derivative of h(t))
Now to find maximum of h(t), we set h`(t) = 0 and solve for t:
0 = 160 - 32t (on substituting h`(t) = 0)
32t = 160 (on solving for t)
t = 160/32 (on dividing both sides by 5)
t= 5
Now we have found that at 5 seconds, we will reach our maximum height. So to find this maximum height, we'll have to substitute t=5 into h(t) = 160t - 16t^2.
h(5) = 160(5) -16(5)^2
h(5) = 800 - 400
h(5) = 400 feet
So, once again we have shown that maximum height is 400 feet and is reached after 5 seconds.
Jorge solves the equation 4 x minus (x + 2) + 6 = 2 (3 x + 8) using the steps below. Step 1: 4 x minus x + 2 + 6 = 6 x + 16 Step 2: 3 x + 8 = 6 x + 16 Step 3: 8 minus 16 = 6 x minus 3 x Step 4: Negative 8 = 3 x Step 5: Negative StartFraction 8 Over 3 EndFraction = x BRAINLISEST
Answer:
The solution of the given equation is x = -4
Step-by-step explanation:
Explanation:-
Given expression 4 x - (x +2) +6 = 2 (3 x+8)
Step(i):-
4 x - (x +2) +6 = 2 (3 x+8)
4 x - x -2 + 6 = 6 x + 16
step(ii):-
3 x + 4 = 6 x + 16
subtracting '4' on both sides , we get
3 x + 4 - 4 = 6 x + 16 - 4
3 x = 6 x + 12
Step(iii):-
Subtracting '6x' on both sides , we get
3 x - 6 x = 6 x - 6 x + 12
- 3 x = 12
Step(iv):-
Dividing '-3' on both sides , we get
[tex]\frac{-3x}{-3} = \frac{12}{-3}[/tex]
x = - 4
Final answer:-
The solution of the given equation is x = -4
Verification:-
4 x - (x +2) +6 = 2 (3 x+8)
put x = -4
4 ( -4) - ( - 4 +2) +6 = 2 (3(-4)+8)
-16+2+6 = 2 (-12+8)
-8 = -8
Both are equal
Answer:
For everyone on Edge, It's A: He distributed incorrectly.
Step-by-step explanation:
he didn't distribute at all so
im pretty sure.
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
359, 352, 345, ...
Find the 44th term.
Answer:
Submit Answer
attempt out of 2
(DELTAMATH VERSION)
Answer:
[tex]58[/tex]
Step-by-step explanation:
[tex]-7n+366[/tex]
[tex]-7(44)+366[/tex]
[tex]-308+366[/tex]
[tex]=58[/tex]
Probability Race game
Read the whole thing. Question 2 will be posted separately to make the question simple.
Question 1:
Why should you not play this game with Roland? Use probability to prove that
the game is unfair and Roland is likely to win. SHOW ALL YOUR WORK!
Answer:
see below
Step-by-step explanation:
There are 36 possible outcomes when rolling 2 die
P( number) = number of times the sum appears / total outcomes
p(1) =0/36
P(2) = 1/36
p(3) = 2/36
p(4) = 3/36
p(5) = 4/36
p(6) = 5/36
p(7) = 6/36
p(8) = 5/36
p(9) = 4/36
p(10) = 3/36
p(11) = 2/36
p(12) = 1/36
Since he picked first he has the greatest odds so he is most likely to win
A motorcycle has an initial speed of u m/s. It accelerates to a speed of 1.2u in 10 seconds. The motorcycle then travels at a constant speed of 1.2u m/s for 15 seconds. Assuming that the acceleration is constant, express the total distance, D in metres, traveled by the motorcycle.
Answer:
Step-by-step explanation:
A motorcycle has an initial speed of u m/s. It accelerates to a speed of 1.2u in 10 seconds
V = U + at
1.2u = u + a*10
=> a = 0.02u
S= ut + (1/2)at²
Distance in 1st 10 secs
S = u(10) + (1/2)(0.02)(10)²
=> S = 10u + u
=> S = 11u m
Constant speed 1.2u for 15 secs
S = 1.2u * 15
=> S = 18u m
Total Distance Covered d = 11u + 18u = 29u m
7
Eddie had lunch at 10 minutes to 1 in the afternoon.
Fatimah had lunch at 11 45 on the same day.
Who had lunch later? How much later?
Answer: Eddie had lunch later than Fatimah.
Step-by-step explanation: Eddie had lunch at 10 minutes to one, which is 12:50. Fatimah had lunch at 11:45. So if you subtract 11:45 from 12:50, you find that Eddie had lunch 1:05 later than Fatimah.
Answer:
Eddie had lunch later.
He had lunch 1 hour 5 minutes later
Step-by-step explanation:
Eddie had lunch 10 min before 1
which means at 12 50.
Fatimah had lunch at 11 45 . Earlier than Eddie.
Eddie had lunch after her.
and How much later?
11 45 to 12 45 is 1 hour.
12 45 plus 5 minute is 12 50.
so it is 1 hour 5 minute
A hummingbird’s nest is 6 meters high in a tree. A flower is on the ground 14 meters away from the base of the tree. How far will the hummingbird need to fly to get from its nest to the flower if it takes a direct path?
Answer:
15.23 m
Step-by-step explanation:
The problem given describes the shape of a right angled triangle.
From the diagram below:
The height of the tree is the opposite = 6 m
The distance of the flower from the base of the tree = adjacent = 14 m
The distance the bird must fly to get from the nest to the flower = hypotenuse = h
According to Pythagoras rule:
[tex]hyp^2 = opp^2 + adj^2[/tex]
Therefore:
[tex]h^2 = 6^2 + 14^2\\\\h^2 = 36 + 196\\\\h^2 = 232\\\\h = \sqrt{232} \\\\h = 15.23 m[/tex]
The bird will have to fly 15.23 m to get from its nest to the flower in a direct path.
Multiply. (3x - 2)(x + 5) A: 3x² + 17x - 7 B: 3x² + 17x - 10 C: 3x² + 13x - 10 D: 3x² + 6x - 7
Answer:
The answer is C.
Step-by-step explanation:
You have to use Ditributive Law,
[tex]a(m + n) = am + an[/tex]
So for this question :
[tex](3x - 2)(x + 5)[/tex]
[tex] = 3x(x) + 3x(5) - 2(x) - 2(5)[/tex]
[tex] = 3 {x}^{2} + 15x - 2x - 10[/tex]
[tex] = 3 {x}^{2} + 13x - 10[/tex]
Answer:
C. 3x^2+13x-10
Step-by-step explanation:
Just did this on A-pex
Good job CHERLYN
Which linear inequality is represented by the graph
I need help pleasee please
Answer:
We just have to do 15 ÷ 15/4 = 15 * 4/15 = 4.
If f(x) = 5x + 40, what is f(x) when x = –5? pls help a. -9 b. -8 c. 7 d, 15
Answer:
D.
Step-by-step explanation:
f(5) = -25 + 40
f(5) = 15
Answer:
The answer is D) 15
Step-by-step explanation:
F(x)= 5x + 40 (substitute -5 for x)
= F(x)= 5(-5)+ 40
= F(x)= -25+40
F(x)= 15
What is the value of x?
57+3x+6=90degree
60+3x=90
3x=90-60
3x=30
x=30/3
x=10
Answer:
[tex] \boxed{x \degree = 9 \degree} [/tex]
Step-by-step explanation:
[tex] = > 90\degree + 57\degree + (3x + 6)\degree = 180\degree \\ \\ = > 57\degree + (3x + 6)\degree = 180\degree - 90\degree \\ \\ = > 57\degree + (3x + 6)\degree = 90\degree [/tex]
Two Angles are Complementary when they add up to 90° (a Right Angle).
[tex] = > 57 \degree + (3x + 6) \degree = 90 \degree \\ \\ = > 57 \degree + 3x \degree + 6 \degree = 90 \degree \\ \\ = > 63 \degree + 3x \degree = 90 \degree \\ \\ = > 3x \degree = 90 \degree - 63 \degree \\ \\ = > 3x \degree = 27 \degree \\ \\ = > x\degree = \frac{27}{3}\degree \\ \\ = > x\degree = 9\degree[/tex]
Juan recorded the number of pages each student read this week. His data are shown: 73, 79, 81, 50, 72, 112, 83, 76, 75, 80, 81 How many outliers do Juan’s data have?
a.0
b.1
c.2
d.3
Answer:
2
Step-by-step explanation:
50 and 112 are significantly different from the other data
An employee at a homemade wooden toy store earned $860 over the past week. The employee needs to pay 14% for Federal Income Tax and 3% for State Income Tax, both on the initial amount he earned. How much will the employee earn after paying both taxes?
Answer:
$713.8
Step-by-step explanation:
14%of 860 = 120.4
3% of 860 = 25.8
so, subtract the sum of the above 2 values from 860.
860 - (120.4+25.8) = 860-146.2 = 713.8
Hope this helps
Answer:
$713.008
Step-by-step explanation:
£2200 is deposited in a bank paying 0.5% simple interest per annum. How much interest will have been paid after 18 years?
Answer:
The answer would be £198
principal (p) = 2200
Rate (R) = 0.5%
Time (T) = 18
Interest(I) = ?
Now,
or, Interest. = P×T×R/100
or, Interest = 2200×18×0.5/100
or, Interest = 19800/100
Hence, Interest = 198
Which of the following is a quadratic function?
in photo..
Answer:
[tex]f(x)=-3x^2[/tex]
Step-by-step explanation:
A quadratic function is a function in which its degree (Highest power of the variable) is 2.
[tex]f(x)=-3x^2[/tex] is the function that has a degree of 2.
37 POINTS pls help time limit 13 minute left...
Answer:
first 3
Step-by-step explanation:
Answer:
A B C and D are all true not the last one!
Step-by-step explanation:
n over 24 = 15 over 18?
Answer:
n = 20
Step-by-step explanation:
cross multiply and divide
18n = 360
n = 20
Which expression is shown using the model below?
Answer:
C
Step-by-step explanation:
Hopefully
C
I did it on edge hopefully this helps you and don't think i copied the other person
Please answer I need help no rush.
Answer:
12 divided by -6
Step-by-step explanation:
12÷(-6) (3) + (-2)
PEMDAS
P There are no operations inside the parentheses
E There are no exponents
MD Multiply and divide from left to right
12 divided by -6 is the first from left to right
If x – 9 is a factor of x2 – 5x – 36, what is the other factor? x – 4 x 4 x – 6 x 6
Answer:
(x+4)
Step-by-step explanation:
Solve by factoring. Think about what numbers multiply to be -36 (the last term) BUT also subtract/add up to be -5, which is the middle term. The answer to this is 4 and -9. Therefore, the two factors are (x-9)(x+4)
Answer:
b (x+4)
Step-by-step explanation:
edge
1) Simplify 16x – 7y - 19x - 4y
Answer:
-3x-11y is the answer.
Answer: -3x-11y
Add them in groups
Suppose it costs you $100 to rent a jet ski, plus another $150 per hour
of use. Using the equation C = 150h + 100, where C represents the
total cost for the rental and h represents the number of hours you rent
the jet ski, identify the slope and y-intercept.
A single story house is to be built on a rectangular lot 70 feet wide by 100 feet deep. The shorter side of the lot is along the street. The house must be set back 30 feet from the street. It also must be 20 feet from the back lot line and 10 feet from each side lot line. What is the greatest area that the house can have, in sq feet?
Answer:
250 sq ft
Step-by-step explanation:
Since the shorter side is along the street and the setback is 10ft from each side, the house is 50 ft wide
and 100 -20 -30 = 50 ft long
50 x 50 = 250 sq ft
The greatest area of the given house is 2500 square feet.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
To find the greatest area that the house can have, you need to determine the dimensions of the house.
The width of the house will be the distance between the two side lot lines, which is 70 feet - 10 feet - 10 feet = 50 feet.
The depth of the house will be the distance between the front and back lot lines, which is 100 feet - 30 feet - 20 feet = 50 feet.
The area of the house is :
50 feet x 50 feet = 2500 sq feet.
This is the greatest area that the house can have.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
#SPJ2
Write each as an algebraic expression
Answer:
4^3
11>6
y>2
13-x
Step-by-step explanation:
4 is to the third power
11 is greater than 6 which means u use this sign >
y is greater than 2
13 subtract x
The revenue from selling xshirts is r(x) = 12x.
The cost of buying x shirts is c(x) = 5x + 20
The profit from selling x shirts is p(x) = r(x)-c(x).
What is P(x)?
A. p(x)=7x+20
B. p(x)=17x-20
C. p(x)=17x+20
D. p(x)=7x-20
Answer:
D. [tex]p(x)=7x-20[/tex]
Step-by-step explanation:
[tex]r(x) = 12x\\c(x) = 5x + 20\\p(x) = r(x)-c(x)\\p(x)=12x-(5x+20)\\p(x)=12x-5x-20\\p(x)=7x-20[/tex]
Simply subtract the two functions from each other and simplify to get the result.
Find the size of the final unknown exterior angle in a polygon whose
other exterior angles are:
57° 68° 32°, 59° and 72º.
Answer:
72
Step-by-step explanation:
The sum of exterior angles is 360
360-57-68-32-59-72 =. 72
You have $6 and earn $0.50 for each cup of orange juice you sell. Write an equation in two variables that represent the total amount A (in dollars) you have after selling j cups of orange juice.
A=
Can you help me plz ASAP
Answer:
A = 0.50j + 6.......u r correct
he started with 6....and he is selling each cup (j) for 0.50
so lets say he sold 10 cups...u would sub in 10 for j
A = 0.50(10) + 6
A = 5 + 6
A = 11......and he would have $ 11
HELP ASAP
15 POINTS
If the plane intersects the cylinder vertically along an edge of the cylinder, the cross section is
A. Circle
B. Line
C. Rectangle
D. Oval
Answer:
Option C.
Step-by-step explanation:
Cross section: In three-dimensional space, the non-empty intersection of a solid body and a plane is known as cross section.
A cylinder has two circular plane surface called edges (top and bottom) and curved surface.
If the plane intersects the cylinder vertically along an edge of the cylinder, then the plane is perpendicular to both edges and we get two pairs of opposite sides which are equal.
It means, the cross section of plane and cylinder is a rectangle.
Therefore, the correct option is C.
What is the inverse of the function f(x) =1/4x – 12?
Answer:
f(x) = 4x + 48
Step-by-step explanation:
Replace the positions of x and y and isolate y to find the inverse of a function.
y = 1/4x – 12
x = 1/4y – 12
x + 12 = y/4
4(x + 12) = y
4x + 48 = y
f(x) = 4x + 48
