im having trouble with this word problem. A train travels 160 km in the same time that a plane covers 720 km. if the speed of the plane is 20 km per hour less than 5 times the speed of the train, find both speeds. Not sure how to solve.

Answers

Answer 1

Plane is traveling at 780km

Answer 2

The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.

To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:

Time taken by the train = Distance / Speed of the train = 160 / x

Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)

Since the time is the same for both:

160 / x = 720 / (5x - 20)

Cross-multiply to solve for x:

160(5x - 20) = 720x

800x - 3200 = 720x

80x = 3200

x = 40

Related Questions

What is a counterexample for the conjecture? Any number that is divisible by four is also divisible by eight

Answers

The value 12 is a good counterexample. It is divisible by 4 (since 12/4 = 3 is a whole number with no remainders or decimal portions) but 12 is not divisible by 8 (note how 12/8 = 1 remainder 4 = 1.5)

To find other examples, add 8 to 12 to get 20. Then add on 8 more to get 28. This pattern continues on forever.

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?

Answers

Consider this option:
1. if the point (4;6) is the centre of the circle and the point (2;5) is the first endpoint of its diameter, then point (4;6) is the middle point of the diameter (it means that is the middle between the 1st and the 2d endpoints of diameter).
2. using the property described above:
for x of the 2d endpoint of the diameter: x=4*2-2=6;
for y of the 2d endpoint of the diameter: y=6*2-5=7.

answer: (6;7)

Answer:

(6,7)

Step-by-step explanation:

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5)

Since center is the mid point of two end points of diameter .

So, we will use mid point formula

[tex](x,y)=(4,6)[/tex]

[tex](x_1,y_1)=(2,5)[/tex]

Mid point formula : [tex]x =\frac{x_1+x_2}{2}[/tex] and [tex]y =\frac{y_1+y_2}{2}[/tex]

Substitute the values

[tex]4 =\frac{2+x_2}{2}[/tex] and [tex]6 =\frac{5+y_2}{2}[/tex]

[tex]8 =2+x_2[/tex] and [tex]12 =5+y_2[/tex]

[tex]6=x_2[/tex] and [tex]7=y_2[/tex]

Thus [tex](x_2,y_2)=(6,7)/tex]

Thus the other endpoint of the diameter is (6,7)

In the Chang family's budget, 0.6% of the expenses are for internet service. What is the fraction of the family's expenses is for internet service? Write the fraction in the simplest form.

Answers

A percent is actually a fraction already. (If you break up the words to have "per cent," this might seem more intuitive. "Cent" is from Latin centum, and is the same root in words like century. Here, it's like per hundred.)

You probably know intuitively that 100% is one whole, for example. But it's also the same as saying [tex] \frac{100}{100} [/tex]. Likewise, 67%, for instance, is actually [tex] \frac{67}{100} [/tex].

In this case, you can write [tex] \dfrac{0.6}{100}[/tex]. But you may realize that you shouldn't have a decimal in a fraction. For every number after the decimal, you multiply the whole thing by a corresponding power of ten. Here, you write [tex] \dfrac{0.6}{100} * \dfrac{10}{10} = \dfrac{6}{1,000} [/tex]. Since 10/10 is equal to 1, we aren't changing anything (Identity Property). If you had 0.06/100, you would multiply by 100/100, and so on...

So, now we have [tex] \dfrac{6}{1000} [/tex]. Our next step is to simplify. The greatest common factor of these two numbers is 2, we rewrite as [tex] \dfrac{3}{500} [/tex] to put it into simplest form. And that's all there is to it.

X^3-64=0
Solve the equation

Answers

x^3 - 64 = 0

We want to solve for x. Start by getting x by itself on one side.
We can do this by adding 64 to both sides of the equation.

x^3 = 64

Now, to get rid of the 3rd power that x is raised to, we can raise both sides to the 1/3 power

(x^3)^1/3 = 64^1/3

(x^3)^1/3 is the same as x

So x = 64^(1/3) and 64^(1/3) = 4

So x = 4 :)

Angles C and D are complementary. The measure of angle D is 25 degrees greater than the measure of angle C. What is the measure of each angle?

Answers

32.5 + 57.5. It adds up to 90 degrees.

Final answer:

Angle C measures 32.5 degrees and angle D measures 57.5 degrees.

Explanation:

Let's represent the measure of angle C as x. Angle D is 25 degrees greater than angle C, so we can represent the measure of angle D as x + 25.

We know that angles C and D are complementary, so their measures must add up to 90 degrees.

Therefore, we can set up the equation:

x + (x + 25) = 90

Combining like terms, we get:

2x + 25 = 90

Subtracting 25 from both sides, we get:

2x = 65

Dividing both sides by 2, we get:

x = 32.5

So, the measure of angle C is 32.5 degrees, and the measure of angle D is 57.5 degrees.

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A square is ____ a parallelogram. always sometimes never submit

Answers

A square is ALWAYS a parallelogram.

You may recall that a square is a special case of rectangle, that is, one in which all the sides are equal (congruent). Additionally, a rectangle is a special case of a parallelogram, that is, one in which each angle is equal to 90° (a right angle). A parallelogram is a quadrilateral (four-sided polygon) with parallel and congruent opposite sides. A square meets these criteria 100 percent of the time, because all its sides are parallel and congruent, so choose always.

the ratio of cookies to glasses of milk is 3:1 if there are 25 glasses of milk how many cookies are there

Answers

answer is 75:25 because if you multiply on one side, you do the same to the other

Elliot buys a 5 pound package of ground beef for 12.50. At the same unit price, how much would 8 pounds of ground beef cost

Answers

12.5/5=2.5 which is the the price per pound
So 8*2.5=20
It should be 20 dollars

12.5 / 5 = 2.5

2.5 x 8 = 20

8 pounds of ground beef would cost $20.

write an expression that is equivalent to 5 cubed

Answers

5*5*5

5^3 is three 5s multiplied together.

I need help I would really thank wheeler answers this for me

Answers

The absolute value of a number is however many places a number is away from 0 on a number line.

a. |-15| + |-26|
15 + 26
41

b. -|-40|
-40

c. |0.5| + |-1 1/2|
0.5 + 1 1/2
0.5 = 1/2
1/2 + 1 1/2
2

Imagine that you are pouring cement into cinder blocks to build a very sturdy wall. Each cinder block is 1.3 feet long, 0.67 feet high, and 0.67 feet wide. If 1 bag of cement is equivalent to 5 cubic feet, what is the number of bags of cement that you will need to fill the entire wall? Show the work

Answers

How many bricks are there or how many feet long and tall is it?

To find out how many cement bags are needed, calculate the volume of one cinder block and see how many such blocks fit in a cement bag. Then, divide the total number of cinder blocks by the number of blocks one bag can fill and round up to the nearest whole number.

To determine the number of cement bags needed to fill a cinder block wall with the given measurements, first calculate the volume of one cinder block. Then, figure out how many cinder blocks fit into one bag of cement.

The volume of one cinder block is:

V = length × height × width

V = 1.3 ft × 0.67 ft × 0.67 ft

V [tex]\approx[/tex] 0.5809 cubic feet

Now, since one bag of cement is equivalent to 5 cubic feet, determine how many cinder blocks one bag can fill:

Number of blocks per bag = 5 cubic feet / 0.5809 cubic feet per block

Number of blocks per bag [tex]\approx[/tex] 8.61 blocks

We need the total number of cinder blocks for the entire wall. Assuming we know the total wall dimensions, let's say we have a total of 100 blocks (for example purposes).

Total number of bags = Total number of blocks / Number of blocks per bag

Total number of bags = 100 / 8.61

Total number of bags [tex]\approx[/tex] 11.62

Since you can't buy a fraction of a bag, you would need to round up to the next whole number, so you would need 12 bags of cement to fill the wall.

A cruise boat travels 48 miles Downstream in 2 hours and returns Upstream in 3 hours. Find the speed of the boat in still water and the rate of the Stream.

Answers

Let x be the speed of the boat in still water and y be the speed of the current of the river.
The downstream speed will be x+y, the upstream speed will be x-y.
but:
distance=speed*time
therefore; as the boat travels in 2 hours downstream we shall have:
2(x+y)=48......i
and as the boat travels upstream we shall have:
3(x-y)=48........ii
simplifying i and ii we get:
x+y=24....iii
x-y=16....iv
adding the above iii and iv we get
2x=40
x=40/2=20
substituting x=20 into iii we obtain:
20+y=24
y=24-20
y=4
so the speed of the boat in still waters is 20 miles per hour
the rate of the stream is 4 miles per hour

Final answer:

The speed of the cruise boat in still water is 20 mph and the rate of the stream is 4 mph.

Explanation:

The student is asking about a problem related to the rate of the boat in still water and the rate of the stream, given the times it takes to travel downstream and upstream. To solve this, we can use the following steps:

Let the speed of the boat in still water be b mph and the rate of the stream be s mph.Downstream, the effective speed is b + s and upstream it's b - s.Using the formula distance = speed imes time, we have two equations based on the given information: 48 miles = (b + s) imes 2 hours for downstream and 48 miles = (b - s) imes 3 hours for upstream.Solve the two equations simultaneously to find the values of b and s.

Let's solve the equations:

48 = 2(b + s) => 24 = b + s48 = 3(b - s) => 16 = b - s

Adding both equations:

24 + 16 = (b + s) + (b - s) => 40 = 2b => b = 20 mph (boat speed in still water)Subtracting the upstream equation from the downstream equation:24 - 16 = (b + s) - (b - s) => 8 = 2s => s = 4 mph (rate of the stream)

Therefore, the speed of the boat in still water is 20 mph and the rate of the stream is 4 mph.

Can you share 35 equally?

Answers

it depends how many people or things

Most numbers can be divided equally with fractions. 17 1/2 is your answer. Hope this helps.

The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression. A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour. B. The initial number of bacteria is 57, and the growth rate is 31% per hour. C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour. D. The initial number of bacteria is 131, and the growth rate is 57% per hour.

Answers

Answer:

The answer on edgenuity for dividing fractions is -3 on the assignment good luck!

Step-by-step explanation:

what is the value of x in the diagram
a.1/2
b.4/21
c.2
d.4

Answers

◆ Triangles ◆

Hey !!

Check the attachment.
Hope it helps you :)

Answer:

2 so your answer would be C.

(30 points)
What are genes?

A. The ovservable characteristic.
B. The expressed trait.
C. The basic unit of inheritance.
D. The measurable factor.

Answers

C) Basic unit of inheritance

Genes can be inherited by offspring from parent. They can determine a characteristic/trait, but usually many genes influence each. Genes can't be "measured" with a unit.

The answer is C. Genes are the basic unit of inheritance as they define our DNA and determine our characteristics.

Given: segment AB || segment DE, C is the midpoint of segment DB. Prove: ΔACB ≅ ΔECD Fill in the missing reason for the proof. A) definition of midpoint B) vertical angles are congruent C) all right angles are congruent D) supplementary angles are congruent

Answers

Answer:

Given: Segment AB || segment DE, C is the midpoint of segment DB.

Prove: ΔA CB ≅ ΔE CD

Proof: In ΔA CB and ΔE CD

C is the Mid point of B D.

BC=C D→ definition of midpoint

∠A CB= ∠ EC D→→vertical angles are congruent

∠BAC=∠DEC→→[AB║DE,so alternate angles are equal]

→→ΔA CB ≅ ΔE CD[A AS or A SA]

Option B: vertical angles are congruent

Answer:

The answer is A) Definition of midpoint

Step-by-step explanation:

Answer B is wrong. I just did the test

Consider the system of equations. x – 3y = 9 1/5x - 2y = -1

Answers

x – 3y = 9 ------------ (1)
1/5x - 2y = -1---------- (2)

(1):
x - 3y = 9
x = 9 + 3y ----------- (1a)

(2):
1/5x - 2y = -1
x - 10y = -5 --------- (2a)

Sub (1a) into (2a):
9 + 3y - 10y = -5
9 - 7y = -5
-7y = -5 - 9
-7y = -14
7y = 14
y = 2 ---------- Sub into (1a)

x = 9 + 3y
x = 9 + 3(2)
x = 9 + 6
x = 15

Ans: x = 15, y = 2

Answer:

Step-by-step explanation:

$10.00 divided by $1.49

Answers

$6.71 is the answer that you are looking for.

10.00/1.49
6.7 is the answer

The first class had a kids in it, the second had b kids in it, and the third class had c kids in it. Kids from all three classes were equally divided between two buses. How many kids were on each bus?

Answers

(a+b+c)/2. this is your answer. if it had the numbers i would solve it fully, but it only has variables.

there are no numbers and only variables so I can't tell you the amount of kids on each bus but here is the equation:
(a*b*c)/2

Describe the vector as an ordered pair. Round the coordinates to the nearest tenth. The diagram is not drawn to scale.

Answers

ANSWER

[tex]

\angle19.4,50.4 \: > [/tex]

EXPLANATION

The given vector has magnitude 54 units.

The vector is making an angle of 69° with the x-axis.

The horizontal component of the vector is

[tex] = 54 \cos(69) [/tex]

[tex] = 19.35[/tex]

To the nearest tenth, we have,

[tex] = 19.4[/tex]

The vertical component is

[tex] = 54 \sin(69 \degree) [/tex]

[tex] = 50.41[/tex]

[tex] = 50.4[/tex]

to the nearest tenth.

The required vector is

[tex]

\angle19.4,50.4 \: > [/tex]

The components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.

What is a vector?

A vector is a quantity that has both magnitude and direction. It has two components a vertical component(Sine) and a horizontal component(Cosine). The component of a vector can be written as,

Vertical component, [tex]V_y = \vec V\ Sin(\theta)[/tex]

Horizontal component, [tex]V_x = \vec V\ Cos(\theta)[/tex]

We know that a vector can be divided into two components a horizontal component and a vertical component, therefore, the vector components can be written as,

[tex]V_y = \vec V Sin\theta\\\\V_y = 54\ Sin(69^o)\\\\V_y = 50.4133[/tex]

[tex]V_x = \vec V Cos\theta\\\\V_x = 54\ Cos(69^o)\\\\V_x = 19.3519[/tex]

Hence, the components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.

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5 is one-fourth of a number c.

Answers

The value of number c is 20

5 as one-fourth of a number c is represented using the following equation

[tex]5 = \frac 14 \times c[/tex]

Multiply both sides of the above equation by 4

[tex]4\times 5 = \frac 14 \times c \times 4[/tex]

Evaluate the products

[tex]20 = c[/tex]

Rewrite the above equation as

[tex]c = 20[/tex]

Hence, the value of number c is 20

Answers

9 +3 = 12 students

9 are male
1st = 9/12 = 3/4
2nd = 8/11

3/4 * 8/11 = 6/11

Answer = D) 6/11

The probability that two student chosen at random is a male is 6/11.

What is the Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Here, Class contains 3 females and 9 males it means total 12 students.

Probability for having 1st student male = 9/12 = 3/4

Probability for having 2nd student is also male = 8/11

Overall Probability = [tex]\frac{3}{4} X \frac{8}{11}[/tex]

= 6/11

Thus, the probability that two student chosen at random is a male is 6/11.

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You bought the meat for Saturdays cookout. A package of hot dogs cost $1.60 and a package of hamburgers cost $5. You bought a total of 8 packages of meat and you spent $23. How many packages of hamburger meat did you buy?

Answers

The number of hamburger meat he bought is 3.

How to find the number of hamburger meat bought?

A package of hot dogs cost $1.60 and a package of hamburgers cost $5.

You bought a total of 8 packages of meat and you spent $23.

Therefore,

let

x = number of package of hot dogs

y = number of package of hamburger

Hence,

x + y = 8

1.60x + 5y = 23

multiply equation(i) by 5

5x + 5y = 40

1.60x + 5y = 23

Subtract equation(ii) from equation(i)

3.4x = 17

x = 17 / 3.4

x = 5

y = 8 - 5

y = 3

Therefore, the number of hamburger meat he bought is 3.

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A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 130 popped kernels. There are 1,450 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last box? Please explain how you get the answer

Answers

12 boxes are needed and 20 will be in the last box.

1450/130 is 11.15 so You round up and need 12 boxes (because you can’t have .15 of a box) so you get the 11 boxes and multiply by how much it can hold (130) and get 1430 which is 20 short of 1450 so 20 would be in the last box .

Answer:

12 boxes are needed in all.

Last box will contain only 20 kernels.

Step-by-step explanation:

Given is :

The popped corn is put into small popcorn boxes that each hold 130 popped kernels.

There are 1450 kernels in a pound of un popped popcorn.

If all the boxes are filled except for the last box, then how many boxes are needed?

Number of boxes = Total number of kernels/Number of kernel in each box

=> [tex]\frac{1450}{130}= 11.15[/tex]

Therefore, a total of 11+1 = 12 boxes are needed as 11.15 is more than 11.

And the last box will contain = [tex]1450-1430=20[/tex] kernels.

Therefore, the last box will have 20 kernels.

What is the solution to this equation?

3(4x + 3) = 2x - 5(3 - x) + 2

Answers

Remove the brackets.
12x + 9 = 2x - 15 + 5x + 2

Collect the like terms.
12x + 9 = 7x - 13

Subtract 7x from both sides.
12x - 7x + 9 = -13
5x + 9 = -13

Subtract 9 from both sides.
5x = - 22

Divide by 9
x = - 22/5
x = - 4.4

Check
=====
3(4*-4.4 + 3) = 2(-4.4) - 5(3 - -4.4) + 2
3(-17.6 + 3) = -8.8 - 5(7.4) + 2
3(-14.6) = - 8.8 - 37 + 2
-43.8 =? - 45.8 + 2
-43.8 = -43.8

And it does check.

Mama Mia restaurant used start fraction, 1, divided by, 2, end fraction of their mozzarella cheese making pizza and the remaining 646464 ounces making pasta.
How many pounds of mozzarella cheese did Mama Mia start with?

Answers

the correct question is
Mama Mia restaurant used start fraction, 1, divided by, 2, end fraction of their mozzarella cheese making pizza and the remaining 64 ounces making pasta.
How many pounds of mozzarella cheese did Mama Mia start with?

Let
x---------------> total ounces of mozzarella

we know that

making pizza-----------> (1/2)*x------> x/2
therefore
making pasta-------> [x-x/2]--------> (2x-x)/2-----> x/2
making pizza=making pasta=x/2
(x/2)=64---------------> x=64*2-----------> x=128 ounces

remember that
1 ounces----------------> 0.0625 pounds
then
128 ounces*0.0625=8 pounds

the answer is 8 pounds

NEED HELP ASAP PLEASE!

Answers

5(x+5) < 85
5x + 25 < 85
5x < 85 - 25
5x < 60
x < 60 ÷ 5
x < 12

Answer:
x < 12

Explanation:
To solve this, we will need to isolate the x on one side of the inequality as follows:
5(x+5) < 85
x+5 < 85/5
x+5 < 17
x+5-5 < 17-5
x < 12

Hope this helps :)

5a - {3b - 5[a - (b + -4a)]}

Answers

Interesting problem. When computers first came out (when dinosaurs ruled the planet), we had to deal with problems that were many brackets deep. So this has practical applications.

Start at the very right and keep on removing brackets and collecting like terms.

5a - {3b - 5[a - (b - 4a)]} I just changed the sign on the right bracket.
5a - {3b - 5[a - b + 4a]}
5a - {3b - 5[5a - b]} Now deal with []. You are still on the right.
5a - {3b - 25a + 5b}
5a - {8b - 25a} Finally remove {}
5a - 8b + 25a
30a - 8b
If you can solve another like this, you are well on your way to being good in computer science.

Frankie is practicing for a 5-kilometer race. His normal time is 31 minutes 21 seconds. Yesterday it took him only 29 minutes 38 seconds. How much faster was Frankie yesterday than his normal time?

Answers

31 min 21 sec
- 29 min 38 sec

=1 min 47 sec

Its Simple! 1 minute and 47 seconds! You gotta do 31 mins and 21 seconds - 29 mins and 38 seconds! Which give you a whooping 1 minute and 47 seconds! I hope i helped you!

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