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
The 3rd and 6th term of a
linear sequence are 16 and
34 respectively. Find the
sum of the first six terms.
Answer:
hope this helps
In one hour, Frank earns the money shown below. How much does he earn in 7 weeks if he works 3 hours each week?
↓↓
$12
↑↑
ITS DUE TODAY HELP PLEASE
Answer:
$252
Step-by-step explanation:
If Frank earns $12 an hour and works 3 hours a week, he makes $36 a week. So for 7 weeks, he earns $252 because $36x7 weeks= $252 in 7 weeks
Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home.
If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
Answer:
4/9
Step-by-step explanation:
The possibilities of transportation: (The first will be for morning, second will be for afternoon)
B, B
B, C
B, T
C, B
C, C
C, T
T, B
T, C
T, T
It is clearly seen that there are 9 transportation options.
(Using cab 1 time we have BC, CB, CT, TC. So four of the transportation methods use cab one time.)
Therefore, the probability that she will use a cab only once is 4/9.
Solve it by factorisation method
Answer:
Hope it helped you.
Step-by-step explanation:
It was hard to type on a keyboard so I did it somewhere else...
Florence Tyler invests $5000 in a 1-year CD that earns interest at an annual rate of 4% compounded monthly. The amount per $1.00 is 1.040742. What is the interest earned?
Answer:
$203.71
Step-by-step explanation:
Given;
Principal = $5,000
The amount per $1.00 is given as 1.040742
The total amount earned is equal to the product of the principal and the amount per dollar.
A = Principal × amount per dollar
Substituting the values;
A = $5000 × 1.040742
A = $5203.71
Interest earned = Total amount earned - principal
Interest earned = $5203.71 - $5000
Interest earned = $203.71
Dawn raises money for her school in a jog-a-thon. She will get three dollars for every lap she completes. If it takes 4 laps to jog 1 mile, and Dawn jogs a total of 12 miles, how much money will Dawn raise for her school?pls help
Answer:
$144
Step-by-step explanation:
[tex]\dfrac{\$3}{\text{lap}} \cdot \dfrac{4\text{ laps}}{\text{mile}}\cdot 12\text{ miles} =[/tex]
[tex]\boxed{\$144}[/tex]
Hope this helps!
Please help meeee !!
Answer:
The answer is B
A line passes through (-1,7) and (2,10) which answer is the equation of the line
Answer: -x + y = 8
Step-by-step explanation:
So first you are going to want to find the slope of the equation. The equation for that it (y2 - y1)/(x2 - x1) = (10 - 7)/(2 - -1) and that equals 1. So your slope will be 1.
Now you have half of your equation complete, currently it looks like, y = x + b. So we have to find the y intercept. You can do that by plugging in a pair of coordinates into the current equation and solve for b.
Lets plug in (2,10)
10 = 2 + b
10 - 2 = b
b = 8
So now you have your equation in slope intercept form, y = x + 8. Just move the x over to the left side and there is your answer.
-x + y = 8
what is the slope-intercept equation for the line below
Answer:
A
Step-by-step explanation:
If I'm completely honest I'm not really sure of this cause I hv another way of doing this...
,
help me please !!!!!!
Answer:
256 ft^250 ft^225 ft^2281 ft^2Step-by-step explanation:
Prism Area
The total surface area of a rectangular prism is given by ...
SA = 2(LW +H(L +W))
For L = 12 ft, W = 5 ft, H = 4 ft, the surface area is ...
SA = 2((12 ft)(5 ft) +(4 ft)(12 ft +5 ft)) = 2(60 ft^2 +(4 ft)(17 ft))
= 2(60 ft^2 +68 ft^2) = 256 ft^2 . . . blank 1
__
Pyramid Lateral Area
The lateral area of the pyramid is 4 times the area of one triangular face:
LA = 4(1/2)bh = 2(5 ft)(5 ft) = 50 ft^2 . . . blank 2
__
Pyramid Base Area
The area of the square base of the pyramid is the square of the length of one edge:
B = (5 ft)^2 = 25 ft^2 . . . blank 3
__
Total Exposed Area
The exposed area of the prism is its area less that of the base of the pyramid. The total exposed area is the sum of prism exposed area and lateral area of the pyramid.
total exposed area = (exposed prism area) + (pyramid lateral area)
= (prism area) - (pyramid base area) + (pyramid lateral area)
= 256 ft^2 - 25 ft^2 + 50 ft^2
total exposed area = 281 ft^2 . . . blank 4
Wayne charges the following for repairing washing machines:£28 call out charge +£16 for each half-hour he spends on the repair what will the total cost be for a repair which takes one and a half hours?
Answer:
The cost for a repair that takes one and a half hour is £52
Step-by-step explanation:
We can create a function that relates the value Wayne charges in function of the time it takes for him to fix the washing machine in hours. Since there's a fixed cost of 28 and another charge that is variable of 16 per half hour, then the function below represents the cost of the repair:
[tex]cost(t) = 28 + 32*t[/tex]
In this case the variable value "16" was multiplied by two, because it's easier when the time is given in hours and every hour contains two half-hours. If the repair took 1.5 h, then:
[tex]cost(1.5) = 28 + 16*1.5\\cost(1.5) = 52\\[/tex]
The cost for a repair that takes one and a half hour is £52
What is the slope of the line that passes through the points (4,7) and (5,3)?
I will be showing you the graphing method.
To find the slope of the line using the graphing method,
we start by plotting our two points.
We will call (4,7) point A and (5,3) point B.
Now daw a line that contains these points.
Now remember that the slope or m is equal to the rise/run.
So to get from point A to point B, we rise -4 units
and run 1 unit so our slope is -4/1 or -4.
Which of the following best describes perpendicular rays?
A. Rays that intersect
B. Rays that are coplanar
C. Rays that intersect at a right angle
D. Rays that never intersect
Answer:
C.
Step-by-step explanation:
Rays that intersect at a right angle (90° angle) are always perpendicular
Find the number missing from the following equivalent fractions: 12/16= 3/?
Answer:
4
Step-by-step explanation:
Whatever you multiply or divide to the numerator, you do to he denominator.
Here, 12 was divided by 4 to obtain 3 in the other fraction. So, the missing number has to be 16 divided by 4, which gives 4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
In this question we are presented with [tex]\frac{12}{16}[/tex] and we want to simplify to have a numerator of 3. When simplifying fractions it's important to do the operation on both the numerator and the denominator so,
[tex]\frac{12}{16}[/tex] → Half the numerator and the denominator → [tex]\frac{6}{8}[/tex] → Half the numerator and the denominator again → [tex]\frac{3}{4}[/tex]
Help idk how to solve this
[tex]answer \\ = 4 \\ solution \\ to \: find \: the \: value \: of \: x \\ in \: an \: equilateral \: triangle \: all \: interior \\ angles \: are \: equal \: and \: measures \: 60 \: \\ degree. \\ 10x + 20 = 60 \\ or \: 10x = 60 - 20 \\ or \: 10x = 40 \\ or \: x = \frac{40}{10} \\ x = 4 \\ hope \: it \: helps[/tex]
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
in a equilateral triangle all the interior angles are equal and measure 60 degrees,
will solve now,
[tex]10x + 20 = 60 \\ 10x = 60 - 20 \\ 10x = 40 \\ \frac{10x}{10} = \frac{40}{10} \\ x = 4[/tex]
hope this helps
Use cross products to identify the equation needed to solve this proportion: 5/x = 2/9
Answer:
x=22.5
Step-by-step explanation:
We are given the proportion:
5/x=2/9
Cross multiply. Multiply the numerator (top number) of the first fraction by the denominator (bottom number) of the second. Then multiply the denominator of the first by the numerator of the second.
5*9=2*x
45=2x
2 and x are being multiplied. The opposite of multiplication is division. Divide both sides by 2. This will cancel out the 2 being multiplied by x, and leave x by itself.
45/2=2x/2
45/2=x
22.5=x
If we substitute 22.5 in for x, the final proportion will be:
5/22.5=2/9
Answer: 22.5 = x
Step-by-step explanation: First, write the problem, 5/x = 2/9. Next, cross multiply. Write the equation, 5 x 9 = 2x. After, write the equation in a multiplying fraction sentence. 45/2 = 2x/2. Lastly, solve for x by dividing 45 by 2. You should end up with a result of 22.5 = x.
pls help me for brainliest answer answer needs to be correct
Answer:
a) 17, 29, 41, 53, 65....
b) 12n + 5
136 degrees is the same as what radians
Answer:
34/45 pi
Step-by-step explanation:
To change from degrees to radians, multiply by pi/180
136 * pi/180
34/45 pi
If PQRS is a rhombus, which statements must be true? Check all that apply.
Answer:
Options (B), (C) and (F) are correct.
Step-by-step explanation:
Properties of a rhombus,
1). All sides of a rhombus are equal in measure.
2). Both the diagonals of a rhombus are the perpendicular.
3). Diagonals bisect the vertex angles.
By these properties of a rhombus,
Option (B): PR is perpendicular to QS.
Option (C): ∠QPR ≅ ∠SPR
Option (F): PQ ≅ QR
Therefore, options (B), (C) and (F) are correct.
Answer:
B, C, F, and E are all correct.
Step-by-step explanation:
5x + 3 = 7x – 1
what is x
Answer:
First lets subtract 3 from both sides. That gives us 5x = 7x-4. Then lets move the -4 to the other side reversing the sign. 5x+4=7x. Now lets subtract 5x from both sides. That will give us 2x = 4. Now all we need to do as a last step is divide by 2. That will give us x = 2. That is how you solve it in a nutshell
brainliest?
I hope you liked my answer!
Which is the equation of the graphed line written in standard form? y = x x – x minus StartFraction one-half EndFraction y equals 0.y = 0 x – y = 0 y = y equals StartFraction one-half EndFraction x.x
Answer:
its is C. X-Y= 0
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
plz let me know if this is incorrect
B oranges cost 60c. How much will 7 oranges cost
Answer: 53 c
Step-by-step explanation:
If 8 oranges cost 60c
7 oranges will cost (7 x 0.60) / 8 = 0.53
What is the value of x? Round to the nearest tenth and show your work
Answer: A. mark as brainliest
Step-by-step explanation: dont need to
what is the c value?
answer in x= form
What two integers multiply to be 20 and add to be 12
Answer:
10 and 2
Step-by-step explanation:
[tex]10*2=20\\\\10+2=12[/tex]
Answer:
10 and 2
Step-by-step explanation:
Use trial and error method Or, I recommend finding the factors of 20.
The first ones that come to mid would be:
10, 2
4,5
20,1
Then we try each of them out, by adding the corresponding factors.
this way, we see that 10 and 2 are the only ones.
Please mark brainiest
What is the product (40 + (-10))((36 + (-9))(32 + (-8))...(-32 + 8)(-36 + 9)(-40 + 10) where the first number in each factor is decreasing by 4 and second number in each factor is increasing by 1?
Answer:
0
Step-by-step explanation:
The first number is 40 and decreases by 4 in each factor, and the second number is -10 and increases by 1 in each factor.
The first number is positive and decreases by 10% its value in each factor, and the second number is negative and increases by 10% its absolute value in each factor. That means we will have a factor where both numbers are 0 (in the 11th value, we will have the first number 40 - 4*10 = 0 and the second number -10 + 1*10 = 0), so the factor will be 0 + 0 = 0, and then whole product will be zero.
The length of a field in yards is a function f( n ) of the the length in n feet. Write a function rule for this situation.
Answer:
[tex]f(n)=\frac{1}{3}n[/tex]
Step-by-step explanation:
To convert from feet to yards, divide by the value 3.
Matías compró un cuarto kilogramo de jamón y lo utilizó para hacer tres tortas así No sobró y a cada torta le puso la misma cantidad de jamón cuánto le tocó a cada torta
Answer:
The amount of ham in each cake = 1/12 kg
Question:
Matías bought a quarter kilogram of ham and used it to make three cakes like that. There was no leftover and he put the same amount of ham in each cake, how much he touched in each cake.
Step-by-step explanation:
Matías bought = 1/4 kilogram of ham
1/4 kilogram of ham = 3 cakes
There was no remainder
the same amount of ham is in each cake.
To find the amount of ham in each cake, we need to know the fraction of ham in each cake.
Since 3cakes = 1/4kg
1cake = (1/4kg×1cake)/3cakes
= 1/4kg ÷ 3 = 1/4 × 1/3
The fraction of ham in each cake = 1/12
The amount of ham in each cake = 1/12 kg
Mary wants to make a box she starts with a piece of cardboard whose length is 15cm and width is 10cm then she cuts them in congrats square with side 3cm at he four comes what is the area of the cardboard after she cuts the 4 comes
Answer:
V = 108 cm^3
the volume of the box is 108 cm^3
Corrected question;
Mary wants to make a box. She starts with a piece of cardboard whose length is 15 centimeters and width is 10 centimeters. Then she cuts 4 congruent squares with sides of 3 centimeters at the four corners and folded at the broken lines to make the box. What is the volume of the box?
Step-by-step explanation:
The volume of a box V is;
V = length × breadth × height
V = l×b×h ......1
Length l of the box that would be formed after cutting squares with sides 3 cm from the edges of a cardboard of length 15 cm is;
l = 15 - 2(3) = 9 cm
Breadth b of the box that would be formed after cutting squares with sides 3 cm from the edges of a cardboard of breadth 10 cm is;
b = 10 - 2(3) = 4 cm
Height of the box is the length of the squares cut;
h = 3 cm
Substituting the values into equation 1;
V = 9 × 4 × 3 cm^3
V = 108 cm^3
the volume of the box is 108 cm^3
An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?
The side labeled "a" is made the longer side. These are the two congruent sides. So a > b.
We are told that the longer side is 6.3, so a = 6.3, meaning that
2a+b = 15.7
2(6.3)+b = 15.7
12.6+b = 15.7
b = 15.7-12.6
b = 3.1
The triangle has sides of: 6.3, 6.3, 3.1
The perimeter is 6.3+6.3+3.1 = 15.7
Going back to the question "which equation can be used to find the length of the base?", it sounds like either you were given a list of multiple choice answers, or you just fill in the blank. If multiple choice, then try to see which answer matches with what I wrote above. If fill in the blank, then I would just enter either 2(6.3)+b = 15.7 or 12.6+b = 15.7
Answer:
2(6.3)+b = 15.7 or 12.6+b = 15.7
Step-by-step explanation: